Consider any heat engine that operates between a hot reservoir at temperature TH and a cold reservoir at temperature TC (TH>TC). In one complete cycle it absorbs heat QH from the hot reservoir and rejects heat QC to the cold reservoir while producing work W.
(i) Write the first law of thermodynamics for one cycle of the engine.
(ii) Assuming the hot and cold reservoirs are so large that their temperatures remain constant, write the total entropy change of the two reservoirs for one cycle in terms of QH,QC,TH and TC.
(iii) Using the requirement imposed by the second law on the sign of the total entropy change of the universe, derive an inequality connecting QH,QC,TH and TC.
(iv) From this inequality, obtain an expression showing that the efficiency η=QHW of any heat engine working between the given temperatures cannot exceed 1−THTC.