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Say I have a cup of broth with volume V1 and it's too hot to drink. I want to cool it down as quickly as possible.

  • the current temp of the cup is T1
  • I want to drink the cup when it cools to T2
  • I have a glass of water at volume V2 that is at temperature T3, which is less than T1, and I am willing to pour the entire glass of water with the cup of soup.

What is the optimal time to pour the glass of water into the cup of soup to cool it down? Perhaps we can assume a continuous pour over time, or a discrete one time pour, they might be two different solutions, I am not sure.

Is there some formula/function we can use to determine the optimal time?

The question is based around how the cooling of the cup is non-linear wrt to the temperature differential between T1 and T2.

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