Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 121

1124
Determine the ratio (pV/RT) at the critical point for a gas which obeys
the equation of state (Dieterici's equation)

p(V - b) = RTexp(-a/RTV).

Give the numerical answer accurately to two significant figures.

(UC, Berkeley)

Solution:

The critical point satisfies

From the equation of state, we get

a(V - b)

e RTV ,

[ RTV2

($)T = RT (V - b)2

a(V - b)

RTV2

Consequently, -1=o.

Using this result, we get

a a

4b

Thus, - - 2 = 0. Then, V = 26, RT = -.

RTV

Substituting these back in the equation of state, we find - PV = 0.27.

RT

1125

Find the relation between the equilibrium radius r, the potential 4,

and the excess of ambient pressure over internal pressure Ap of a charged

soap bubble, assuming that surface tension can be neglected.

( wi3 c 0 fl3 in)