Estimate the electricity a household saves in one winter by heating with a heat pump…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics

Thermal Physics, Ch Heat engines, refrigerators and the Carnot cycle

Problem

Estimate the electricity a household saves in one winter by heating with a heat pump instead of a resistive heater. Use the following figures and state your answer to two significant figures. The house needs heat delivered at a mean rate of

6.0\,\mathrm{kW}

over a heating season of

180

days. The inside is held at

20

°C; the mean outdoor temperature over the season is

4

°C. Take

0

°C

= 273.15\,\mathrm{K}

and treat the outside air and the interior as reservoirs at these mean temperatures. The resistive heater turns electricity into heat with no loss. The heat pump achieves a seasonal coefficient of performance equal to

0.25

of the Carnot value for these two temperatures (a realistic fraction for an installed unit). ((a)) Estimate the heat the house needs over the season, in

\mathrm{kW\,h}

. ((b)) Estimate the electricity each system uses, and hence the electricity saved.

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