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Thermal PhysicsThermal Physics

Chapter 10Chapter 10

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ThermodynamicsThermodynamics

Concerned with the concepts of energy Concerned with the concepts of energy transfers between a system and its transfers between a system and its environment and the resulting environment and the resulting temperature variationstemperature variations

Historically, the development of Historically, the development of thermodynamics paralleled the thermodynamics paralleled the development of atomic theorydevelopment of atomic theory

Concerns itself with the physical and Concerns itself with the physical and chemical transformations of matter in chemical transformations of matter in all of its forms: solid, liquid, and gasall of its forms: solid, liquid, and gas

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HeatHeat

The process by which energy is The process by which energy is exchanged between objects because exchanged between objects because of temperature differences is called of temperature differences is called heatheat

Objects are in Objects are in thermal contactthermal contact if if energy can be exchanged between energy can be exchanged between themthem

Thermal equilibriumThermal equilibrium exists when two exists when two objects in thermal contact with each objects in thermal contact with each other cease to exchange energyother cease to exchange energy

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Zeroth Law of Zeroth Law of ThermodynamicsThermodynamics

If objects A and B are in thermal equilibrium If objects A and B are in thermal equilibrium with a third object, C, then A and B are in with a third object, C, then A and B are in thermal contact with each other.thermal contact with each other.

Allows a definition of temperatureAllows a definition of temperature

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Temperature from the Temperature from the Zeroth Law of Zeroth Law of ThermodynamicsThermodynamics

Two objects in thermal equilibrium Two objects in thermal equilibrium with each other are at the with each other are at the same same temperaturetemperature

TemperatureTemperature is the property that is the property that determines whether or not an determines whether or not an object is in thermal equilibrium object is in thermal equilibrium with other objectswith other objects

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ThermometersThermometers

Thermometers Thermometers are devices used are devices used to measure the to measure the temperature of an temperature of an object or a systemobject or a system

Mercury Mercury thermometer is thermometer is an example of a an example of a common common thermometerthermometer

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ThermometersThermometers

Make use of physical properties that Make use of physical properties that change with temperaturechange with temperature

Many physical properties can be usedMany physical properties can be used volume of a liquidvolume of a liquid length of a solidlength of a solid pressure of a gas held at constant volumepressure of a gas held at constant volume volume of a gas held at constant pressurevolume of a gas held at constant pressure electric resistance of a conductorelectric resistance of a conductor color of a very hot objectcolor of a very hot object

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Temperature ScalesTemperature Scales

Thermometers can be calibrated Thermometers can be calibrated by placing them in thermal contact by placing them in thermal contact with an environment that remains with an environment that remains at constant temperatureat constant temperature Environment could be mixture of ice Environment could be mixture of ice

and water in thermal equilibriumand water in thermal equilibrium Also commonly used is water and Also commonly used is water and

steam in thermal equilibriumsteam in thermal equilibrium

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Celsius ScaleCelsius Scale

Temperature of an ice-water Temperature of an ice-water mixture is defined as 0º Cmixture is defined as 0º C This is the This is the freezing pointfreezing point of water of water

Temperature of a water-steam Temperature of a water-steam mixture is defined as 100º Cmixture is defined as 100º C This is the This is the boiling pointboiling point of water of water

Distance between these points is Distance between these points is divided into 100 segmentsdivided into 100 segments

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Kelvin ScaleKelvin Scale

When the pressure of a gas goes to When the pressure of a gas goes to zero, its temperature is –273.15º Czero, its temperature is –273.15º C

This temperature is called This temperature is called absolute absolute zerozero

This is the zero point of the Kelvin This is the zero point of the Kelvin scalescale ––273.15º C = 0 K273.15º C = 0 K

To convert: TTo convert: TC C = T= TKK – 273.15 – 273.15

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Gas ThermometerGas Thermometer

Temperature Temperature readings are readings are nearly nearly independent of independent of the gasthe gas

Pressure varies Pressure varies with temperature with temperature when maintaining when maintaining a constant volumea constant volume

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Pressure-Temperature Pressure-Temperature GraphGraph

All gases All gases extrapolate to the extrapolate to the same same temperature at temperature at zero pressurezero pressure

This temperature This temperature is is absolute zeroabsolute zero

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Modern Definition of Modern Definition of Kelvin ScaleKelvin Scale

Defined in terms of two pointsDefined in terms of two points Agreed upon by International Committee on Agreed upon by International Committee on

Weights and Measures in 1954Weights and Measures in 1954 First point is absolute zeroFirst point is absolute zero Second point is the Second point is the triple pointtriple point of water of water

Triple point is the single point where water Triple point is the single point where water can exist as solid, liquid, and gascan exist as solid, liquid, and gas

Single temperature and pressureSingle temperature and pressure Occurs at 0.01º C and P = 4.58 mm HgOccurs at 0.01º C and P = 4.58 mm Hg

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Some KelvinSome KelvinTemperaturesTemperatures

Some Some representative representative Kelvin Kelvin temperaturestemperatures

Note, this scale is Note, this scale is logarithmiclogarithmic

Absolute zero has Absolute zero has never been never been reachedreached

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Fahrenheit ScalesFahrenheit Scales

Most common scale used in the USMost common scale used in the US Temperature of the freezing point Temperature of the freezing point

is 32ºis 32º Temperature of the boiling point is Temperature of the boiling point is

212º212º 180 divisions between the points180 divisions between the points

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Comparing Temperature Comparing Temperature ScalesScales

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Converting Among Converting Among Temperature ScalesTemperature Scales

5

9

100

180

100

180

15.273

C

F

C

F

KC

T

T

T

T

TT

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Thermal ExpansionThermal Expansion

The thermal expansion of an object is a The thermal expansion of an object is a consequence of the change in the consequence of the change in the average separation between its average separation between its constituent atoms or moleculesconstituent atoms or molecules

At ordinary temperatures, molecules At ordinary temperatures, molecules vibrate with a small amplitudevibrate with a small amplitude

As temperature increases, the As temperature increases, the amplitude increasesamplitude increases This causes the overall object as a whole to This causes the overall object as a whole to

expandexpand

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Linear ExpansionLinear Expansion

For small changes in temperatureFor small changes in temperature

The coefficient of linear expansion, The coefficient of linear expansion, , depends on the material , depends on the material See table 10.1See table 10.1 These are average coefficients, they These are average coefficients, they

can vary somewhat with temperaturecan vary somewhat with temperature

tLL o

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Area ExpansionArea Expansion

Two dimensions expandTwo dimensions expand

2,tAA o

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Volume ExpansionVolume Expansion

Three dimensions expandThree dimensions expand

For liquids, the coefficient of volume For liquids, the coefficient of volume expansion is given in the tableexpansion is given in the table

3,solidsfor

tVV o

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Applications of Thermal Applications of Thermal Expansion – Bimetallic Expansion – Bimetallic StripStrip

ThermostatsThermostats Use a Use a bimetallic stripbimetallic strip Two metals expand differentlyTwo metals expand differently

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Unusual Behavior of WaterUnusual Behavior of Water

At the temperature of water increases from At the temperature of water increases from 0ºC to 4 ºC, it contracts and its density 0ºC to 4 ºC, it contracts and its density increasesincreases

Above 4 ºC, water exhibits the expected Above 4 ºC, water exhibits the expected expansion with increasing temperatureexpansion with increasing temperature

Maximum density of water is 1000 kg/mMaximum density of water is 1000 kg/m33 at 4 at 4 ºC ºC

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Ideal GasIdeal Gas

A gas does not have a fixed A gas does not have a fixed volume or pressurevolume or pressure

In a container, the gas expands to In a container, the gas expands to fill the containerfill the container

Most gases at room temperature Most gases at room temperature and pressure behave and pressure behave approximately as an ideal gasapproximately as an ideal gas

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Characteristics of an Ideal Characteristics of an Ideal GasGas

Collection of atoms or molecules Collection of atoms or molecules that move randomlythat move randomly

Exert no long-range force on one Exert no long-range force on one anotheranother

Occupy a negligible fraction of the Occupy a negligible fraction of the volume of their containervolume of their container

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MolesMoles

It’s convenient to express the amount of It’s convenient to express the amount of gas in a given volume in terms of the gas in a given volume in terms of the number of moles, nnumber of moles, n

One mole is the amount of the One mole is the amount of the substance that contains as many substance that contains as many particles as there are atoms in 12 g of particles as there are atoms in 12 g of carbon-12carbon-12

massmolar

massn

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Avogadro’s NumberAvogadro’s Number

The number of particles in a mole The number of particles in a mole is called is called Avogadro’s NumberAvogadro’s Number NNAA=6.02 x 10=6.02 x 102323 particles / mole particles / mole

The mass of an individual atom The mass of an individual atom can be calculated:can be calculated:

Aatom N

massmolarm

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Equation of State for an Equation of State for an Ideal GasIdeal Gas

Boyle’s LawBoyle’s Law At a constant temperature, pressure At a constant temperature, pressure

is inversely proportional to the volumeis inversely proportional to the volume

Charles’ LawCharles’ Law At a constant pressure, the At a constant pressure, the

temperature is directly proportional to temperature is directly proportional to the volumethe volume

Gay-Lussac’s LawGay-Lussac’s Law At a constant volume, the pressure is At a constant volume, the pressure is

directly proportional to the directly proportional to the temperaturetemperature

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Ideal Gas LawIdeal Gas Law

Summarizes Boyle’s Law, Charles’ Summarizes Boyle’s Law, Charles’ Law, and Guy-Lussac’s LawLaw, and Guy-Lussac’s Law

PV = n R TPV = n R T R is the R is the Universal Gas ConstantUniversal Gas Constant R = 8.31 J / mole KR = 8.31 J / mole K R = 0.0821 L atm / mole KR = 0.0821 L atm / mole K

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Avogadro’s HypothesisAvogadro’s Hypothesis

Equal volumes of gas at the same Equal volumes of gas at the same temperature and pressure contain temperature and pressure contain the same numbers of moleculesthe same numbers of molecules Corollary: At standard temperature and Corollary: At standard temperature and

pressure, one mole quantities of all pressure, one mole quantities of all gases contain the same number of gases contain the same number of moleculesmolecules

This number is NThis number is NAA

Can also look at the total number of Can also look at the total number of particles: N = n Nparticles: N = n NAA

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Ideal Gas Law revisitedIdeal Gas Law revisited

P V = N kP V = N kBB T T kkBB is is Boltzmann’s ConstantBoltzmann’s Constant

kkBB = R / N = R / NAA = 1.38 x 10 = 1.38 x 10-23-23 J/ K J/ K

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Kinetic Theory of Gases -- Kinetic Theory of Gases -- AssumptionsAssumptions

The number of molecules in the The number of molecules in the gas is large and the average gas is large and the average separation between them is large separation between them is large compared to their dimensionscompared to their dimensions

The molecules obey Newton’s laws The molecules obey Newton’s laws of motion, but as a whole they of motion, but as a whole they move randomlymove randomly

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Kinetic Theory of Gases – Kinetic Theory of Gases – Assumptions, cont.Assumptions, cont.

The molecules interact only by The molecules interact only by short-range forces during elastic short-range forces during elastic collisionscollisions

The molecules make elastic The molecules make elastic collisions with the wallscollisions with the walls

The gas under consideration is a The gas under consideration is a pure substance, all the molecules pure substance, all the molecules are identicalare identical

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Pressure of an Ideal GasPressure of an Ideal Gas

The pressure is The pressure is proportional to the proportional to the number of molecules number of molecules per unit volume and per unit volume and to the average to the average translational kinetic translational kinetic energy of a moleculeenergy of a molecule

2mv

2

1

V

N

2

3P

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Molecular Interpretation of Molecular Interpretation of TemperatureTemperature

Temperature is proportional to the Temperature is proportional to the average kinetic energy of the average kinetic energy of the moleculesmolecules

The total kinetic energy is The total kinetic energy is proportional to the absolute proportional to the absolute temperaturetemperature

Tk2

3mv2

1B

2

nRT2

3KE total

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Internal EnergyInternal Energy

In a monatomic gas, the KE is the only In a monatomic gas, the KE is the only type of energy the molecules can havetype of energy the molecules can have

U is the U is the internal energyinternal energy of the gas of the gas In a polyatomic gas, additional In a polyatomic gas, additional

possibilities for contributions to the possibilities for contributions to the internal energy are rotational and internal energy are rotational and vibrational energy in the moleculesvibrational energy in the molecules

nRT2

3U

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Speed of the MoleculesSpeed of the Molecules

Expressed as the Expressed as the root-mean-squareroot-mean-square (rms) speed(rms) speed

At a given temperature, lighter At a given temperature, lighter molecules move faster, on average, molecules move faster, on average, than heavier onesthan heavier ones Lighter molecules can more easily reach Lighter molecules can more easily reach

escape speed from the earthescape speed from the earth

M

TR3

m

Tk3v Brms