Consider a cyclic device that can operate either as a refrigerator or as a heat pump between the same cold reservoir at 0 °C and hot reservoir at 25 °C. Answer the following questions.
(i) Define the coefficient of performance (COP) for (a) a refrigerator and (b) a heat pump.
(ii) Using the principle of conservation of energy for a complete cycle, derive an algebraic relationship connecting the COP of the heat pump and the COP of the refrigerator operating between the same two reservoirs.
(iii) In the heat-pump mode the device delivers 9.0 kJ of heat to the room each cycle while consuming 0.75 kJ of mechanical work. When the same device is used as a refrigerator between the same reservoirs, calculate its COP.