An imaginary ideal-gas engine operates in a cycle, which forms a rectangle with sides parallel to the axes of a PV diagram. Call P and P the lower and higher pressures, respectively; call V and V the lower and higher volumes, respectively. (a) Calculate the work done in one cycle. (b) Indicate which parts of the cycle involve heat flow into the gas, and calculate the amount of heat flowing into the gas in one cycle. (Assume constant heat capa- cities.) (c) Show that the efficiency of this engine is Y-1 = YP2 + P - P V V - V1