Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics^9

Solution:
(a) From H = U + pV, we obtain

(%)p= (%),+p(%) P *

Let U = U[T, V(T, p)]. The above expression becomes

Hence

P

(b) For the Van der Waals gas, we have

R

RT 2a(V - b)

v

Hence ,

R

cp - C" =

1 - 2a( 1 - b/V)2/VRT '

When V -+ 00, cp - c, + R, which is just the result for an ideal gas.

1010

One mole of gas obeys Van der Waals equation of state. If its molar

internal energy is given by u = cT - a/V (in which V is the molar volume,

a is one of the constants in the equation of state, and c is a constant),

calculate the molar heat capacities C, and C,.

Solution:

( was co nsin)

c,=(%) =c,

%= (g)p+p(%)p= (%)v+ [(3,+Pl

V

x(%) =c+(&+p)(E).

P P