During 2 hours one winter afternoon, when the outside temperature was 12° C, a h

Question

During 2 hours one winter afternoon, when the outside temperature was 12° C, a house heated by electricity was kept at 21° C with the expenditure of 58 kwh (kilowatt·hours) of electric energy.
(a) What was the average energy leakage in joules per second (watts) through the walls of the house to the environment (the outside air and ground)?
watts

(b) The rate at which energy is transferred between two systems due to a temperature difference is often proportional to their temperature difference. Assuming this to hold in this case, if the house temperature had been kept at 24° C (75.2° F), how many kwh of electricity would have been consumed?
kwh

Explanation / Answer

energy needed by electricity is due to the fact that it is being leaked to outside of room due to temprature difference

so whole energy is going outside

=> 58 * 1000 watt /hour

= 58 * 1000 * 2 watts in 2 hours

=116000 Joules /s

earlier rate = K * (21 -12)   .................(a)

now

rate = K * (24 -12) .....................(b)

a/b => 9/12 = 58 /x

=> x = 77.33 kwh

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