Figure P5.10 shows two power cycles, denoted 1 and 2,

Chapter 5, Problem 5.10

(choose chapter or problem)

Figure P5.10 shows two power cycles, denoted 1 and 2, operating in series, together with three thermal reservoirs. The energy transfer by heat into cycle 2 is equal in magnitude to the energy transfer by heat from cycle 1. All energy transfers are positive in the directions of the arrows.

(a) Determine an expression for the thermal efficiency of an overall cycle consisting of cycles 1 and 2 expressed in terms of their individual thermal efficiencies.

(b) If cycles 1 and 2 are each reversible, use the result of part (a) to obtain an expression for the thermal efficiency of the overall cycle in terms of the temperatures of the three reservoirs, \(T_{\mathrm{H}}\), T, and \(T_{\mathrm{C}}\), as required. Comment.

(c) If cycles 1 and 2 are each reversible and have the same thermal efficiency, obtain an expression for the intermediate temperature T in terms of \(T_{\mathrm{H}}\) and \(T_{\mathrm{C}}\).

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