Thermodynamics (heat loss problem)

[snowsquirrel1]

During 4 hours one winter afternoon, when the outside temperature was 5° C, a house heated by electricity was kept at 20° C with the expenditure of 45 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)?
(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 23° C (77° F), how many kwh of electricity would have been consumed?



E=W+Q



I did part a pretty quickly (getting 11250W), but I'm stuck on part B. If the energy transfer is proportional to their temp. difference, I assumed that I could use a proportion to solve it.

so I tried: 23/20=X/45, so X=51.75. Unfortunately it was wrong, and I can't figure out what to do. Please help me!

 

[nasu]

(b) The rate at which energy is transferred between two systems due to a temperature difference is often proportional to their temperature difference.

See the underlined part above.

 

[baba89]

For part B, you are on the right track by using a proportion. However, you need to use the proportion to find the amount of energy consumed, not the temperature difference. The proportion should be set up as follows:

(23-5)/(20-5) = X/45

Solving for X, we get X = 51.75 kwh. This means that if the house temperature had been kept at 23° C, it would have consumed 51.75 kwh of electricity in 4 hours. This is an increase of 6.75 kwh compared to the original temperature of 20° C.