Carnot Engines in air conditioning

[tralblaz]

Homework Statement

Under many conditions, the rate at which heat enters as air conditioned building on a hot summer day is proportional to the difference in the temperature between the inside and outside, Th-Tc. (If the heat enters entirley by conduction,this statement will certainly be true. Radiation from the direct sunlight would be an exception.) Show that, under these condtions, the cost of air condtioning should be roughly proportional to the square of the temperature difference.

Homework Equations

use what is known about COP (coefficent of performance)

COP=Q/W

The Attempt at a Solution

I am thoroughly lost in how to approach this problem. I know that the COP is involved, but I have no idea where or how to start.

Could someone please get me started? Thanks

 

[tim_lou]

these are give away hints... but anyway.

1. consider the ideal COP, what is its relation to the temperature difference?

2. consider the work input (relating to cost of electricity) and its relationship between COP.

3. consider heat entering the house... if the air conditioner is "combating" this heat flow, how much heat must it take out (in relation to difference of temperature)?

4. relate 1, 2 and 3. So, what is cost of electricity proportional to?