A heat pump is used to keep a house warm at 20C How much wor

A heat pump is used to keep a house warm at 20°C. How much work is required of the pump to deliver 3300 J of heat into the house if the outdoor temperature is each of the following? Assume ideal (Carnot) behavior. (a) 0°C J (b) -15°C J

Solution

E = (Q₁ - Q₂) / Q₁

E= ( (20 + 273) - (0 + 273 ) ) / (20 + 273)

E = 0.0683 %

E = W / Q_H

0.0683 = W / 3300

W = 225.3 J

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b) E = ( (20 + 273) - (-15 + 273) ) / (20 + 273)

E = 0.119

0.119 = W / 3300

W = 392.7 J