Two Carnot engines A and B are operated in series. Engine A receives heat from a source at 900 K and rejects heat to an intermediate sink at temperature T . Engine B receives the heat rejected by A and rejects heat to a final sink at 400 K . Let T₁ be the value of T when the two engines produce equal work, and T₂ be the value of T when the two engines have equal efficiencies. The value of T₁ - T₂ is:

Step-by-step solution

For two Carnot engines in series producing equal work, the intermediate temperature is the arithmetic mean of the source and final sink temperatures: T₁ = T_ source + T_ sink 2 = 900 + 400 2 = 650 K For two Carnot engines in series having equal efficiencies, the intermediate temperature is the geometric mean of the source and final sink temperatures: _A = _B 1 - T₂ 900 = 1 - 400 T₂ T₂ 900 = 400 T₂ T₂^2 = 900 400 = 360000 T₂ = 600 K The difference between the two intermediate temperatures is: T₁ - T₂ = 650 K - 600 K