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Chapter 10

Thermal Physics

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Outline

Temperature and 0th law of ThermodynamicsThermometers, temperature scalesThermal expansionIdeal gas - macroscopic description and kinetic theory

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Thermal Physics

Thermal physics is the study of TemperatureThermal energy transfer (heat)Thermal properties of matter

Transformation between states of matterMacroscopic properties (T,V,P)Relationship with microscopic properties

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HeatThe process by which energy is exchanged between objects because of temperature differences is called heatObjects are in thermal contact if energy can be exchanged between themThermal equilibrium exists when two objects in thermal contact with each other cease to exchange energy

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Zeroth Law of Thermodynamics

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

Allows a definition of temperature

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Temperature from the Zeroth Law

Two objects in thermal equilibrium with each other are at the same temperatureTemperature is the property that determines whether or not an object is in thermal equilibrium with other objects

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ThermometersUsed to measure the temperature of an object or a systemMake use of physical properties that change with temperatureMany physical properties can be used

volume of a liquidlength of a solidpressure of a gas held at constant volumevolume of a gas held at constant pressureelectric resistance of a conductorcolor of a very hot object

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Thermometers, contA mercury thermometer is an example of a common thermometerThe level of the mercury rises due to thermal expansionTemperature can be defined by the height of the mercury column

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Temperature Scales

Thermometers can be calibrated by placing them in thermal contact with an environment that remains at constant temperature

Environment could be mixture of ice and water in thermal equilibriumAlso commonly used is water and steam in thermal equilibrium

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Celsius ScaleTemperature of an ice-water mixture is defined as 0º C

This is the freezing point of water

Temperature of a water-steam mixture is defined as 100º C

This is the boiling point of water

Distance between these points is divided into 100 segments or degrees

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Gas ThermometerTemperature readings are nearly independent of the gasPressure varies with temperature when maintaining a constant volume

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Kelvin ScaleWhen the pressure of a gas goes to zero, its temperature is –273.15º CThis temperature is called absolute zeroThis is the zero point of the Kelvin scale

–273.15º C = 0 K

To convert: TC = TK – 273.15The size of the degree in the Kelvin scale is the same as the size of a Celsius degree

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Pressure-Temperature GraphAll gases extrapolate to the same temperature at zero pressureThis temperature is absolute zero

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Modern Definition of Kelvin Scale

Defined in terms of two pointsAgreed upon by International Committee on Weights and Measures in 1954

First point is absolute zeroSecond point is the triple point of water

Triple point is the single point where water can exist as solid, liquid, and gasSingle temperature and pressureOccurs at 0.01º C and P = 4.58 mm Hg

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Modern Definition of Kelvin Scale, cont

The temperature of the triple point on the Kelvin scale is 273.16 KTherefore, the current definition of of the Kelvin is defined as 1/273.16 of the temperature of the triple point of water

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Some KelvinTemperatures

Some representative Kelvin temperaturesNote, this scale is logarithmicAbsolute zero has never been reached

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Fahrenheit Scales

Most common scale used in the USTemperature of the freezing point is 32ºTemperature of the boiling point is 212º180 divisions between the points

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Comparing Temperature Scales

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Converting Among Temperature Scales

( )

273.15

932

55

32995

C K

F C

C F

F C

T T

T T

T T

T T

= −

= +

= −

∆ = ∆

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Thermal ExpansionThe thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or moleculesAt ordinary temperatures, molecules vibrate with a small amplitudeAs temperature increases, the amplitude increases

This causes the overall object as a whole to expand

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Linear ExpansionFor small changes in temperature

, the coefficient of linear expansion, depends on the material∆T - change in temperature

See table 10.1These are average coefficients, they can vary somewhat with temperature

α

TLL ∆=∆ 0α

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Applications of Thermal Expansion – Bimetallic Strip

ThermostatsUse a bimetallic stripTwo metals expand differently

Since they have different coefficients of expansion

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Area ExpansionTwo dimensions expand according to

γ is the coefficient of area expansion

αγγ2

0

=∆=∆ TAA

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Volume Expansion

Three dimensions expand

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

αββ

3,solidsfor =∆=∆ TVV o

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Quick Quiz 10.3Fluid for a very sensitive thermometer:

a) mercury, b) alcohol, c) gasoline, d) glycerin

TVV o ∆=∆ β

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More Applications of Thermal Expansion

Pyrex GlassThermal stresses are smaller than for ordinary glass (αpyrex~1/3αglass)

Sea levelsWarming the oceans will increase the volume of the oceans

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Unusual Behavior of Water

As the temperature of water increases from 0ºC to 4 ºC, it contracts and its density increasesAbove 4 ºC, water exhibits the expected expansion with increasing temperatureMaximum density of water is 1000 kg/m3 at 4 ºC

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Example: Problem #14

Aluminum cubeV0 = 1.00 m3

T = 20oC∆V = 100 cm3

∆T - ? TVV o ∆=∆ β

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Gas properties

A gas does not have a fixed volume or pressureIn a container, the gas expands to fill the containerMost gases at room temperature and pressure behave approximately as an ideal gas

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Characteristics of an Ideal Gas

Collection of atoms or molecules that move randomlyExert no long-range force on one anotherEach particle is individually point-like

Occupying a negligible volume

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

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

massmolarmassn =

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Avogadro’s Number

The number of particles in a mole is called Avogadro’s Number

NA=6.02 x 1023 particles / moleDefined so that 12 g of carbon contains NA atoms

The mass of an individual atom can be calculated:

Aatom N

massmolarm =

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Avogadro’s Number and Masses

The mass in grams of one Avogadro's number of an element is numerically the same as the mass of one atom of the element, expressed in atomic mass units, u=1.66x10-24 gCarbon has a mass of 12 u

12 g of carbon consists of NA atoms of carbon

Holds for molecules also

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Equation of State for Ideal Gas

P - gas pressure, V - gas volumen - quantity of gas in molesR is the Universal Gas Constant

R = 8.31 J / mole.K in SI units

T - absolute temperature in KReal gas at low pressure behaves as ideal

nRTPV =

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Ideal Gas Law, Alternative Version

kB is Boltzmann’s ConstantkB = R / NA = 1.38 x 10-23 J/ KN is the total number of molecules

n = N / NA

n is the number of molesN is the number of molecules

TNkPV B=

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Example: Problem #29V=1.0 cm3

T= 20oCPa=1.013x105 PaPb=1.0x10-11 Pa

Na-?nb-?

nRTPVTNkPV B

==

V, T, P

kB = 1.38 x 10-23 J/ KR = 8.31 J / mole.K

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Kinetic Theory of Gases –Assumptions

The number of molecules in the gas is large and the average separation between them is large compared to their dimensionsThe molecules obey Newton’s laws of motion, but as a whole they move randomly

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Kinetic Theory of Gases –Assumptions, cont.

The molecules interact only by short-range forces during elastic collisionsThe molecules make elastic collisions with the wallsAll the molecules are identical

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Pressure of an Ideal GasThe pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of a molecule

= 2mv

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VN

23P

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Pressure, contThe pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of the moleculePressure can be increased by

Increasing the number of molecules per unit volume in the containerIncreasing the average translational kinetic energy of the molecules

Increasing the temperature of the gas

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Molecular Interpretation of TemperatureTemperature is proportional to the average kinetic energy of the molecules

The total kinetic energy is proportional to the absolute temperature

Tkm B23

21 2 =v

nRTKEtotal 23

=

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Internal EnergyIn a monatomic gas, the KE is the only type of energy the molecules can have

U is the internal energy of the gasIn a polyatomic gas, additional possibilities for contributions to the internal energy are rotational and vibrational energy in the molecules

nRT23U =

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Speed of the MoleculesExpressed as the root-mean-square(rms) speed

At a given temperature, lighter molecules move faster, on average, than heavier ones

Lighter molecules can more easily reach escape speed from the earth

MTR3

mTk3v B

rms ==

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Some rms Speeds

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Maxwell DistributionA system of gas at a given temperature will exhibit a variety of speedsThree speeds are of interest:

Most probableAveragerms

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Maxwell Distribution, cont

For every gas, vmp < vav < vrms

As the temperature rises, these three speeds shift to the rightThe total area under the curve on the graph equals the total number of molecules