Thermodynamics (heat loss problem)

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SUMMARY

The forum discussion centers on a thermodynamics problem involving heat loss from a house maintained at 20° C with an energy expenditure of 45 kWh over 4 hours. The average energy leakage through the walls was calculated to be 11,250 watts. The user encountered difficulty in determining the electricity consumption if the house temperature was increased to 23° C, mistakenly applying a proportionality assumption that led to an incorrect result of 51.75 kWh.

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snowsquirrel1
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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!
 
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snowsquirrel1 said:

(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.
 

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