Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermcdymmica 135

havior of the vapor by treating it as an ideal gas, and may use the fact that
the density of the vapor is negligibly small compared to that of the liquid.)

(c) The latent heat of sublimation at the triple point is 7508 cal/mole.

(UC, Berkeley)

What is the latent heat of melting at the triple point?

Solution:

• 3754/To = 19.49 - 3063/TO, which gives TO = 195 K.

(a) The temperature T of the triple point satisfies the equation 23.03

(b) From the relation between the vapor pressure and temperature of
liquid ammonia
lnp = C - 3063/T ,

we get dp/dT = 3063p/T2.

The Clausius-Clapeyron equation - dP = - L then gives

dT TV

L = 3063pV/T = 3063R = 2.54 x lo4 J/mol

= 6037 cal/mol.

(c) Denote S,,Sl and S, as the entropy for vapor, liquid and solid at

triple point. Then the latent heat of vaporization is To(Sg - Sl), that of

sublimation is To(S, - Sa), and that of melting is

T(S1 - S8) = T(S, - St) - T(Sg - 5’1)

= 7508 - 6037 = 1471 cal/mol.

1158

The high temperature behavior of iron can be summarized as follows.

(a) Below 900°C and above 140OOC a-iron is the stable phase.

(b) Between these temperatures T-iron is stable.

(c) The specific heat of each phase may be taken as constant: C, =

0.775 J/g. K; C, = 0.690 J/g. K.

What is the latent heat at each transition?

(UC, Berkeley)