Question

In the month of January, a certain dwelling requires heat in the amount of 2.4 x 106 kJ per day to maintain its temperature at 20 C. As a means of providing the required heating, a heat pump cycle is under consideration that would operate between the dwelling and a nearby pond at 10 C. The manufacturer claims that the net work input required to operate the heat pump is 1.6 x 105 kJ/day. Evaluate this claim.

Answer 1

Here, the high temperature heat reservoir (or the hot reservoir) is the dwelling and the low temperature heat reservoir(or the cold reservoir) is the pond. A heat pump operates between the hot and cold reservoir.

Given: Temperature of the dwelling, T_H=20⁰C=293.15 K

Temperature of the pond, T_L= 10⁰C= 283.15 K

Work required by the heat pump, W_net= 1.6*10⁵ kJ/day

Heat supplied to the high temperature reservoir, Q_H= 2.4*10⁶ kJ/day

Evaluation of the claim is done by determining the Coefficient of Performance (COP) of a Carnot heat pump and the Actual COP.

The actual COP of a heat pump, COP_actual is calculated as

COP of a Carnot heat pump, COP_Carnot is calculated using the expression

where T_H and T_L is the Temperature of hot and cold reservoir respectively

As COP_actual < COP_Carnot , the claim made is possible.