Two reversible power cycles are arranged in series. The

Chapter 5, Problem 5.27

(choose chapter or problem)

Two reversible power cycles are arranged in series. The first cycle receives energy by heat transfer from a hot reservoir at \(1000^{\circ} \mathrm{R}\) and rejects energy by heat transfer to a reservoir at temperature \(T\left(<1000^{\circ} \mathrm{R}\right)\). The second cycle receives energy by heat transfer from the reservoir at temperature T and rejects energy by heat transfer to a cold reservoir at \(500^{\circ} \mathrm{R}(<T)\). The thermal efficiency of the first cycle is 50% greater than that of the second cycle. Determine

(a) the intermediate temperature T, in \({ }^{\circ} \mathrm{R}\), and the thermal efficiency for each of the two power cycles.

(b) the thermal efficiency of a single reversible power cycle operating between hot and cold reservoirs at \(1000^{\circ} \mathrm{R}\) and \(500^{\circ} \mathrm{R}\), respectively.