Chapter 6, Problem 6.52P

The entropy change between two specified states is the same whether the process is reversible or irreversible.

As shown in the figure below, two reversible cycles arranged in series each produce the same net work, Wcycle. The first cycle receives energy QH by heat transfer from a hot reservoir at TH = 1500°R and rejects energy Q by heat transfer to a reservoir at an intermediate temperature, T. The second cycle receives energy Q by heat transfer from the reservoir at temperature T and rejects energy QC by heat transfer to a reservoir at TC = 450°R. All energy transfers are positive in the directions of the arrows.   Determine:(a) the intermediate temperature T, in °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 1500°R and 450°R, respectively. Also, determine the ratio of the net work developed by the single cycle to the net work developed by each of the two cycles, Wcycle.

As shown in the figure below, two reversible cycles arranged in series each produce the same net work, Wcycle. The first cycle receives energy QH by heat transfer from a hot reservoir at TH = 1000°R and rejects energy Q by heat transfer to a reservoir at an intermediate temperature, T. The second cycle receives energy Q by heat transfer from the reservoir at temperature T and rejects energy Qc by heat transfer to a reservoir at Tc = 500°R. All energy transfers are positive in the directions of the arrows. Determine: Hot reservoir at TH QH Reservoir at T R1 lo ali R2 Qc Cold reservoir at Te W. cycle W cycle (a) the intermediate temperature T, in °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°R and 500°R. respectively. Also, determine the ratio of the net work developed by the single cycle to the net work developed by each of the two cycles, Wcycle.