The work done by a gas as it is taken in a cyclic process (shown in graph) is

Step-by-step solution

Work in a cyclic process equals the area enclosed on the P-V diagram, calculable as the sum of work from each process. Process AB (Isobaric): Pressure remains P while volume expands from V to 3V . Work done by the gas is W_ AB = P V = P(3V - V) = 2PV . Process BC (Isochoric): Volume remains 3V , so W_ BC = 0 . Process CA (Linear Compression): From state C(3V, 4P) to A(V, P) , the work corresponds to the area under the curve. The pressure decreases linearly, forming a trapezoid with parallel sides 4P and P and heigh