A cylinder with initial volume V contains a sample of a gas at pressure p . On o

Question

A cylinder with initial volume V contains a sample of a gas at pressure p. On one end of the cylinder, a piston is let free to move so that the gas slowly expands in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, the piston is pushed in so that the gas is compressed isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure.

Find the work W done on the gas during the entire process.

Explanation / Answer

W in first process = 3p*3v-pv = 8Pv

W in second process = 3p(v-3v) = -6pv

W in third process = 0

net work done = 2PV

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