Assignment:
A cylinder with initial volume V contains a sample of gas at pressure p. The gas is heated in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, it is cooled isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure. Find the mathematical expression for the amount of work W done on the gas during the entire process. Express the work in terms of p and V.