Problems and Solutions on Thermodynamics and Statistical Mechanics

Statidid Physics 227

Solution:

(a) The energy of a dipole in electric field is

~,=-p.E=-pEcosB,

The partition function is then

The polarization is

PE 11

(b) Under the condition -z = - << 1, coth 2 w --z + -, and we have

kT 3x

ji w np2E/3kT.

2061

The entropy of an ideal paramagnet in a magnetic field is given ap-

proximately by

s=so-cu2,

where U is the energy of the spin system and C is a constant with fixed

mechanical parameters of the system.

(a) Using the fundamental definition of the temperature, determine

(b) Sketch a graph of U versus T for all values of T (-m < T < m).

(c) Briefly tell what physical sense you can make of the negative tem-

the energy U of the spin system as a function of T.

perature part of your result.

Solution:

( wis co nsin)

(a) From the definition of temperature,

1

we have U = --

2CT‘