A solar collector system delivers heat to a power plant. It is well known that the thermal collection efficiency η_sc of a solar collector diminishes with increasing solar collection output temperature T_H, or η_sc = A - BTH where A and B are known constants. The thermal efficiency of the power plant η_th is a fixed fraction of the Carnot thermal efficiency, such that η_th = F(1 - T_L/T_H) where F is a known constant assumed here independent of temperatures and T_L is the condenser temperature, also constant for this problem. Here, the solar collection temperature T_H is also taken to be the source temperature for the power plant.

(a) At what temperature T_H should the solar collector be operated to obtain the maximum overall system efficiency?

(b) Develop an expression for the maximum overall system efficiency.