Nonideal Gas Expansion

A gas obeys the equation of state

where B(τ) is a function of the temperature τ only. The gas is initially at temperature τ and volume V₀ and is expanded isothermally and reversibly to volume V₁ = 2V₀.

a) Find the work done in the expansion.

b) Find the heat absorbed in the expansion.

Some Maxwell relations:

SOLUTION

a) The work done in the expansion

(1)

b) To find the heat absorbed in the expansion use the Maxwell relations given in the problem:

(2)

where the prime indicates the derivative with respect to τ. Integrating (2), we obtain

(3)

where f(τ) is some function of τ. The heat absorbed in the expansion

(4)