Problem on Second Law of Thermodynamics

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A reversible engine operates between three thermal reservoirs, A, B, and C, absorbing equal heat from A and B at temperatures Ta and Tb, and rejecting heat to C at temperature Tc. The engine's efficiency is α times that of a reversible engine operating between A and C. The discussion centers on proving the relationship Ta/Tb = (2α - 1) + 2(1 - α)Ta/Tc. This equation highlights the interplay between the efficiencies and temperatures of the reservoirs involved. The problem emphasizes the complexities of thermodynamic efficiency in multi-reservoir systems.
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A reversible engine works between three thermal reservoirs-A,B and C.The engine absorbs an equal amount of heat from the thermal reservoirs A & B kept at temperatures Ta and Tb respectively,and rejects heat to the thermal reservoir C kept at temperature Tc.The efficiency of the engine is \alpha times the efficiency of the reversible engine,which works between the two reservoirs A & C.Prove that:Ta/Tb=(2\alpha-1)+2(1-\alpha)Ta/Tc
 
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