A Carnot heat engine operating between a high T_H and low T_L energy reservoirs has an efficiency given by the temperatures. Compare this to two combined heat engines, one operating between T_H and an intermediate temperature T_M giving out work W_A and the other operating between T_M and T_L giving out work WB. The combination must have the same efficiency as the single heat engine, so the heat transfer ratio Q_H/Q_L =ψ(T_H, T_L)=[Q_H/Q_M] [Q_M/Q_L]. The last two heat transfer ratios can be expressed by the same function ψ() also involving the temperature TM. Use this to show a condition that the function ψ() must satisfy.