At steady state, a refrigeration cycle driven by an

Chapter 5, Problem 5.65

(choose chapter or problem)

At steady state, a refrigeration cycle driven by an electric motor maintains the interior of a building at \(T_{\mathrm{C}}=20^{\circ} \mathrm{C}\) when the outside temperature is \(T_{\mathrm{H}}=35^{\circ} \mathrm{C}\). The rate of heat transfer into the building through its walls and roof is given by \(\mathrm{R}\left(T_{\mathrm{H}}-T_{\mathrm{C}}\right)\), where R is a constant, in kW/K. The coefficient of performance of the cycle is 20% of a reversible refrigeration cycle operating between cold and hot reservoirs at \(T_{\mathrm{C}}\) and \(T_{\mathrm{H}}\), respectively

(a) If the power input to the motor is 3 kW, evaluate R.

(b) If R is reduced by 5%, determine the power input required, in kW, assuming all other data remain the same.