What is the energy consumption at a different temperature?

[mshah3]

Homework Statement

During 4 hours one winter afternoon, when the outside temperature was 4° C, a house heated by electricity was kept at 24° C with the expenditure of 53 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)?
13250 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 27° C (77° F), how many kwh of electricity would have been consumed?
____kwh

Homework Equations

(a) power = work / delta time
energy transfer = work / delta time

(b) ?

The Attempt at a Solution

(a) First, I converted the 52 kwh to be 1.908e8 wsec
Then, I converted the 4hours to 14400 seconds
Doing so, I found the energy transfer to be 13250 watts for part a.

(b) For the second part I'm sure how to use the temperatures given to find the energy consumed

 

[learningphysics]

What is the temperature difference in a) ? and in b)?.

energy leakage is proportional to temperature difference... use ratios...

 

[mshah3]

delta t for a = 24-4 = 20

delta t for b = 27-4 = 23

correct?

so how do i use a ratio to get to the energy?

 

[mshah3]

never mind i figured out to use E/T = E/T

just wasnt thinkin

thanks