A building is maintained at a temperature T by means of an ideal heat pump, which...

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A building is maintained at a temperature T by means of an ideal heat pump, which uses a river at temperature To as a source of heat. The heat pump consumes power W, and the building loses heat to its surroundings at a rate a(T-To), where a is a positive constant. Show that T is given by T = To + (1+√/1+4aTo/W). (13.44) W 2α A building is maintained at a temperature T by means of an ideal heat pump, which uses a river at temperature To as a source of heat. The heat pump consumes power W, and the building loses heat to its surroundings at a rate a(T-To), where a is a positive constant. Show that T is given by T = To + (1+√/1+4aTo/W). (13.44) W 2α