Problems and Solutions on Thermodynamics and Statistical Mechanics

192 Problems tY Solutiotu on Tlrermcdytam'ca tY Stati~tical Mechanica

a = 2 x 10' cm-'
ro = 8 x lo-' cm.
Estimate the temperatures at which rotation (TR) and vibration (Tv) begin
to contribute to the specific heat of hydrogen gas. Give the approximate
values of C, and C, (the molar specific heats at constant volume and at
constant pressure) for the following temperatures:

Neglect ionization and dissociation.

Solution:

librium distance. From

Ti = 25 K, T2 = 250 K, T3 = 2500 K, T4 = 10000 K.

(UC, Berkeley)

The average distance between the two atoms is approximately the equi-

(%) r=d = 0 ,

we obtain d = ro. The frequency of the radial vibration of the two atoms

is r

where p = m~/2 is the reduced mass and

so

w= J?.

The characteristic energy of the rotational level is

then

=75K.

A2

on = ~

kmH ri

The characteristic energy of vibration is kOv = Aw, then