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So I was in Canada this past week, and I began to wonder, "How much warmer is 10 degrees than 5 degrees?" The obvious (and uninteresting answer) is 5 degrees, but I'm thinking in terms of a rate of change, or a comparison. So one might be tempted to say that it is twice as warm, but this is clearly wrong in terms of the heat (Kinetic Energy) present in the atmosphere.

My next thought was: since absolute zero is around -273 Celcius, that means that at 5°C you have enough heat to raise the temperature 278° (from absolute zero), as compared to 283° at 15°C. That means it's only about (5/278)*100 percent warmer- a rather modest increase.

But then I got to wondering if heat works like that. Is heat a linear representation of the Kinetic Energy present in a system? Or is it logarithmic, exponential, etc.?

In other words: Is the amount of heat need to go from 1°K to 2°K the SAME as the amount of heat required to go from say, 2001°K to 2002°K?

Sorry if this is a long winded question- I just wanted to explain myself as clearly as possible. Thanks in advance for your help- I hope that you find this question interesting. My office-mates and I have had a great time trying to figure out the answer, but for all we know that is a trivial old chestnut of a question in the Physics community