THERMODYNAMICS AND STATISTICAL PHYSICS
Formulas and constants
Thermodynamic functions and relations
H
=
E
+
pV F
=
E
?
T S G
=
E
?
T S
+
pV
@E
@S
V
=
T
@E
@V
S
=
?
p
@H
@S
p
=
T
@H
@p
S
=
V
@F
@T
V
=
?
S
@F
@V
T
=
?
p
@G
@T
p
=
?
S
@G
@p
T
=
V
Maxwell relations
@T
@V
S
=
?
@p
@S
V
@T
@p
S
=
@V
@S
p
@S
@V
T
=
@p
@T
V
@S
@p
T
=
?
@V
@T
p
Specic heat
c
V
=
1
dQ
dT
V
c
p
=
1
dQ
dT
p
Entropy
S
=
k
ln
S
=
?
k
P
r
P
r
ln
P
r
S
=
k
(ln
Z
+
E
)
Partition functions
Z
=
P
r
e
?
E
r
Z
=
P
r
e
?
E
r
?
N
r
ln
Z
=
N
P
r
ln
1
e
?
r
?
Clausius-Clapeyron equation
dp
dT
=
S
V
dp
dT
=
L
12
T
V
Fermi energy (
=
?
kT
)
j
=
?
T
@S
@N
j
E;V;N
j
=
@E
@N
j
S;V;N
j
=
@F
@N
j
T;V ;N
j
=
?
@G
@N
j
T;p;N
Stefan-Boltzmann law
P
=
aT
4
=
a
2
k
4
60
c
2
h
3
T
4
Stirlings formula
ln
N
! =
N
ln
N
?
N
+
1
2
ln(2
N
) +
:::
