Problems and Solutions on Thermodynamics and Statistical Mechanics

134 Problerna 8 Solutions on Thermodyamica 8 Statistical Mechanics

in a region where the average melting point of the rock is 1300°C. Assume
a density ratio
Pliquid/Psolid e 0.9
and a latent heat of melting of 100 cal/g. Give your answer in degrees C
per kilometer.
(UC, Berkeley)
Soh tion:
(a) During the phase transtion, pr = pa, where 1 and 3 represent liquid
phase and solid phase respectively. By thermodynamic relation

dp = -SdT + VdP ,

we have (S1 - S,)dT, = (V, - Va)dP, so

1 dT, - V, - Va - v, - v,

Tni dp Trn(Si - Sa) L

Substituting V = l/p into the equation above, we get

dP

dz

(b) Denote the depth as z, we have - = pg.

(c) From the above results, we have

= 37 x "C/cm = 3.7"C/km.

1137

The vapor pressure, in mm of Hg, of solid ammonia is given by the

The vapor pressure, in mm of Hg, of liquid ammonia is given by the

relation: lnp = 23.03 - 3754/T where T = absolute temperature.

relation: lnp = 19.49 - 3063/T.

(a) What is the temperature of the triple point?

(b) Compute the latent heat of vaporization (boiling) at the triple

point. Express your answer in cal/mole. (You may approximate the be-