Chapter 21 Temperature

21-1 Temperature and thermal equilibrium

1. Thermal equilibrium(a) Adiabatic( 绝热 ) ( thermally insulating )Fig 21-1 shows two systems A and B, they are isolatedfrom one another and fromtheir environment, by whichwe mean that neither energy nor matter can enter or leave either system. Fig 21-1

A BAT BT

For example, the systems may be surrounded by wall made of thick slabs of styrofoam( 泡沫聚苯乙烯 ).

(b) Diathermic( 热透性 ), means thermally conducting

(c) Thermal equilibriumWhen the two system are placed in contact through a diathermic wall, the passage of heat energy through the wall causes the properties of

two system to change. The changes goes to until finally all measured properties of each system approach constant values. When this occurs, we say that the two systems are in thermal equilibrium with each other.2. Zeroth law of thermodynamics“If system A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other”

The zeroth law underlies the concept of temperature .

3. Temperature

When two system are in thermal equilibrium we

say that they have the same temperature.

21-2 Temperature Scales （温标）

1. Kelvin scales (T)• The definition: The triple point ( 三相点 ) of water was set to be (in 1954):

• It is one of the seven base units of SI Units.

• Although there is no apparent limit to how high the temperature of a system can be, there is a limit to how low it can be. T > 0 K

K16.273trT

Three temperature scales are defined:Kelvin scale , Celsius scale, and Fahrenheit scale

2. Celsius and Fahrenheit scales (a) Celsius scale (the centigrade scale ):The normal freezing point of water is defined to be ; The normal boiling point of water is defined to be . The triple point of water is found to be (273.16K). (21-2)

(b) Fahrenheit scale (21-3)

c0c100

3259

CF TT

15.273TTC

c01.0

TC=25 TF=77 c F

TC=38 TF=100 c F

21-3 Measuring temperaturesBased on Kelvin scale.1.Any property of a substance that varies with temperature of the system can form the basis for a thermometer( 温度表 ).

•T usually is some function of x, thermometric property. T* = f(x)•The simplest way is to choose linear relationship between T and x:

,* axT (21-5)

where a is a constant.

•The constant ‘a’ can be obtained by measuring x at the triple point of water. If it is at 273.16K, we have

• We express temperature in Eq(21-5) by T* rather than T because the temperature so measured will be “a device sensitive temperature”, not a universal one.

trx

trxxKxT 16.273)(*

trxxTa 16.273*

(21-6)

Sample problem 21-1 The resistance of a certain coil of platinum wire increases by a factor of 1.392 between the triple point of water and the boiling point of water at atmospheric pressure. What temperature for the normal boiling point of water is measured by this thermometer? Solution:

KR

RTRTtr

boiltrboil 2.380)392.1)(16.273()(*

This value gives “platinum resistance temperature” of boiling water. Other thermometers will give different values.

2. The constant—volume gas thermometer

Bulb

capillaryh

mercury reservoir

Level marker

mano-meter

Fig 21-4trP

2H2N

2O

0 200 400 600 800

T(K)

Fig 21-5N2

Gas

We define an “ideal gas temperature scale”:

(21-7) Vtconstr

P PPLimKT

tr

tan0

)16.273(

In this context, we define an ‘ideal gas’ to be a gas that would read the same temperature T at all pressure, with no need for extrapolation.

21-4 Thermal expansion

The change in any linear dimension of the solid, such as its length, width, or thickness, is called “a linear expansion” (21-8)

is the change in length; L is the length; is the change in temperature; is called the coefficient of linear

expansion.T

L

TLL

1. Linear expansion

2. We define the coefficient of volume expansion as (21-12)where V is the volume of a solid ( or liquid ), is the change in volume.

TVV

V

The rail distorted due to the thermal expansion.

21-5 The ideal gas1. Ideal gas– that is a gas whose properties represent the limiting behavior of real gases at sufficiently low densities.2. For ideal gas, it has following property, to a good approximation: PV=NKT (21-13)Here N is the number of molecules contained in the volume V; K is a Boltzmann constant.

trP

2H2N

2O

0 200 400 600 800

T(K)

Fig 21-5

KJK /1038.1 23T is expressed in Kelvins

It is often more useful to write Eq(21-13) in a slightly different:

ANNn /

MolmoleculesN A /1002.6 23

nRTPV (21-17)

Eqs(21-13) and (21-17) are completely equivalent forms of the “ideal gas Law”.

, the number of moles

AKNR , the moles gas constant

KMolJR /31.8

Now, enjoy some

cartoons!

Students in lecture

are apt to suffer from cognitive overload

Mr Osborne, may I be excused?

My brain is full.

Often I think I teach just to ensure that my pupils get the best exam grades so that my school meets its target.

也是应试教育！

No Sir, I meant why are we here on a Saturday?

Very interesting, Jason, but I’m pretty sure it’s been done.