Question

Learning Goal: To practice Problem-Solving Strategy 19.1 Work in Ideal-gas Processes. A cylinder with initial volume VVV contains a sample of a gas at pressure ppp. 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 3V3V and pressure 3p3p, the piston is pushed in so that the gas is compressed isobarically to its original volume VVV. The gas is then cooled isochorically until it returns to the original volume and pressure. Find the work WWW done on the gas during the entire process.

Answer 1

The work done on the gas is equal to the area under the curve pv diagram w = area of triangle = 1/2 (base)(height) = 1/2 (BC)(Ac) = 1/2 (3v - v)(3p - p) = 1/2 (9 vp - 3 vp - 3vp + vp) = 4 vp/2 W = 2 vp

Check attachment for the diagrammatic representation