Thermodynamics I
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Transcript of Thermodynamics I
AP PHYSICS
Thermodynamics I
RECAP
Thermal PhysicsEquations not on the equation sheet
c specific heat units J(kgK)
L Latent Heat units Jkg
TmcQ
mLQ
The Mole
Quantity in Physics mass ndash quantitative measure of objectrsquos inertia
mole ndash number of particles
Mole amp Mass
Every substance has a unique relationship between its mass and number of moles
Molar Mass (M)the ratio of the mass of a substance in grams to the number of
moles of the substance
How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the
substance in units of grams rather than atomic mass units
Ex What is the molar mass of O2
Methane
What is the molar mass (M) of CH4
What number of moles (n) are there in 40 g of methane gas
How many molecules (N) of CH4 does this include
What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)
Note n number of moles N number of particles
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
RECAP
Thermal PhysicsEquations not on the equation sheet
c specific heat units J(kgK)
L Latent Heat units Jkg
TmcQ
mLQ
The Mole
Quantity in Physics mass ndash quantitative measure of objectrsquos inertia
mole ndash number of particles
Mole amp Mass
Every substance has a unique relationship between its mass and number of moles
Molar Mass (M)the ratio of the mass of a substance in grams to the number of
moles of the substance
How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the
substance in units of grams rather than atomic mass units
Ex What is the molar mass of O2
Methane
What is the molar mass (M) of CH4
What number of moles (n) are there in 40 g of methane gas
How many molecules (N) of CH4 does this include
What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)
Note n number of moles N number of particles
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
The Mole
Quantity in Physics mass ndash quantitative measure of objectrsquos inertia
mole ndash number of particles
Mole amp Mass
Every substance has a unique relationship between its mass and number of moles
Molar Mass (M)the ratio of the mass of a substance in grams to the number of
moles of the substance
How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the
substance in units of grams rather than atomic mass units
Ex What is the molar mass of O2
Methane
What is the molar mass (M) of CH4
What number of moles (n) are there in 40 g of methane gas
How many molecules (N) of CH4 does this include
What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)
Note n number of moles N number of particles
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Mole amp Mass
Every substance has a unique relationship between its mass and number of moles
Molar Mass (M)the ratio of the mass of a substance in grams to the number of
moles of the substance
How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the
substance in units of grams rather than atomic mass units
Ex What is the molar mass of O2
Methane
What is the molar mass (M) of CH4
What number of moles (n) are there in 40 g of methane gas
How many molecules (N) of CH4 does this include
What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)
Note n number of moles N number of particles
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Methane
What is the molar mass (M) of CH4
What number of moles (n) are there in 40 g of methane gas
How many molecules (N) of CH4 does this include
What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)
Note n number of moles N number of particles
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Ideal Gases Volume and Number
The behaviors of ideal gases at low pressures are relatively easy to describe
The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Ideal Gases Boylersquos Law
Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as
an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)
Boylersquos LawThe volume V varies inversely with the pressure P
when temperature (T) and amount of gas (n) are constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Ideal Gases Charlesrsquo Law
Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist
Charlesrsquo LawThe pressure P is directly proportional to the
absolute temperature T (temperature in Kelvin) when volume V and amount n are constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Ideal Gas Law
Combining of Boylersquos Law and Charlesrsquo Law
Adding Avogadrorsquos Law yields
R is the ideal gas constant or R = 008206
L∙atm(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need
[Answer in units of liters 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of
identical molecules each with mass m The container has perfectly rigid walls that do not move
2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container
3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container
4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Kinetic Theory of an Ideal Gas
For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T
The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB
What is the value of the Boltzmann constant including units
Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation
then what is their average speed
TkK Bavg 23
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Kinetic Energy of A Molecule
a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas
b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature
c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)
[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion Therefore
1 the particles have some velocity
2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of
the individual particlesrsquo kinetic energy
This is true of material in any phase (solid liguid gas plasma)
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Internal Energy amp Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer
There are two ways to transfer energy to an object1 Heat the object2 do Work on the object
Both of these energy transfer methods add to the internal energy of the object
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Work Done during Volume Change
Classic Thermodynamic SystemGas in a cylinder confined by a piston
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
PV Diagrams
Area under the curve is the work done by the
gas
Notice the arrow denoting direction of the
process
Work
Pressure
VolumeVo Vf
P
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Thermodynamic Processes
Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Isothermal
The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm
For the curve PV is constant and is directly proportional to T (Boylersquos Law)
Volume
Pressure
Va Vb
Pa
Pb
Work
For Ideal Gases
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Isobaric
The curve is called an isobar
The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system
Volume
Pressure
Va Vb
P
Work
isotherms
Ta
Tb
Ta gt Tb
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Isochoric (Isometric or Isovolumetric)
The curve is called an isochor
There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy
Volume
Pressure
V
Pa
isotherms
Pb
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Adiabatic
The curve is called an adiabat
No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)
Volume
Pressure
Va Vb
Pa Wor
kisotherms
Pb
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Isobaric Example
Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam
when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute
a) the work done by the water when it vaporizesb) its increase in internal energy
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Isochoric (Isovolumetric) Example
Heating WaterWater with a mass of 20 kg is held at constant volume in
a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings
a)What is the increase in internal energyb)What is the increase in temperature
[the specific heat of water is 4186 Jkg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated
where C is a quantity different for different materials called the molar heat capacity of the material
Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar
massC = Mc
Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip
Q = nCΔT
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes
1LT ΔU = Q+W Q = ΔU ndash W
IsochoricW = -PΔV = 0
Q = ΔU ndash o
Q = ΔU
All of the heat gainedlost results directly in a change in internal energy
Molar heat for a constant volume Cv
IsobaricFor pressure to remain constant the
volume must change
W = -PΔV
Q = ΔU + PΔV
Some of the heat gained by the system is converted into work as the system expands
Molar heat for a constant pressure Cp
Molar Heat Capacities amp 1LT
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant
Relationship between Cv and Cp
Cp = Cv + RR universal gas constant