At steady state, a reversible heat pump cycle discharges

Chapter 5, Problem 5.45

(choose chapter or problem)

At steady state, a reversible heat pump cycle discharges energy at the rate \(\dot{Q}_{\mathrm{H}}\) to a hot reservoir at temperature \(T_{\mathrm{H}}\), while receiving energy at the rate \(\dot{Q}_{\mathrm{C}}\) from a cold reservoir at temperature \(T_{\mathrm{C}}\).

(a) If \(T_{\mathrm{H}}=13^{\circ} \mathrm{C}\) and \(T_{\mathrm{C}}=2^{\circ} \mathrm{C}\), determine the coefficient of performance.

(b) If \(\dot{Q}_{\mathrm{H}}=10.5 \mathrm{\ kW}, \dot{Q}_{\mathrm{C}}=8.75 \mathrm{\ kW}\), and \(T_{\mathrm{C}}=0^{\circ} \mathrm{C}\), determine \(T_{\mathrm{H}}\), in \({ }^{\circ} \mathrm{C}\).

(c) If the coefficient of performance is 10 and \(T_{\mathrm{H}}=27^{\circ} \mathrm{C}\), determine \(T_{\mathrm{C}}\), in \({ }^{\circ} \mathrm{C}\).