Thermodynamics · Thermodynamic potentials and Legendre transforms
Two reversible Carnot heat engines operate in series
Problem
Two reversible Carnot heat engines operate in series. Engine 1 absorbs heat from a reservoir at 900 K and rejects heat to an intermediate reservoir at temperature T_m. Engine 2 absorbs the entire heat rejected by Engine 1 from that intermediate reservoir and rejects heat to a reservoir at 300 K. Engine 1 absorbs heat at a rate of 2.40 MW. The two engines produce equal net power. (a) Determine T_m. (b) Determine the power of each engine and the rate of heat rejection by Engine 2. (c) Determine the thermal efficiency of each engine and the overall thermal efficiency of the combined plant, and show that the overall efficiency equals that of a single Carnot engine operating between 900 K and 300 K.
Hint
Two Carnot engines in series sharing the intermediate heat share the intermediate temperature through \(Q_{C1}=Q_{H2}=Q_{H1}T_m/T_H\).
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