Question

A heat pump is used to heat a house with an indoor temperature of 21 ◦C. Assume the outdoor temperature is -9 ◦C. What is the maximal energy that could be delivered to the house in one second if the work done on the heat pump is 1500 W (1500 J/s)?

(a) 3000 J (b) 3500 J (c) 15.0 kJ (d) 200 J (e) 10.7 kJ

Answer 1

The coefficient of power of a heat pump is defined as the ratio of useful heat to the work done on the pump

The useful heat in the given case is the heat entering the house

The theoretical maximum efficiency of a heat pump is given by

T_{​​​​​​h} is the temprature of hot reservoir, T_{​​​​​​c} is the temprature of the cold reservoir.

Substituting T_{​​​​​c}=-9°C=-9+273=264K, T_{​​​​​h}=21°C=21+273=294, we get

The heat output of the heat pump into the room is

The maximum energy delivered to the house in one second is

(c) 15.0 kJ