Chemistry 5302 Homework Problem Set 1 1. McQuarrie, Problem 1

Chemistry 5302 Homework Problem Set 1
McQuarrie, Chapters 1 and 2
1. McQuarrie, Problem 1-29: Use the thermodynamic square to derive the equation of
state:
∂E
∂p
−T
= −p
(1)
∂V N,T
∂T N,V
2. Use the canonical ensemble partition function to derive the equation of state:
∂p
∂E
+β
= −p
∂V N,β
∂β N,V
(2)
3. McQuarrie, Problem 2-1: Use the equivalence of the equations of state in (1) and (2)
to show that:
1
(3)
β∝
T
Why can’t β = constant × T ?
4. Equating the statistical mechanical energy E with the thermodynamic internal energy
E, show that E can be written:
∂ ln Q
2
E = kT
(4)
∂T
N,V
1