Question

A cylinder with initial volume V contains a sample of 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. Find the amount of work W done on the gas during the entire process. Express your answer in terms of some or all of the variables p and V.

Answer 1

Answer:

The work done on the gas = 2PV

Explanation:

In this question, we need to apply the basic gas laws to determine the word done.

For this question, we need to draw a PV diagram (a pressure-volume diagram), which I have made and attached in the attachment. So please refer to that attachment. I will be using this diagram to solve for the work done on the gas.

So, Please refer to the attachment number 1. where x -axis is of volume and y-axis is of pressure.

As we know that, the work done on the gas is equal to the area under the curve.

W = Area of the triangle

W = 0.5 x ( base) x ( height)

W = 0.5 x (BC) x (AC)

W = 0.5 x (3V-V) x (3P-P)

W = 2PV

Hence, the work done on the gas = 2PV