In extremely cold weather conditions where the inside thermostat is set to 27 C
ID: 2118330 • Letter: I
Question
In extremely cold weather conditions where the inside thermostat is set to 27 C and the outside temperature is -20C, your 1200 square ft house might lose heat through the walls at a rate of 3980 W.
A.How much energy might you lose in one week?
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?
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)
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?
Explanation / Answer
A) ENERGY LOST = 3980 * ( 7 * 24 * 60 * 60 ) = 2407104000 J = 2407.104 M J
b) b)total=10*2407104000/(36*10^5)=6686.4cents
c) COPheating=(300)/(300-253)=6.383
energy to be removed for week = 2407104000 J
energy consumed by heater = ( 2407104000 / 6.383 ) = 377112960 J = 377. 11 M J
new cost = 10*377112960/(36*10^5)=1047.5cents
d) COPheating=(300)/(300-288)=25
energy consumed by heater = ( 2407104000 / 25) = 96284160 = 96.284 M J
new cost = 10*96284160/(36*10^5)=267.5cents