Isochoric Cooling and Isobaric Expansion

An ideal gas of total mass m and molecular weight μ is isochorically (at constant volume) cooled to a pressure times smaller than the initial pressure P₁. The gas is then expanded at constant pressure so that in the final state the temperature T₂ coincides with the initial temperature T₁. Calculate the work done by the gas.

SOLUTION

The process diagram is shown in Figure 1.1. The work W done by the gas occurs only during the 2→3 leg since there is no work done during the 1→2 leg. The work is given by

(1)

Figure 1.1

Using the ideal gas law, we may relate V₁ and V₂:

(2)

since the initial and final temperatures are the same. Substituting into (1) we find

(3)