Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamic 8 123

From the condition of equilibrium: dU = 0,dS = Olpl = p2, dVl =
-dV2 and d(N1+N2) = 0, we get (p1-po)dVl = udr, or pl-po = udr/dVl,
dr 2
where - = - Hence pi - po = 2u/r.
dV1 r
m

is the molecular weight of air, we have

Since plV1 = -RT, where m is the mass of air inside the bubble, M

M

4T M

3 RT

m= --r3 (Po+ F).

4rMpor3

3RT

(b) When po >> 2u/r, Le., r >> 2a/po, we have rn =

1127

Derive the vapor pressure equation (Clausius-Clapeyron equation):

(UC, Berkeley)

dpldT =?

Solution:
Conservation of energy gives

where V1 is the volume of the vapor, and V2 is the volume of the liquid. In
phase transition from liquid to vapor, chemical potential is invariant, i.e.,
p1 = p2, so that one has the vapor pressure equation:

where L is the latent heat of vaporization.
Usually V2 << Vl, and this equation can be simplified to

dv L