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- 1.
- Estimate the thermal speed of an oxygen molecule at room
temperature.
**Hint:**- There are
*N*_{A}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*/*N*_{A}. Recalling from Thermo course that , we obtain: This is about

- 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) **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 3*kT*/2 per particle, or 3*NkT*/2 per*N*particles

© 1997

Thu Sep 18 22:50:29 EDT 1997