1.
Estimate the thermal speed of an oxygen molecule at room temperature.
Hint:
There are NA molecules in

Solution:
Since , average velocity is

An average material scientist might not remember the mass of oxygen molecule, but she/he certainly remembers its molar mass . Then m=M/NA. Recalling from Thermo course that , we obtain:

2.
Calculate the chemical potential of ideal gas .
Solution:
Since

Chemical potential of ideal gas is kT log of the concentration (up to a constant)!

3.
Calculate the energy of the ideal gas without internal degrees of freedom (). If you are too lazy (or too smart) to calculate it from equation

 E = Nf(T)-NTf'(T) (1)

try to guess the answer. How would you do this?
Solution:
There are two ways to solve this problem.
(a)
Hard way. If ,

and

so

(b)
Smart way. If there are no internal degrees of freedom, all the energy is kinetic energy K. This is 3kT/2 per particle, or 3NkT/2 per N particles

Next: Interaction Energy Up: Imperfect Gases and Liquids. Previous: Imperfect Gases and Liquids.

© 1997 Boris Veytsman and Michael Kotelyanskii
Thu Sep 18 22:50:29 EDT 1997