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Prunestand OP t1_iu9k2dz wrote

A simulation of a cooling cup of coffee with the following parameters used:

Constants Value
Room temp T0=20 °C
Initial coffee temp T1=95 °C
Milk temp Tm=6 °C
Share of milk b=0.2
Cooling constant k=0.09 per minute

Plotted with Python.

My previous graph had a sign error in the code generating it, and I therefore deleted it. I also think people missed the point with the graph, so I'll add it here. Suppose you want your coffee after, say, 10 minutes. What will make it the coolest: adding the milk directly or wait until the end? The answer is to wait until the very end; that way it will be the coolest.

The reverse is true as well, pour the milk into the coffee at the very beginning if you want the coffee to be as warm as possible.

The answer is kind of obvious when you realize that the cup of coffee dissipates more heat the larger the temperature difference is, but the point of the graph is to illustrate this fact.

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StrangerAttractor t1_iu9ma8c wrote

The xkcd style is nice. Also since here mostly the qualitative result matters, it's not a problem that it isn't that precise.

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Prunestand OP t1_iu9mpy7 wrote

> Also since here mostly the qualitative result matters, it's not a problem that it isn't that precise.

Yeah, I agree with this. The graph is there to make an illustrative point. The exact numbers will depend on the volume of the coffee, the size, shape and material of the mug, the material of the table the mug stands on and various other factors.

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