Question

An ideal gas, at initial temperature T1 and initial volume 3.1 m3, is expanded adiabatically to a volume of 7.1 m3, then expanded isothermally to a volume of 23 m3, and then compressed adiabatically back to T1. What is its final volume?

Answer 1

10.0 m³

Step-by-step explanation:

The gas initially starts expanding adiabatically from state 1 until it reaches state 2, with V2 being 7.1 m³ then it goes on to continue on to state 3 isothermally, with V3 being 23 m³ and finally gets compressed adiabatically to reach state 4.

For the adiabatic process in stage 1 to 2, we have that

P1V'1 = P2V'2

For the isothermal process in stage 2 to 3, we have that

P2V2 = P3V3

For the adiabatic process in stage 3 to 4, we have that

P3V'3 = P4V'4

Starting from the ending, we see that

P4 = P3 * (V3/V4)',

Going backwards we see that

P4 = P2 * (V2/V3) * (V3/V4)'

Going further backwards, we see that

P4 = P1 * (V1/V2)' * (V2/V3) * (V3/V4)'

We substitute expression for P4 into the equation P1V1 = P4V4 with T being constant, and then get V1V3 = V2V4

Trying to solve for V4, we get

V4 = V1V3/V2

V4 = (3.1 * 23) / 7.1

V4 = 71.3 / 7.1

V4 = 10.0 m³