• # question_answer A building in a cold climate is to be heated by a Carnot heat pump. The minimum outside temperature is $-\,23{}^\circ C.$ If the building is to he kept at $27{}^\circ C$ and heat requirement is at the rate of 30 kW, what is the minimum power required for heat pump? A) 180 k W           B) 30 k WC) 6 k W               D) 5 k W

${{T}_{1}}=273+27=300\,\,K,$ ${{T}_{2}}=273-23=250\,K$ ${{(COP)}_{HP}}=\frac{{{T}_{1}}}{{{T}_{1}}-{{T}_{2}}}=\frac{300}{300-250}=\frac{300}{50}=6=\frac{W}{Q}$ $W\,\,=\,\,30\,\,\times \,\,6\,\,=\,\,180\,\,k\,W$