Really easy but difficult problem with temps

[korec123]

Homework Statement

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.

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

Please help me

 

[PeroK]

Homework Statement

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.

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

Please help me

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

 

[korec123]

I was trying but still it doesn't give me anything. Can you write more or describe it?

 

[PeroK]

I was trying but still it doesn't give me anything. Can you write more or describe it?

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?

 

[korec123]

About heat loss to the air , of course if i add milk first the heat loss will be smaller. I don't really know about heat transfer beetween coffe and milk

 

[PeroK]

About heat loss to the air , of course if i add milk first the heat loss will be smaller. I don't really know about heat transfer beetween coffe and milk

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.

 

[mfb]

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

 

[PeroK]

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

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

 

[Chestermiller]

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