Problems and Solutions on Thermodynamics and Statistical Mechanics

296 Problems 6' Solutiow on Thermodynamics 6' Statistical Mechanics

2119

A useful way to cool He3 is to apply pressure P at sufficiently low

temperature T to a co-existing liquid-solid mixture. Describe qualitatively

how this works on the basis of the following assumptions:

(a) The molar volume of the liquid VL is greater than that of the solid
Vs at all temperatures.

(b) The molar liquid entropy is given by

SL = 7RT with 7 - 4.6 K-'.

(c) The entropy of the solid Ss comes entirely from the disorder asso-
ciated with the nuclear spins (s = 1/2).

Note: Include in your answer a semi-quantitative graph of the p-T diagram

of He3 at low temperatures (derived using the above information).

(Chicago)

Solution:

The Clausius-Clapeyron equation is

dp AS SL - Ss

dT AV VL-VS '

_- - -- -

1 I I z

Tmin T

Fig. 2.24.

1

For particles of spin -, SS = kNA In 2. Thus

2

dp 7RT-kNAln2 - 7RT-Rln2

_- -

dT - VL - vs VL - vs.