Define the second-law efficiency of a heat pump operating on the vapor-compression refrigeration cycle and provide two alternative definitions and show that one can be derived from the other.

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Chapter 11.10, Problem 26P

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Define the second-law efficiency of a heat pump operating on the vapor-compression refrigeration cycle and provide two alternative definitions and show that one can be derived from the other.

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A heat pump cycle using water as the working fluid consists of a compressor, a condenser, an expansion valve, and an evaporator. Saturated vapor with mass flow rate of 1 kg/s at 0.5 MPa (state 1) enters the condenser and leaves it as saturated liquid at the same pressure (state 2). The pressure in the evaporator is 0.01 MPa. The condenser and the evaporator processes are isobaric. The compressor is adiabatic and reversible. The valve is adiabatic. A. List all the known information and assumptions. B. Determine the heat output of the condenser (QH) C. Determine the heat input of the evaporator(Qc) D. Determine the coefficient of performance of the heat pump. E. Determine the coefficient of performance of a Carnot heat pump running between the same temperatures TH and TC at the evaporator and condenser. F. Calculate the entropy generation in the compressor. G. Draw the TS diagram for the cycle on paper. (Hint: you must calculate T1, T2, T3, T4, h1, h2, h3, h4, s1, s2, s3, s4, and draw…