Really easy but difficult problem with temps

1. Sep 5, 2015

korec123

1. The problem statement, all variables and given/known data
Hello,
I have got this question. At first sorry for some mistakes
We have 2 hot coffes and and milk with room temp. We have long distance to go with this coffes through the room with room temp :). Which coffe will have higher temp after going through the room : this mixed with milk at first or this mixed with milk after going through long room and why
Only the time of adding milk is diffrent.

3. The attempt at a solution
Im thinking about it so long and i still thinking that it wound be the same. If we mix it at first the coffe will lose less energy to the air in the room and if we mix after coffe will lose less temp to heat the milk

2. Sep 5, 2015

PeroK

Perhaps a good approach is to write down the assumptions about heat loss from coffee, milk and milk-coffee.

3. Sep 6, 2015

korec123

I was trying but still it doesnt give me anything. Can you write more or describe it?

4. Sep 6, 2015

PeroK

Let's take two different sets of assumptions. These are extreme cases to illusrate the point:

a) Assume that milk and milk-coffee lose heat very slowly, but that coffee on its own loses heat very quickly.

In this case, it's easy to see that you should add the milk immediately and it will stay warm.

b) Assume that coffee loses heat very slowly, but milk and milk-coffee loses heat very quickly.

In this case, it's easy to see that you should add the milk at the end.

So, there is clearly no answer unless you make some assumptions about the relative heat loss in each case.

The heat transfer between the coffee and the milk will depend on two things. Do you know what they are?

The heat loss to the air will depend on the cooling constant. What can you assume about the cooling constant in each case?

5. Sep 6, 2015

korec123

About heat loss to the air , of course if i add milk first the heat loss will be smaller. I dont really know about heat transfer beetween coffe and milk

6. Sep 6, 2015

PeroK

When you mix two substances, the heat transfer depends on:

1) The mass of each substance.
2) The specific heat capacity of each substance.

That is fairly elementary, I have to say.

To answer your problem properly, you have to use Newton's law of cooling and solve, or at least analyse, the resulting equations using your assumptions about the cooling constant in each case.

7. Sep 6, 2015

Staff: Mentor

Evaporation should dominate the heat loss, and this reduces significantly if you cool down the coffee a bit.

8. Sep 6, 2015

PeroK

That's probably the answer they are looking for, although most coffee containers have lids these days!

9. Sep 6, 2015

Staff: Mentor

Korec123:

If you really want to model this, as PeroK alluded to in post #6, we can help you do it, but you are going to have to participate. Interested?

Chet