Newton's Law of Cooling model

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Hey Folks,


I was showing my students Newton's Law of cooling (precalc class) and one of my students pointed out that this doesn't really model the cooling of an object, he said that he had recently learned in chemistry that the temperature of the object that is cooling actually dips down below the "room temperature" and then asymptotically approaches it from below.

I admitted ignorance, its not my area but am curious to learn about this, if this is the chase. So my question: Given a cup of coffee at 110 degrees (for example) in a room at 65 degrees will the coffee ever have a temperature lower than 65 degrees.

Thanks,

Kevin
 

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Tide
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That's a little tricky. The problem is that the temperature of the liquid isn't really uniform until thermal equilibrium is achieved. What the student left out of his/her explanation is that evaporative cooling is taking place at the exposed surface of the coffee thereby cooling SOME of the liquid to below room temperature (i.e. the hottest molecules leave by evaporation leaving cooler molecules behind). But the remaining molecules are interacting with the hotter ones below it.

The details of how a liquid undergoing evaporation and with nonuniform temperature throughout its volume approaches equilibrium is complicated. Newton's Law of cooling doesn't account for those details but often provides a decent approximation.
 

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