last one i need help on! :)?

Question

A heat pump is used to heat a house with an interior temperature of 20.4°C. On a chilly day with an outdoor temperature of -10.9°C, what is the minimum work that the pump requires in order to deliver 1.3 kJ of heat to the house?

Answer 1

EDITED: Please note correction (temps should be in ºK) and change in terminlogy.

The coefficient of performance of a heat pump in heating mode is given by

COP = Thot/(Thot - Tcool)

Heat needed to move 1.3 kJ = 1.3/COP.

In your problem, COP = 314ºK/(314ºK - 282.7ºK) =314ºK/31.3ºK = 10.0. The minimum work input is then 1.3/10 = 0.13 kJ.