MadSci Network: Physics

Re: Coffee with milk cools more slowly than coffee without milk

Date: Tue Sep 19 11:23:21 2000
Posted By: Andreas Kieron P. Bender, Grad student, Chemistry, Trinity College Dublin
Area of science: Physics
ID: 968168628.Ph

Hi Tommy,

actually your observation contradicts the laws as people think they're right! I want to repeat what you observed - that your glass of coffee is warmer if you wait ten minutes, then add the milk - than if you add the milk, and then wait ten minutes.

There is a simple reason why it should be the other way 'round. Every body of a given heat and a given material (here it's pretty close to pure water, at least nearly) is capable of saving a certain amount of energy as heat. The amount of energy is the product of:

E= m * T * cp where E is the heat energy, m the mass and T the temperature; cp is the heat capacity if the pressure is constant.

The other thing you have to know is, that, if you mix two liquids, the resulting temperature will be

Tnew=T1 * p1 + T2 * p2 ... where T is the temperature of the substance (water, milk ...) and p is the percentage (0.9, 0.1 or so in those cases).

There is one more thing you have to know - if a body is hot, the so-called heat gradient is greater what means that more energy will be transferred at the same time. That's why ice is quite cold (sucks a lot of energy from your skin) than cool water.

So, all you have to think now is: You start at the same starting point. A is mixed, so the mixture is warm, not hot anymore. B is still unmixed - means that the hot coffee is loosing more energy to the environment. After 10 minutes (in B) you put the milk in the coffee - but that "coffee B" already lost much more energy than coffee A because it was hotter all the time before!

I hope that helped,

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