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An ideal heat pump is used to maintain the inside temperature of a house at Tin...

An ideal heat pump is used to maintain the inside temperature of a house at Tin = 20 ∘C when the outside temperature is Tout. Assume that when it is operating, the heat pump does work at a rate of 1700 W . Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by (650W/∘C)(Tin−Tout).

For what outside temperature would the heat pump have to operate at all times in order to maintain the house at an inside temperature of 20 ∘C?

If the outside temperature is 7 ∘C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 20 ∘C?

Express your answer using two significant figures.

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