PRACTICE PROBLEMS Set 2 – Solutions to some of the problems
 H 
 V 
  V  T 
1. Show that: 

 T  p
 p T
     
  
2. Show that: 
 0
 p T  T  p
 U 
3. 
 
 T  p
?
 V 
 p

 T  p

 S   
4. 
    
 V T  V 

 p 
 S 

   
 V  T  T V 
5. 3.5 moles of an ideal gas is expanded from 450K and an initial pressure of 5 bar to
a final pressure of 1 bar and Cp,m=5/2R. Calculate w for the following two cases:
(i) the expansion is isothermal and reversible (ii) the expansion is adiabatic and
reversible. What do you expect in both cases in an irreversible situation?
Ans:(i) 21,080 J (ii) 236.4 K, w =-9324 J
In the irreversible case the temp for the adiabatic
process will be different than the reversible case
6. Calculate the entropy change in heating 1.00 mol of Al from 300 K to 500 K at
constant pressure. The constant pressure heat capacity of Al is given to good
approximation by C p  20.67 JK 1mol 1  12.38 103  JK 2 mol 1 .
Answer: The calculation is
7. 10 moles of a gas are contained under high pressure so that the volume is 0.5 L.
The external pressure is suddenly reduced and the gas allowed to expand into a
50L container. Assume the gas is a van der Waals gas with a=3.7 atm L2 mol-2 and
b=0.043 Lmol-1. The temperature is constant at 298K. Determine the change in
entropy of the gas for this volume change.
8. The composition of dry air is approximately 78% N2, 21% O2, and 1% Ar by
volume (which is the same as mole percent). What is the molar entropy of mixing
of air?
9. Determine the value of G per mole for the freezing of supercooled water at -60C.
(Latent heat of fusion of ice 80 cal gm-1)
10. Find the change in Gibbs free energy accompanying the compression of 1 mole of
ethane at 500C from 20 to 250 bars.
Hint: Use pressure dependence formula