Thermodynamics, Statistical Physics, and Quantum Mechanics

20 PROBLEMS

where is the averagenumber ofmoleculesfound in thevolume
V.

4.36 Polarization of Ideal Gas (Moscow Phys-Tech)

Calculate the electricpolarization of an idealgas,consisting of molecules

having a constant electric dipole moment in a homogeneous external

electric fieldE at temperature What is the dielectric constant of this

gas at small fields?

4.37 Two-Dipole Interaction (Princeton)

Two classical dipoles with dipole moments and are separated by a
distance R so that only the orientation of the magnetic moments is free.
They are in thermal equilibrium at a temperature Compute the mean
force between thedipoles for thehigh-temperaturelimit
Hint: The potential energy of interaction of two dipoles is

4.38 Entropy of Ideal Gas (Princeton)

A vessel of volume contains N molecules of an ideal gas held at temper-

ature and pressure The energy of a molecule may be written in the

form

where denotes the energy levels corresponding to the internal states of
the molecules of the gas.

Evaluate the free energy F. Explicitly display the dependence on the

volume

a)

Now consider another vessel, also at temperature containing the same
number of molecules of the identical gas held at pressure

Give an expression for the total entropy of the two gases in terms of

The vessels are then connected to permit the gases to mix without

doing work.Evaluate explicitly the change in entropy of the system.

Check whether your answer makes sense by considering the special

case

c)

b)