Thermodynamics, Statistical Physics, and Quantum Mechanics

26 PROBLEMS

Write the partition function for the system.

Calculate theaverage length as afunction of and the tempera-

ture

Assume that and Estimate the average length

in the absence of the tensile force as a function of tempera-

ture. What are the high- and low-temperature limits, and what is the

characteristic temperature at which the changeover between the two

limits occurs?

Calculate the linear responsefunction

Produce a general argument to show that

Nonideal Gas

Heat Capacities (Princeton)

Consider a gaswith arbitrary equation ofstate at a temper-

ature where is a criticaltemperature ofthis gas.

Calculate for this gas in terms of Does always

have the same sign?

Using the result of (a), calculate for one mole of a van der

Waals gas.

a)

b)

4.50 Return of Heat Capacities (Michigan)

In a certain range of temperature and pressure the specific volume
of a substance is described by the equation

where arepositiveconstants.Fromthisinformation, determine
(insofar aspossible) as afunction of temperature and pressure thefollowing
quantities:

a)

b)

c)

d)

a)

b)

c)

4.49