Calculate amount of heat flowing into gas in one cycle

Question

Solve the following problem:

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_I and P₂ the lower and higher pressures, respectively; call V_I and V₂ 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 capacities.)

(c) Show that the efficiency of this engine is

η  = γ - 1/ (γP₂/P₂ - P₁) + (V₁/V₂ - V₁)