A.) The water in a deep underground well is used as the cold reservoir of a Carn
ID: 2103043 • Letter: A
Question
A.) The water in a deep underground well is used as the cold reservoir of a Carnot heat pump that maintains the temperature of a house at 294 K. To deposit 14380 J of heat in the house, the heat pump requires 819 J of work. Determine the temperature of the well water. Give answer in K. Do not enter unit.
B.) How long would a 2.60 kW space heater have to run to put into a kitchen the same amount of heat as a refrigerator (coefficient of performance = 2.69) does when it freezes 1.68 kg of water at 20.2
Explanation / Answer
The coefficient of performance of your heat pump is:
COP = Q_h / W = 14260J / 796J = 17.91
The COP of a Carnot heat pump (= the maximum attainable COP) in a heating application is
COP = T_h/(T_h - T_c)
=>
T_c = T_h ? ( COP - 1)/COP
= 296K ? (17.91 - 1)/17.91
= 279K
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