Using the Kelvin-Planck statement of the second law of thermodynamics, demonstrate the following corollaries: a. The coefficient of performance of an irreversible refrigeration cycle is always less than the coefficient of performance of a reversible refrigeration cycle when both exchange energy by heat transfer with the same two reservoirs. b. All reversible refrigeration cycles operating between the same two reservoirs have the same coefficient of performance. c. The coefficient of performance of an irreversible heat pump cycle is always less than the coefficient of performance of a reversible heat pump cycle when both exchange energy by heat transfer with the same two reservoirs. d. All reversible heat pump cycles operating between the same two reservoirs have the same coefficient of performance.