Question

In extremely cold weather conditions where the inside thermostat is set to 27 C and the outside temperature is -20 C, your 1200 square ft house might lose heat through the walls at a rate of 4470 W.

(See questions below.)

Answer 1

a) How much energy might you lose in one week?
Express your answer using three significant figures in unit J.

b) Electric heat can be 100% efficient. At 10 cents per kilowatt-hour how much would it cost to heat your house for one week under such cold conditions? Answer in $.

c) For an air conditioner used as a heat pump, the coefficient of performance can be as high as the inverse of the Carnot efficiency which is run between the temperature inside (27 C) and the temperature outside (-20 C). How much would it cost to heat your house for one week using such a heat pump? (Note that a real air conditionier usually has a COP which is half that for a Carnot cycle.) Answer in $.

d) An even more efficient system is a geothermal air conditioner, where the heat pump runs between the inside temperature (27 C) and pipes which are buried underground below the frost line where the temperature is always 59 F or 15 C. How much would it cost to heat your house for one weak using such a geothermal system? Answer in $.

Answer 2

a) Energy loss in kWhr = power (in kW) x time (in hours)
b) Cost in $ = energy (in kWhr) x cost per kWhr (in $)
c) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatpump.html
d) Same sort of reasoning as in c) but with a different temperature.

Answer 3

Thanks!!