A cup of coffee anyone? (Newton's Law of Cooling)

peckywecky88

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It's that time of the term again when all exams are popping up! I'm just wondering if you'd be able to help me with this maths question that I'm a bit stuck on.

What we have to basically do is find out whether a cup of coffee will stay hotter longer when the milk is poured in first, or when it's poured in after the hot water. Our teacher isn't too fussy on which option we got out in the end, he is just interested in the steps we took to come to that conclusion.

Anyway, I have recorded the temperature over a period of time for each coffee ie. (milk in first, and milk in last). By using Newton's Law of Cooling (which we were required to use), I have found the equations for T(t) where T=temperature and t=time, for both the coffees.

I am now just wondering how do I show which coffee type decreases at a faster rate? Any help will be greatly appreciated.

Thanks for your time.
Chantelle.
 
Who pours water into a cup of coffee? Into a cup with a tea-bag, sure, but coffee...? :shock:

Eliz.
 
Newton's Law of Cooling (NLC) refers to a change in SURFACE temperature and the difference in temperature of a substance and its SURROUNDING environment. This would seem to suggest that AFTER you add and stir, NLC has nothing to do with it.

There are three elements to this problem:
1) Coffee - hot
2) Milk (or water?) - cold
3) Surrounding air - in between?

It seems the only difference in the two experiments it in the air. If you pour in the milk first, NLC suggests that the milk will warm up a bit and the air in the cup will cool down a bit. This MAY influence the initial temperature upon mixing. Which way? No clue.
 
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