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Thermal Physics
A Contemporary Perspective
Hiroshi Matsuoka
I. What is Thermal Physics?
This first part of the text gives an overview of thermal physics, which consists of two parts:
thermodynamics and statistical mechanics. The main goal of thermal phy
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Homework#6
Solutions
cP / R
2. (a) (1 point)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
200
400
600
800
1000
T (K)
c P is an increasing function of T and it does not remain constant over any temperature
range. In contrast. cV , the molar specific heat at constant volu
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Homework#9 (10 points)
1. (a) (2 points)
" U %
3
CV = $
' = nR
# T & V ,n 2
" n%2
nRT
" P%
nR
P=
a$ '
=$ ' =
# V&
V bn
T # T & V , n V bn
and
S = S (T,V,n ) S (T0 ,V0 ,n ) =
T
T0
=
T
T0
V
CV (T,V0 ,n )
(T,V ,n )
dT +
dV
T
V0 T (T,V ,n )
V
3
dT V
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Thermal Physics Homework#7: Solutions
I found that people are still not paying close attention to significant figures. Try to make it
a habit to check significant figures as well as units.
1. (2 points) Internal energy as a window to the microscopic lev
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Homework#3 (10 points)
1. (3 points) Exploring the van der Waals equation of state
(a) (1 point)
For v = const , P increases as T increases. For T = const , P decreases as v increases.
They appear different near the critical point P, v, T = (1,1,1) ,
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Thermal Physics Homework #4
Solutions
1. (6 points)
(a) (1 point)
S =
1
mass w
2
=
1
(1.2 kg
m
3
) (340 m s)
2
=
1
1
Pa 1 =
Pa 1 = 7.110 6 Pa 1 .
5
1.4 10 5
1.2 ) (1.2 10 )
(
(b) (3 points)
v=
RT
P
so that
1 $ v '
1$ R' R
1
= & ) = & )=
=
v % T ( P v
Homework#8: Solutions
1. (2 points)
120
s (J/(mol K)
100
80
60
40
20
0
0
500 1000 1500 2000 2500 3000 3500
T (K)
s(T, P) is an increasing function of T.
As c P is roughly constant in the temperature range, 220 K T 320 K , s(T, P) should
vary logarithmical
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II Equilibrium Thermodynamics
(Hiroshi Matsuoka)
5 Equations of state and phases of matter
5.1 Equation of state
As we discussed in Sec.4.1, the pressure P, volume V, absolute temperature T, and mole
number n of a single-component system are related wit
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Thermal Physics Homework#1
Solutions
1. (5 points) Mass density as a window to the microscopic level
The main point of this problem is that although the mass density mass of a macroscopic
system is clearly a macroscopic quantity readily measurable on th
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4.2 Macro versus micro
(Hiroshi Matsuoka)
Macroscopic thermodynamics and microscopic statistical mechanics
Thermodynamics is a framework for macroscopic descriptions of thermal properties and
energy-transfer processes at finite temperature. It is based
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5.4 Exploring the equation of state for steam
(Hiroshi Matsuoka)
v versus T
Since the time of the industrial revolution, we have accumulated a vast amount of data for
steam or gaseous water as we have tried to improve steam engines. For example, we now
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4. An overview of equilibrium thermal physics
(Hiroshi Matsuoka)
4.1 An overview of equilibrium thermodynamics
Macroscopic single-component systems
The ultimate goal of thermal physics is to contribute to our understanding of physical nature
of macrosco
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Homework#10: Solutions
1. (a)
The partition function for this system is given by
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Z(T ) = # exp[!" s / ( kB T )] = 1 + 4 exp[!$ / (k B T)] + 4exp[!2$ / ( kB T )]
s=1
cfw_
= 1+ 2 exp[!$ / (k B T)]
2
1. (b)
We then find the Helmholtz free energy to be
c
Homework#5 (10 points)
1. (5 points)
(a) (1 point)
5
cP / R
4
3
2
1
0
0
500 1000 1500 2000 2500 3000 3500
T (K)
For 220 K T 320 K , c P R 3.5 so that cv = c P R = (5 2) R = cfw_(3 + 2) 2R , which
implies that the translational and the rotational motion of