Solved: An ideal heat pump is used to maintain the inside

Chapter 15, Problem 77GP

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An ideal heat pump is used to maintain the inside temperature of a house at \(T_{i n}\)= \(22^{0} \mathrm{C}\) when the outside temperature is \(T_{\text {out }}\). Assume that when it is operating, the heat pump does work at a rate of 1500 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by \(\left.650 \mathrm{~W} /{ }^{0} \mathrm{C}\right)\left(T_{\text {in }}-T_{\text {out }}\right)\). (a) For what outside temperature would the heat pump have to operate all the time in order to maintain the house at an inside temperature of \(22^{0} \mathrm{C}\)? (b) If the outside temperature is \(8^{0} C\), what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of \(22^{0} \mathrm{C}\)?

Equation transcription:

Text transcription:

T{i n}

22^{0}{C}

T{{out }}

650{~W} /{ }^{0}{C})(T{{in }}-T{ {out }})

8^{0} C