A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 27

4.51 Nonideal Gas Expansion (Michigan State)

A gas obeys the equation of state

where is a function of the temperature only. The gas is initially at

temperature and volume and is expanded isothermally and reversibly

to volume

Find the work done in the expansion.

Find the heat absorbed in the expansion.

Some Maxwell relations:

4.52 van der Waals (MIT)

A monatomic gas obeys the van der Waals equation

and has a heat capacity in the limit

Prove, using thermodynamic identities and the equation of state, that

Use the preceding result to determine the entropy of the van der Waals

gas, to within an additive constant.

Calculate the internal energy to within an additive constant.

What is the final temperature when the gas is adiabatically com-

pressed from to final volume

How much work is done in this compression?

a)

b)

b)

c)

d)

e)

a)