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I'm need to understand the following: to keep the room at confortable temperature (70 degree, for example), how does the amount of energy consumed by the AC grow as the outside air temperature rises in the summer over the same length of time (a day, say)? Is it more or less linear? quadratic? exponential? or anything else?

I posted the same question on another StackExchange site, but I figured that physicist may provide more help because it seems to me that it is related to both heat conduction and the working mechanism of AC.

Thanks.

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Without getting too complicated I'd say it's linear.

Two bodies in contact exchange heat at a rate that's proportional to the temperature difference between them. The rate of heat transfer in with an outside temperature of 80 degrees will be twice the rate at 75 degrees (assuming your 70-degree room temperature).

Your AC needs to pump this heat out as fast as it comes in to maintain 70 degrees, so it will need to do it twice as fast when it's 80 degrees outsite than when it's 75 degrees.

This is a linear relationship.

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Thanks! It makse sense. –  GWu Apr 13 '11 at 22:12
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An ideal AC is a Carnot machine running backward. So it does not work really linearly. Some practical things like friction make it definitely nonlinear. –  Georg Apr 13 '11 at 22:20
    
@Georg: Good point. But isn't the efficiency difference only about 5% over the range of temperatures we're talking about? –  John Apr 13 '11 at 22:36
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If the AC had perfect carnot efficiency, it would be quadratic, i.e. the energy cost to move a unit of heat against a temperature increase, is proportional to that increase. Because of friction and heat loses etc. it is most likely close to linear at least for small differences in temperature. –  Omega Centauri Apr 13 '11 at 22:38
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Jerry, I was making the assumption that deltaT is much smaller than the absolute temperature. I.E. throw out the next higher order term in the expansion. –  Omega Centauri Apr 14 '11 at 4:19

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