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Chapter 19 TEMPERATURE
19.1 Thermodynamics
Thermodynamics
Molecular kinematics
This chapter deals with temperature, a concept that deeply
underlies all laws of thermodynamics.
Temperature is one of the seven SI base quantities. The
unit of it is Kelvin.
19-2 The Zeroth Law of Thermodynamics
19-2-1 Thermal equilibrium
Systems A and B are isolated from one another and from
their environment by adiabatic walls, called thermally
insulating, by which changes in the measured properties of
either system have no effect on the properties of the other
system.
When the two systems are placed in contact through a
diathermic wall, the passage of heat energy through the wall
 if it occurs  causes the properties of the two systems to
change. And 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.
19-2-2 The zeroth law of thermal dynamics
The zeroth law of thermodynamics:
If systems A and B are each in thermal equilibrium with a
third system C, then A and B are in thermal equilibrium with
each other.
19-2-3 Temperature
When two systems are in thermal equilibrium, we say that
they have the same temperature.
A statement of the zeroth law in terms of temperature is
the following:
There exists a scalar quantity called temperature,
which is a property of all thermodynamics in equilibrium. Two
systems are in thermal equilibrium if and only if their
temperatures are equal.
19-3 Measuring Temperature
19-3-1 Temperature scales
To measure a temperature, we need to set up a temperature
scale, in which three factors have to be considered: the
substance for measuring temperature, the property of relying on
temperature, and the standard points.
Celsius temperature scale (centigrade scale):
0 C = the freezing point of water
100 C = the boiling point of water
Fahrenheit temperature scale:
32 F = the freezing point of water
212 F = the boiling point of water
19-3-2 The triple point of water
Absolute temperature scale:
Ttr = 273.16 K (exactly)
where K (= Kelvin) is the
base unit of temperature on
the Kelvin scale.
TC  T  273.15 o
9
TF  TC  32 o
5
9 F = 5 C
19-3-3 The constant-volume gas thermometer
The choice of one of a properties of the substance leads to
a device-sensitive or “private” temperature scale that is defined
only for that property and that does not necessarily agree with
other choices we might make.
T *  aX
X
T * ( X )  (273.16 K )
X tr
A constant-volume
gas thermometer
p
T  (273.16 K ) lim
p tr 0 p
tr
(constant V)
19-3-4 The ideal gas
An ideal gas is the gas whose properties represent the
limiting behavior of real gases at sufficiently low densities.
pV  NkT
k is a constant called the
Boltzmann constant
1. R. Boyle’ law:
pV  constant
2. L. J. Gay-Lussac’ law
V  Vo (1   V TC )
3. J. A. C. Charles’ law
p  p o (1   p TC )
4. Avogadro’s law:
V  N for constant p and T
The equation for an ideal gas
pV  NkT
where k is a constant called the Boltzmann constant
k  1.38 10 23 J/K
Or
pV  nRT
where R = kNA is a new constant, called the molar gas constant.
R  8.31 J/mol  K
And A is Avogadro constant
NA  6.02 10 23 molecules/ mol
19-4 Thermal Expansion
19-4-1 Thermal expansion
We can thus visualize the solid body as a microscopic
bedspring. These “springs” are quite stiff and not at all ideal,
and there are about 1023 of them per cubic centimeter. At any
temperature the atoms of the solid are vibrating. The amplitude
of vibration is about 109 cm, about one-tenth of an atomic
diameter, and the frequency is about 1013 Hz. When the
temperature is increased, the atoms vibrate at larger amplitude,
and the average distance between atoms increases. This leads
to an expansion of the whole solid body.
A microscopic bedspring
19-4-2 Linear expansion
The change in any linear dimension of the solid, such as
its length, width, or thickness, is called a linear expansion.
L  LT
, called the coefficient of linear expansion,
L / L

T
 (106 per C)
Subatance
Ice
51
Lead
29
Aluminum
23
Brass
19
Copper
17
Steel
Glass (ordinary)
11
9
Glass (Pyrex)
3.2
Invar alloy
0.7
Quartz (fused)
0.5
19-4-3 Volume expansion
For volume expansion:
V  VT
For volume expansion of a isotropic solid:
V  3VT
Typical values of  for liquids at room temperature are in
the range of 200  106 /C to 1000  106 /C
The volume expansion
curve for water
19-4-4 Microscopic basis of thermal expansion
19-5Temperature and Heat
19-5-1 Heat: Energy in transit
Heat is energy that flows between a system and its
environment because of a temperature difference between them.
Heat is positive when energy is transferred to a system’s
thermal energy from its environment (we say that heat is
absorbed). Heat is negative when energy is transferred from a
system’s thermal energy to its environment (we say that heat is
released or lost).
Like other forms of energy, heat can be expressed in the SI
unit of joules (J). Another unit for heat is calorie (cal).
19-5-2 Misconceptions about heat
As we indicated, in common usage, heat is often confused
with temperature or internal energy.
19-6 The Absorption of Heat by Solids and Liquids
19-6-1 Heat capacity
The heat capacity C of an object is the proportionality
constant between the heat Q that the object absorbs or loses and
the resulting temperature change T of the object
Q  CT  C (T f  Ti )
Heat capacity C has the unit of energy per Kelvin.
19-6-2 Specific heat
Two objects made of the same material will have heat
capacities proportional to their masses. It is therefore convenient
to define a “heat capacity per unit mass” or specific heat c that
refers not to an object but to a unit mass of the material of which
the object is made. The equation becomes
Q  cmT  cm(T f  Ti )
or
C
Q
c 
m mT
Neither the heat capacity of a body nor the specific heat of a
material is constant; both depend on the temperature (and possibly
on other variables as well, such as pressure).
N
Q   mcn Tn
n 1
In the differential limit this becomes
Tf
Q  m  cdT
Ti
19-6-3 Molar specific heat
In many instances the most convenient unit for specifying
the amount of a substance is the mole (mol), where
1 mol = 6.02  1023 elementary units
of any substance.
When quantities are expressed in moles, specific heats must
also involve moles (rather than a mass unit); they are then called
molar specific heats.
We must also specify the conditions under which the heat Q
is added to the material.
To obtain a unique value for c we must indicate the
conditions, such as specific heat at constant pressure cp, specific
heat at constant volume cV, and so on.
Q  Lm
19-6-4 Heats of transformation
When heat enters a solid or a liquid, the temperature of the
sample does not necessarily rise. Instead, the sample may change
from one phase or state (that is, solid, liquid, or gas) to another.
The amount of heat per unit mass that must be transferred to
produce a phase change is called the heat of transformation or
latent heat (symbol L) for the process. The total heat transferred
in a phase change is then
Q  Lm
The heat transferred during melting or freezing is called the heat
of fusion (symbol Lf), and the heat transferred during boiling or
condensing is called the heat of vaporization (symbol Lv).
Substance
Melting
Point
(K)
Heat of
Fusion
(kJ/kg)
Boiling
Point
(K)
Heat of
vaporization
(kJ/kg)
Hydrogen
14.0
58.6
20.3
452
Oxygen
54.8
13.8
90.2
213
Mercury
234
11.3
630
296
Water
273
333
373
2256
Lead
601
24.7
2013
858
Silver
1356
205
2840
4730
19-6-5 Heat capacities of solids
Samples with the same number of moles have the same
number of atoms, and we conclude that the heat energy required
per atom to raise the temperature of a solid by a given amount
seems  with a few exceptions  to be about the same for all
solids. (See page 435 TABLE 19-3.)
The variation of the
molar heat capacity of
tantalum for temperatures
in the range 3 – 5.5 K.
The specific heat
capacity of brass in the
range 300 – 600C.
19-7 A Closer Look at Heat and Work
19-7-1 Work done on or by an ideal gas
If we increase the temperature of the gas in the cylinder, the
gas expands and raises the piston
against gravity; the gas does
(positive) work on the piston.
W   Fx dx   pAdx
19-7-2 Work done at constant volume
The work is zero for any process in which the volume
remains constant:
W 0
19-7-3 Work done at constant pressure
Here we can easily apply the equation, because the constant
p comes out of the integral:
W  p  dV  p(Vf  Vi )
19-7-4 Work done at constant temperature
In the gas expands or contracts at constant temperature, the
relationship between p and V, given by the ideal gas law (pV =
nRT), is
pV  constant
Thus, the work done by a gas during an isothermal process is
Vf
Vf
Vi
Vi
W   pdV  
Vf
nRT
dV  nRT ln
V
Vi
19-7-5 Work done in thermal isolation
A process carried out in
thermal isolation is called an
adiabatic process. the path it will
follow is represented on a pV
diagram by the parabolic-like curve:
pV   constant
Thus, the adiabatic work is
W   pdV  
Vf
Vf
Vi
Vi
piVi 
1
dV 
( pf Vf  piVi )

V
 1
19-8 The First Law of Thermodynamics
Experimentally, the quantity Q  W is the same for all
processes. It depends only on the initial and final states and does
not depend at all on how the system gets from one to the other.
The quantity Q  W must represent a change in some
intrinsic property of the system. We call this property the
internal energy Eint and we write
Eint  Eint, f  Eint,i  Q  W
This is the first law of thermodynamics.
If the thermodynamic system undergoes only a differential
change, the first law is
dEint  dQ  dW
The first law of thermodynamics is a general result that is
thought to apply to every process in nature that proceeds between
equilibrium states. It is not necessary that every stage of the
process be an equilibrium state, only the initial and the final states.
In thermal physics as in mechanics, you must be quite clear as
to the system to which you are applying fundamental laws.
19-9 Some Special Cases of the First Law of Thermodynamics
19-9-1 Adiabatic processes
An adiabatic process is one that occurs so rapidly or occurs
in a system that is so well insulated that no transfer of energy as
heat occurs between the system and its environment.
Eint  W
This tells us that if work is done by the system (that is, if W
is positive), the internal energy of the system decreases by the
amount of work.
10-9-2 Constant-volume processes
If the volume of a system (such as a gas) is held constant,
that system can do no work.
Eint  Q
Thus, if heat is absorbed by a system (that is, if Q is positive),
the internal energy of the system increases.
10-9-3 Cyclical processes
There are processes in which, after certain interchanges of
heat and work, the system is restored to its initial state.
Q W
Thus, the net work done during the process must exactly
equal the net amount of energy transferred as heat; the store of
internal energy of the system remains unchanged.
10-9-4 Free expansions
These are adiabatic processes in which no transfer of heat
occurs between the system and its environment and no work is
done or by the system. Thus, Q = W = 0 and the first law requires
that
Eint  0
A free expansion differs from all other processes we have
considered because it cannot be done slowly and in a controlled
way. As a result, at any given instant during the sudden
expansion, the gas is not in thermal equilibrium and its pressure
is not the same everywhere.
19-10 Heat Transfer Mechanisms
19-10-1 Conduction
Thermal conduction is heat transferring from high
temperature region to low temperature region in a material.
Consider the rate H ( = Q/t) at which heat is transferred
through the slab. Experiment shows that H is (1) directly
proportional to the area A; (2) inversely proportional to the
length x; and (3) directly proportional to temperature
difference T, which can be summarized as
T
H  kA
x
k is called the thermal conductivity of the material.
TABLE 19-6 on page 443 shows some values of k for
selected substances.
19-10-2 Thermal resistance to conduction (R-value)
A thermal resistance or R-value is defined by
L
R
k
where L is the thickness of the material through which the heat is
transferred. Thus the lower the conductivity is, the higher is the
R-value: good insulators have high R-values.
19-10-3 Conduction through a composite slab
SAMPLE PROBLEM 1: Consider a compound slab consisting of
two materials having different thickness, L1 and L2, and
different thermal conductivities, k1 and k2. If the temperatures of
the outer surfaces are T1 and T2 (with T2 > T1), find the rate of
heat transfer through the compound slab in a steady state.
SOLUTION:
SAMPLE PROBLEM 2: A thin, cylindrical metal pipe is carrying
steam at a temperature of TS = 100C. The pipe has a diameter of
5.4 cm and is wrapped with a thickness of 5.2 cm of fiberglass
insulation. A length D = 6.2 m of the pipe passes through a room
in which the temperature is TR = 11C. (a) At what rate does heat
energy pass through the insulation? (b) How much additional
insulation must be added to reduce the heat transfer rate by half?
SOLUTION:
19-10-4 Convection
Heat transfer by convection occurs when a fluid, such as air
or water, is in contact with an object whose temperature is higher
than that of its surroundings. The temperature of the fluid that is
in contact with the hot object increases, and (in most cases) the
fluid expands. The warm fluid is less dense than the surrounding
cooler fluid, so it rises because of buoyant forces. The
surrounding cooler fluid falls to take the place of the rising
warmer fluid, and a convective circulation is set up.
Air rises by convection
around a heated cylinder. The
dark areas represent regions
of uniform temperature.
19-10-5 Radiation
Energy is carried from the Sun to us by electromagnetic
waves that travel freely through the near vacuum of the
intervening space. If you stand near a bonfire or an open
fireplace, you are warmed by the same process. All objects emit
such electromagnetic radiation because of their temperature and
also absorb some of the radiation that falls on them from other
objects. The higher the temperature of an object is, the more it
radiates. The energy radiated by an object is proportional to the
fourth power of its temperature.
Solar radiation
is intercepted by
the Earth and is
(mostly) absorbed.
Problems:
1.
2.
3.
4.
5.
6.
7.
8.
9.
19-7 (on page 449),
19-20,
19-35,
19-41,
19-48,
19-50,
19-53,
19-60,
19-64.