To increase the thermal efficiency of a reversible power

Chapter 5, Problem 5.14

(choose chapter or problem)

Figure P5.14 shows a system consisting of a reversible power cycle driving a reversible heat pump. The power cycle receives \(Q_{\mathrm{s}}\) by heat transfer at \(T_{\mathrm{s}}\) from a high-temperature source and delivers \(Q_{\mathrm{1}}\) to a dwelling at \(T_{\mathrm{d}}\). The heat pump receives \(Q_{\mathrm{0}}\) from the outdoors at \(T_{\mathrm{0}}\) and delivers \(Q_{\mathrm{2}}\) to the dwelling. Obtain an expression for the ratio of the total heating provided to the dwelling to the heat transfer supplied from the high-temperature source: \(\left(Q_{1}+Q_{2}\right) / Q_{\mathrm{s}}\) in terms of the temperatures \(T_{\mathrm{s}}, T_{\mathrm{d}}\), and \(T_{0}\).