Interesting Heating and Cooling topics?

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AHUGEMUSHROOM
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I have to present an investigation on a topic that is related to healing and cooling. In class we're studying kinetic theory, ideal gas laws, heat, temperature, specific capacity, change of state, boiling and evaporation, energy conservation and degradation, and the transfer of heat.

Are there any interesting topics relating to the above?

I was thinking of presenting an investigation on "Heat Death of the Universe". Would this be relevant to the above areas of interest?

Thanks
 
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If you can solve some PDEs, try solving the problem that lead to Fourier's discovery of the famous series named after him.
Essentially, let's say we have a square metal sheet with uniform qualities, and we heat one side proportional to the distance from an adjacent edge on the sheet, how would the heat spread?
 
How about modeling the efficiency of a a heat pump/air conditioner on an insulated house as a function of average daily temperature over a year. This covers just about all of your topics - heating, cooling, ideal gas, specific capacity, boiling, evaporation, conservation of energy , etc.
 
Water injection for internal combustion engines.