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