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An irreversible heat pump heats a home on a cold winter’s day. The home loses heat to the outdoors at a rate of Q̇ = B (Tin − Tout), where B is a constant equal to 0.5 [kW/K]. The coefficient of performance (COP) of irreversible heat pump is 50% of that for a reversible heat pump (i.e., β ′ = 0.5 β ′ rev ). If the indoor temperature is to be maintained at 20 °C and the power input to the heat pump is 5 kW: a) Determine the outdoor temperature, Tout. [5 marks] b) Determine the coefficient of performance of the heat pump, β′. [5 marks]