Chapter 12
description
Transcript of Chapter 12
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Chapter 12Chapter 12The Laws of The Laws of
ThermodynamicsThermodynamics
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Work in Thermodynamic Work in Thermodynamic Processes – State Processes – State VariablesVariables
State of a systemState of a system Description of the system in terms of Description of the system in terms of
state variablesstate variables PressurePressure VolumeVolume TemperatureTemperature Internal EnergyInternal Energy
A A macroscopic statemacroscopic state of an isolated of an isolated system can be specified only if the system can be specified only if the system is in internal thermal equilibriumsystem is in internal thermal equilibrium
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Work in Thermodynamic Work in Thermodynamic ProcessesProcesses
Work is an important energy Work is an important energy transfer mechanism in transfer mechanism in thermodynamic systemsthermodynamic systems
Heat is another energy transfer Heat is another energy transfer mechanismmechanism
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Work in a Gas CylinderWork in a Gas Cylinder The gas is contained in The gas is contained in
a cylinder with a a cylinder with a moveable pistonmoveable piston
The gas occupies a The gas occupies a volume V and exerts volume V and exerts pressure P on the walls pressure P on the walls of the cylinder and on of the cylinder and on the pistonthe piston
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Work in a Gas Cylinder, Work in a Gas Cylinder, cont.cont.
A force is applied A force is applied to slowly to slowly compress the gascompress the gas The compression is The compression is
slow enough for all slow enough for all the system to the system to remain essentially remain essentially in thermal in thermal equilibriumequilibrium
W = - P W = - P ΔVΔV This is the work This is the work
done done onon the gas the gas
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More about Work on a Gas More about Work on a Gas CylinderCylinder
When the gas is compressedWhen the gas is compressed ΔV is negative ΔV is negative The work done on the gas is positiveThe work done on the gas is positive
When the gas is allowed to expandWhen the gas is allowed to expand ΔV is positiveΔV is positive The work done on the gas is negativeThe work done on the gas is negative
When the volume remains constantWhen the volume remains constant No work is done on the gasNo work is done on the gas
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Notes about the Work Notes about the Work EquationEquation
The pressure remains constant The pressure remains constant during the expansion or during the expansion or compressioncompression This is called an This is called an isobaricisobaric process process
If the pressure changes, the If the pressure changes, the average pressure may be used to average pressure may be used to estimate the work doneestimate the work done
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PV DiagramsPV Diagrams Used when the pressure Used when the pressure
and volume are known and volume are known at each step of the at each step of the processprocess
The work done on a gas The work done on a gas that takes it from some that takes it from some initial state to some final initial state to some final state is the negative of state is the negative of the area under the curve the area under the curve on the PV diagramon the PV diagram This is true whether or not This is true whether or not
the pressure stays the pressure stays constantconstant
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PV Diagrams, cont.PV Diagrams, cont. The curve on the diagram is called the The curve on the diagram is called the pathpath
taken between the initial and final statestaken between the initial and final states The work done depends on the particular pathThe work done depends on the particular path
Same initial and final states, but different amounts of Same initial and final states, but different amounts of work are donework are done
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Other ProcessesOther Processes IsovolumetricIsovolumetric
Volume stays constantVolume stays constant Vertical line on the PV diagramVertical line on the PV diagram
IsothermalIsothermal Temperature stays the sameTemperature stays the same
AdiabaticAdiabatic No heat is exchanged with the No heat is exchanged with the
surroundingssurroundings
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Processes for Transferring Processes for Transferring EnergyEnergy
By doing workBy doing work Requires a macroscopic displacement of the point Requires a macroscopic displacement of the point
of application of a forceof application of a force By heatBy heat
Occurs by random molecular collisionsOccurs by random molecular collisions Results of bothResults of both
Change in internal energy of the systemChange in internal energy of the system Generally accompanied by measurable Generally accompanied by measurable
macroscopic variablesmacroscopic variables PressurePressure TemperatureTemperature VolumeVolume
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First Law of First Law of ThermodynamicsThermodynamics
Terms in the equationTerms in the equation QQ
HeatHeat Positive if energy is transferred Positive if energy is transferred toto the system the system
WW WorkWork Positive if done Positive if done onon the system the system
UU Internal energyInternal energy Positive if the temperature increasesPositive if the temperature increases
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First Law of First Law of Thermodynamics, contThermodynamics, cont
The relationship among U, W, and Q The relationship among U, W, and Q can be expressed ascan be expressed as ΔU = UΔU = Uff – U – Uii = Q + W = Q + W
This means that the change in This means that the change in internal energy of a system is equal internal energy of a system is equal to the sum of the energy transferred to the sum of the energy transferred across the system boundary by heat across the system boundary by heat and the energy transferred by workand the energy transferred by work
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Applications of the First Applications of the First Law –Law –Isolated SystemIsolated System
An An isolated systemisolated system does not does not interact with its surroundingsinteract with its surroundings
No energy transfer takes place and No energy transfer takes place and no work is doneno work is done
Therefore, the internal energy of Therefore, the internal energy of the isolated system remains the isolated system remains constantconstant
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Applications of the First Applications of the First Law –Law –Cyclic ProcessesCyclic Processes
A cyclic process is one in which the A cyclic process is one in which the process originates and ends at the process originates and ends at the same statesame state UUff = U = Uii and Q = -W and Q = -W
The net work done per cycle by the The net work done per cycle by the gas is equal to the area enclosed by gas is equal to the area enclosed by the path representing the process the path representing the process on a PV diagramon a PV diagram
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Cyclic Process in a PV Cyclic Process in a PV DiagramDiagram
This is an ideal This is an ideal monatomic gas monatomic gas confined in a cylinder confined in a cylinder by a moveable pistonby a moveable piston
A to B is an A to B is an isovolumetric process isovolumetric process which increases the which increases the pressurepressure
B to C is an isothermal B to C is an isothermal expansion and lowers expansion and lowers the pressurethe pressure
C to A is an isobaric C to A is an isobaric compressioncompression
The gas returns to its The gas returns to its original state at point Aoriginal state at point A
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Applications of the First Applications of the First Law –Law –Isothermal ProcessesIsothermal Processes
Isothermal means constant Isothermal means constant temperaturetemperature
The cylinder and gas are in The cylinder and gas are in thermal contact with a thermal contact with a large source of energylarge source of energy
Allow the energy to transfer Allow the energy to transfer into the gas (by heat)into the gas (by heat)
The gas expands and The gas expands and pressure falls to maintain a pressure falls to maintain a constant temperatureconstant temperature
The work done is the The work done is the negative of the heat addednegative of the heat added
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Applications of the First Applications of the First Law – Adiabatic ProcessLaw – Adiabatic Process
Energy transferred by heat is zeroEnergy transferred by heat is zero The work done is equal to the change in The work done is equal to the change in
the internal energy of the systemthe internal energy of the system One way to accomplish a process with no One way to accomplish a process with no
heat exchange is to have it happen very heat exchange is to have it happen very quicklyquickly
In an adiabatic expansion, the work done In an adiabatic expansion, the work done is negative and the internal energy is negative and the internal energy decreasesdecreases
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Applications of the First Applications of the First Law – Law – Isovolumetric ProcessIsovolumetric Process
No change in volume, therefore no No change in volume, therefore no work is donework is done
The energy added to the system The energy added to the system goes into increasing the internal goes into increasing the internal energy of the systemenergy of the system Temperature will increaseTemperature will increase
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Additional Notes About the Additional Notes About the First LawFirst Law
The First Law is a general equation The First Law is a general equation of Conservation of Energyof Conservation of Energy
There is no practical, macroscopic, There is no practical, macroscopic, distinction between the results of distinction between the results of energy transfer by heat and by workenergy transfer by heat and by work
Q and W are related to the Q and W are related to the properties of state for a systemproperties of state for a system
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The First Law and Human The First Law and Human MetabolismMetabolism
The First Law can be applied to living The First Law can be applied to living organismsorganisms
The internal energy stored in humans The internal energy stored in humans goes into other forms needed by the goes into other forms needed by the organs and into work and heatorgans and into work and heat
The The metabolic ratemetabolic rate ( (ΔU / ΔT) is directly ΔU / ΔT) is directly proportional to the rate of oxygen proportional to the rate of oxygen consumption by volumeconsumption by volume Basal metabolic rate (to maintain and run Basal metabolic rate (to maintain and run
organs, etc.) is about 80 Worgans, etc.) is about 80 W
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Various Metabolic RatesVarious Metabolic Rates
Fig. T12.1, p. 369
S lide 11
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Aerobic FitnessAerobic Fitness One way to One way to
measure a measure a person’s physical person’s physical fitness is their fitness is their maximum maximum capacity to use or capacity to use or consume oxygenconsume oxygen
Fig. T12.2, p. 370
Slide 12
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Efficiency of the Human Efficiency of the Human BodyBody
Efficiency is Efficiency is the ratio of the ratio of the the mechanical mechanical power power supplied to supplied to the the metabolic metabolic rate or rate or total power total power inputinput F ig . T 1 2 .3 , p . 3 70
S lide 1 3
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Heat EngineHeat Engine A A heat engineheat engine is a device that is a device that
converts internal energy to other converts internal energy to other useful forms, such as electrical or useful forms, such as electrical or mechanical energymechanical energy
A heat engine carries some A heat engine carries some working substance through a working substance through a cyclical processcyclical process
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Heat Engine, cont.Heat Engine, cont. Energy is transferred Energy is transferred
from a source at a from a source at a high temperature high temperature (Q(Qhh))
Work is done by the Work is done by the engine (Wengine (Wengeng))
Energy is expelled to Energy is expelled to a source at a lower a source at a lower temperature (Qtemperature (Qcc))
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Heat Engine, cont.Heat Engine, cont. Since it is a cyclical Since it is a cyclical
process, process, ΔU = 0ΔU = 0 Its initial and final Its initial and final
internal energies are the internal energies are the samesame
Therefore, QTherefore, Qnetnet = W = Wengeng The work done by the The work done by the
engine equals the net engine equals the net energy absorbed by energy absorbed by the enginethe engine
The work is equal to The work is equal to the area enclosed by the area enclosed by the curve of the PV the curve of the PV diagramdiagram
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Thermal Efficiency of a Thermal Efficiency of a Heat EngineHeat Engine
Thermal efficiency is defined as the Thermal efficiency is defined as the ratio of the work done by the engine ratio of the work done by the engine to the energy absorbed at the higher to the energy absorbed at the higher temperaturetemperature
e = 1 (100% efficiency) only if Qe = 1 (100% efficiency) only if Qcc = 0 = 0 No energy expelled to cold reservoirNo energy expelled to cold reservoir
h
c
h
ch
h
eng
1QQQ
QW
e
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Second Law of Second Law of ThermodynamicsThermodynamics
It is impossible to construct a heat It is impossible to construct a heat engine that, operating in a cycle, engine that, operating in a cycle, produces no other effect than the produces no other effect than the absorption of energy from a reservoir absorption of energy from a reservoir and the performance of an equal and the performance of an equal amount of workamount of work Kelvin – Planck statementKelvin – Planck statement Means that QMeans that Qcc cannot equal 0 cannot equal 0
Some QSome Qcc must be expelled to the environment must be expelled to the environment Means that e cannot equal 100%Means that e cannot equal 100%
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Heat Pumps and Heat Pumps and RefrigeratorsRefrigerators
Heat engines can run in reverseHeat engines can run in reverse Send in energySend in energy Energy is extracted from the cold reservoirEnergy is extracted from the cold reservoir Energy is transferred to the hot reservoirEnergy is transferred to the hot reservoir
This process means the heat engine is This process means the heat engine is running as a heat pumprunning as a heat pump A refrigerator is a common type of heat A refrigerator is a common type of heat
pumppump An air conditioner is another example of a An air conditioner is another example of a
heat pumpheat pump
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Summary of the First and Summary of the First and Second LawsSecond Laws
First LawFirst Law We cannot get a greater amount of We cannot get a greater amount of
energy out of a cyclic process than energy out of a cyclic process than we put inwe put in
Second LawSecond Law We can break evenWe can break even
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Reversible and Irreversible Reversible and Irreversible ProcessesProcesses
A A reversiblereversible process is one in which every process is one in which every state along some path is an equilibrium state along some path is an equilibrium statestate And one for which the system can be And one for which the system can be
returned to its initial state along the same returned to its initial state along the same pathpath
An An irreversibleirreversible process does not meet process does not meet these requirementsthese requirements Most natural processes are irreversibleMost natural processes are irreversible Reversible process are an idealization, but Reversible process are an idealization, but
some real processes are good approximationssome real processes are good approximations
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Carnot EngineCarnot Engine A theoretical engine developed by Sadi A theoretical engine developed by Sadi
CarnotCarnot A heat engine operating in an ideal, A heat engine operating in an ideal,
reversible cycle (now called a reversible cycle (now called a Carnot CycleCarnot Cycle) ) between two reservoirs is the most efficient between two reservoirs is the most efficient engine possibleengine possible
Carnot’s TheoremCarnot’s Theorem: No real engine : No real engine operating between two energy reservoirs operating between two energy reservoirs can be more efficient than a Carnot engine can be more efficient than a Carnot engine operating between the same two reservoirsoperating between the same two reservoirs
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Carnot CycleCarnot Cycle
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Carnot Cycle, A to BCarnot Cycle, A to B A to B is an A to B is an
isothermal expansionisothermal expansion The gas is placed in The gas is placed in
contact with the high contact with the high temperature reservoirtemperature reservoir
The gas absorbs heat The gas absorbs heat QQhh
The gas does work The gas does work WWABAB in raising the in raising the pistonpiston
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Carnot Cycle, B to CCarnot Cycle, B to C B to C is an adiabatic B to C is an adiabatic
expansionexpansion The base of the The base of the
cylinder is replaced by cylinder is replaced by a thermally a thermally nonconducting wallnonconducting wall
No heat enters or No heat enters or leaves the systemleaves the system
The temperature falls The temperature falls from Tfrom Thh to T to Tcc
The gas does work WThe gas does work WBCBC
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Carnot Cycle, C to DCarnot Cycle, C to D The gas is placed in The gas is placed in
contact with the cold contact with the cold temperature reservoirtemperature reservoir
C to D is an C to D is an isothermal isothermal compressioncompression
The gas expels The gas expels energy Qenergy QCC
Work WWork WCDCD is done on is done on the gasthe gas
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Carnot Cycle, D to ACarnot Cycle, D to A D to A is an adiabatic D to A is an adiabatic
compressioncompression The gas is again placed The gas is again placed
against a thermally against a thermally nonconducting wallnonconducting wall So no heat is exchanged So no heat is exchanged
with the surroundingswith the surroundings The temperature of the The temperature of the
gas increases from Tgas increases from TCC to Tto Thh
The work done on the The work done on the gas is Wgas is WCDCD
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Carnot Cycle, PV DiagramCarnot Cycle, PV Diagram The work done by The work done by
the engine is the engine is shown by the shown by the area enclosed by area enclosed by the curvethe curve
The net work is The net work is equal to Qequal to Qhh - Q - Qcc
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Efficiency of a Carnot Efficiency of a Carnot EngineEngine
Carnot showed that the efficiency of Carnot showed that the efficiency of the engine depends on the the engine depends on the temperatures of the reservoirstemperatures of the reservoirs
Temperatures must be in KelvinsTemperatures must be in Kelvins All Carnot engines operating All Carnot engines operating
between the same two temperatures between the same two temperatures will have the same efficiencywill have the same efficiency
h
Cc T
T1e
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Notes About Carnot Notes About Carnot EfficiencyEfficiency
Efficiency is 0 if TEfficiency is 0 if Thh = T = Tcc Efficiency is 100% only if TEfficiency is 100% only if Tcc = 0 K = 0 K
Such reservoirs are not availableSuch reservoirs are not available The efficiency increases at TThe efficiency increases at Tcc is is
lowered and as Tlowered and as Thh is raised is raised In most practical cases, TIn most practical cases, Tcc is near is near
room temperature, 300 Kroom temperature, 300 K So generally TSo generally Thh is raised to increase is raised to increase
efficiencyefficiency
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Real Engines Compared to Real Engines Compared to Carnot EnginesCarnot Engines
All real engines are less efficient All real engines are less efficient than the Carnot enginethan the Carnot engine Real engines are irreversible because Real engines are irreversible because
of frictionof friction Real engines are irreversible because Real engines are irreversible because
they complete cycles in short they complete cycles in short amounts of timeamounts of time
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EntropyEntropy A state variable related to the Second A state variable related to the Second
Law of Thermodynamics, the entropyLaw of Thermodynamics, the entropy The change in entropy, The change in entropy, ΔS, between ΔS, between
two equilibrium states is given by the two equilibrium states is given by the energy, Qenergy, Qrr, transferred along the , transferred along the reversible path divided by the reversible path divided by the absolute temperature, T, of the absolute temperature, T, of the system in this intervalsystem in this interval
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Entropy, cont.Entropy, cont. Mathematically,Mathematically, This applies only to the reversible path, This applies only to the reversible path,
even if the system actually follows an even if the system actually follows an irreversible pathirreversible path To calculate the entropy for an irreversible To calculate the entropy for an irreversible
process, model it as a reversible processprocess, model it as a reversible process When energy is absorbed, Q is positive When energy is absorbed, Q is positive
and entropy increasesand entropy increases When energy is expelled, Q is negative When energy is expelled, Q is negative
and entropy decreasesand entropy decreases
TQS r
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More About EntropyMore About Entropy Note, the equation defines the Note, the equation defines the change in change in
entropyentropy The entropy of the Universe increases in all The entropy of the Universe increases in all
natural processesnatural processes This is another way of expressing the Second Law of This is another way of expressing the Second Law of
ThermodynamicsThermodynamics There are processes in which the entropy of a There are processes in which the entropy of a
system decreasessystem decreases If the entropy of one system, A, decreases it will be If the entropy of one system, A, decreases it will be
accompanied by the increase of entropy of another system, B.accompanied by the increase of entropy of another system, B. The change in entropy in system B will be greater than that of The change in entropy in system B will be greater than that of
system A.system A.
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Perpetual Motion MachinesPerpetual Motion Machines A perpetual motion machine would operate A perpetual motion machine would operate
continuously without input of energy and continuously without input of energy and without any net increase in entropywithout any net increase in entropy
Perpetual motion machines of the first type Perpetual motion machines of the first type would violate the First Law, giving out more would violate the First Law, giving out more energy than was put into the machineenergy than was put into the machine
Perpetual motion machines of the second Perpetual motion machines of the second type would violate the Second Law, possibly type would violate the Second Law, possibly by no exhaustby no exhaust
Perpetual motion machines will never be Perpetual motion machines will never be inventedinvented
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Entropy and DisorderEntropy and Disorder Entropy can be described in terms Entropy can be described in terms
of disorderof disorder A disorderly arrangement is much A disorderly arrangement is much
more probable than an orderly one more probable than an orderly one if the laws of nature are allowed to if the laws of nature are allowed to act without interferenceact without interference This comes from a statistical This comes from a statistical
mechanics developmentmechanics development
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Entropy and Disorder, Entropy and Disorder, cont.cont.
Isolated systems tend toward greater disorder, Isolated systems tend toward greater disorder, and entropy is a measure of that disorderand entropy is a measure of that disorder S = kS = kBB ln W ln W
kkBB is Boltzmann’s constant is Boltzmann’s constant W is a number proportional to the probability that W is a number proportional to the probability that
the system has a particular configurationthe system has a particular configuration This gives the Second Law as a statement of This gives the Second Law as a statement of
what is most probably rather than what must bewhat is most probably rather than what must be The Second Law also defines the direction of The Second Law also defines the direction of
time of all events as the direction in which the time of all events as the direction in which the entropy of the universe increasesentropy of the universe increases
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Grades of EnergyGrades of Energy The tendency of nature to move toward a The tendency of nature to move toward a
state of disorder affects a system’s state of disorder affects a system’s ability to do workability to do work
Various forms of energy can be Various forms of energy can be converted into internal energy, but the converted into internal energy, but the reverse transformation is never completereverse transformation is never complete
If two kinds of energy, A and B, can be If two kinds of energy, A and B, can be completely interconverted, they are of completely interconverted, they are of the the same gradesame grade
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Grades of Energy, cont.Grades of Energy, cont. If form A can be completely converted to If form A can be completely converted to
form B, but the reverse is never complete, form B, but the reverse is never complete, A is a A is a higher gradehigher grade of energy than B of energy than B
When a high-grade energy is converted to When a high-grade energy is converted to internal energy, it can never be fully internal energy, it can never be fully recovered as high-grade energyrecovered as high-grade energy
Degradation of energyDegradation of energy is the conversion is the conversion of high-grade energy to internal energyof high-grade energy to internal energy
In all real processes, the energy available In all real processes, the energy available for doing work decreasesfor doing work decreases
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Heat Death of the Heat Death of the UniverseUniverse
The entropy of the Universe always The entropy of the Universe always increasesincreases
The entropy of the Universe should The entropy of the Universe should ultimately reach a maximumultimately reach a maximum At this time, the Universe will be at a state of At this time, the Universe will be at a state of
uniform temperature and densityuniform temperature and density This state of perfect disorder implies no energy This state of perfect disorder implies no energy
will be available for doing workwill be available for doing work This state is called the This state is called the heat deathheat death of the of the
UniverseUniverse