(Series combination of two reversible engines)
Two identical reversible engines A and B are arranged in series. Engine A operates between a hot reservoir at temperature TH and an intermediate reservoir at temperature T. Engine B operates between the same intermediate reservoir at T and a cold reservoir at temperature TC.
(i) For each engine, write an expression for its efficiency in terms of the appropriate reservoir temperatures.
(ii) Show, by eliminating the intermediate temperature T, that the combined efficiency of engines A and B equals the efficiency of a single reversible engine working directly between TH and TC.
(iii) Engine A absorbs heat QH from the hot reservoir and produces work WA. Engine B receives the heat rejected by A and produces work WB. Derive a relation for the value of T in terms of TH and TC for which WA=WB.