# A practical question about thermodynamics

1. Dec 20, 2008

### KFC

Today, I read a short essay from a magazine about how to preserve the coffee as hot as possible in a short time (if you don't want to drink it right away) by adding the cream in to it as soon as possible. It reads: if you add the cream soon, some amount of heat being transferred to the cream so the temperature b/w the coffee and air will be decreased, this is also make the convection process slower. I am thinking ... what about the sugar? In this sense, should I also add the sugar asap (without stirring of course)? And of course, if I use a black cup instead of light-color one, it will also help to preserve the temperature a bit due to radiation, right? What about the color of cream, will dark one better than light one?

2. Dec 20, 2008

### mgb_phys

Adding the cream will cool the coffee.
The rate of cooling is proportional to the temperature difference between the coffee and surroundings.
So the coffee cools fastest when it is hottest, as it cools the temperature difference is less and the cooling is slower. That might be what you are thinking about by adding the cream first.

To keep it hot the longest you need to reduce the mecahnisms for heat loss.
Conduction - that's why you use a styrofoam cup.
Radiation - probably not a major factor at these temperatures, but a shiny cup will help.
Convection - the hot coffee is at the top, not much you can do about this except put the lid on which stops hot air escaping.

3. Dec 20, 2008

### KFC

Good explanation. Thanks a lot. From your clue, will we use a cup with dark color is better? What about the color the cream being added? I discussed this problem with my friend, he said we should also add the sugar soon (the reason is just like that of adding cream), but I think we shouldn't because sugar will absorb too much heat to dissolve, it will low the temperature too much. What do you think?

4. Dec 21, 2008

### mgb_phys

Sugar will absorb some heat to dissolve, the heat of solution of sucrose is - 16.1 J/g
A teaspoon of sugar will take in about 80J, it takes 4200J to cool a Kg of water by 1degC
So this will cool a large cup of coffee by about 0.05deg C

5. Dec 21, 2008

### Staff: Mentor

Regarding color, no, dark is worse because dark colors radiate heat more efficiently than light ones. This is why good coffee thermoses are polished metal on the inside (plus glass and a vacuum): to block radiation.