Problems and Solutions on Thermodynamics and Statistical Mechanics

208 Problems €4 Solutioru on Thermodynamics €4 Statistical Mechanics

tion.

m

(a) I = ;d2,

;x (2 + 1) - h2 = 3- h2

I I'

k6o =

2

6h

md2

then k6o = - - - 7.3 x J, 60 = 530 K.

As the hydrogen gas had reached thermal equilibrium at high temperature

before the experiment, the ratio of the number of the para- to that of the

orthohydrogen in the experiment is 1:3, which is the ratio of the degrees of

freedom of the spins.

(c) When T >> 60,01, the rotational energy levels are completely ex-

cited. From equipartition of energy, E = nkT, or C, = nk, where n is the

total number of the hydrogen molecules. (Note that here we only consider

the specific heat associated with rotation.)

(d) When T << 00,01 , there are almost no hydrogen atoms in the highly

excited states. Therefore, we consider only the 1st excited state for para-

and orthohydrogen. Noting the degeneracy of the energy levels, we have

for orthohydrogen

Similarly we have for parahydrogen

2

Cip) x npk. 5 ($) e-OoIT.

Note that

3 1

no = zn, np = in,