Homework G
PHY3513
Due: In class Nov. 16, 2009
1. (16.1) Try without looking up the derivations in your textbook.
 ∂U 
2. (16.2) (a) Use the cyclic relation and we derived 
 = ? in the class.
 ∂V  T
3. (16.2) (b)
 ∂Q 
 ∂U 
 ∂U 
4. (16.3) dU = dQ − pdV = 
 dT + 
 dV and C p = 
 and
 ∂T V
 ∂V  T
 ∂T V
 1  ∂V 
β p =  
 .
 V  ∂T  p
5. (16.4) We already worked on the part (a). For the part (b), you have to first show
1  ∂U   ∂   p 
 ∂U 
 ∂p 

 = T
 − p from dU(T,V). Then, show 2 
 =
  .
T  ∂V T  ∂T V  T 
 ∂V  T
 ∂T V
6. Derived the entropy of an ideal gas in two different forms:
S (T , V ) = S o + CV ln T + Nk B ln V
S (T , p ) = S o′ + C p ln T − Nk B ln p
Derive above expressions again and show that they are identical within a constant.
Ex.16.6 shows you how to derive the first expression S(T,V). Follow a similar path to
derive the second expression by choosing S = S(T, p).