Homework H
PHY3513
Due: 8 AM Nov. 24, 2009
1. The internal energy of an ideal gas can be derived using statistical mechanics as
N
U = U ( S , V ) = αNk B  
V 
2/3
e 2 S / 3 Nk B .
where a is a constant. Show that this expression leads to the equation of state for an ideal
gas PV = NkBT. (What is dU?)
2. (17.1)*
3. (17.2)* (In # 2 and #3, you should use the proper Maxwell’s relations. –p f, V L)
4. (17.3) Express N+ and N- in terms of N, L, and a. Then, Sterling’s formula.
5. (17.6)
 ∂f
that 
 ∂T
(The problem says the tension f is proportional to T with a fixed L. This means

 = const > 0 )
L
6. Show the following relation:
Vβ P
.
Cp
When we derived a similar relation involving Cp and Cv, we started from dU.
Here it is reasonable to start from dV as V = V(p,T).
κT − κ S = T
2
7. A block of metal of volume V is subjected to an isothermal reversible increase in
pressure from p1 to p2 at temperature T.
(a) Show that the heat given out by the metal is TVβp(p2 – p1). (4)
(b) Show that the work done on the metal is V(p22-p12)κT/2. (4)
(c) Calculate the change in U. (1st law) (2)
You can assume that βp, κT, and V are constant in small range of pressure.