Does temperature diffuse between two objects at a constant rate or does the difference in temperature determine the rate?
For example, you place two cans of coke in a 35 degree refrigerator. One can is 95 degrees and the other is 40 degrees. Will their temperatures lower at the same rate or will the hotter can diffuse more rapidly?
In: Physics
There are two parts in this: Energy and Temperature.
The rate of cooling depends on the rate of energy flow, the rate of energy flow depends on the temperature difference and the temperature difference depends on the temperature.
The rate at which the energy flows is roughly linearly propotional to the temperature difference between the object and its surrounding.
So doubling the temperature difference doubles the flow of energy. (this doesn’t hold if the temperature is very high. Blackbody radiation grows at T^4 but that is negligble at normal temperatures).
Note that this all needs to be done with kelvins. 35 F ≈ 275 K ≈ 2 C, 40 F ≈ 278 K ≈ 5 C, 96 F ≈ 308 K ≈35 C.
Energy would flow out of 90 F coke about 11 times faster than out of 40 F coke. ( 308 – 275 ) / ( 278 – 275 ) = 11
But the tricky thing is that is only the single moment. The hotter coke would cool down faster than the cooler coke. And so the temperature difference between them would go smaller. And the difference in rate of cooling would also go smaller. I am not going to go into details on math of this. Wikipedia has more details https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling
But I happen to have some code for plotting the results for this kind of thing. The results aren’t exact but they should be decently close to reality.
Yellow line is the temperature of the 35 C (96 F) coke and purple line is the temperature of 5 C (40 F) coke, enviroment is at 2 C (35 F). (numbers are rounded. The time axis may be scaled wrong)
You can see that the hot coke cools down greatly while the cooler coke barely cools down at all at the beginning. But as the hot coke cools down its rate of cooling down also slows down.
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