# Coffee temperature and time of milk addition

1. Dec 7, 2004

### asfd

Youri takes a coffee and adds some milk at room temperature to it.

Saku takes a black coffee and adds the same amount of milk but 10 minutes later.

Which coffee is the hotter and why?

I think that Youri's coffee would be hotter since the temperature variation is proportional to the temperature difference hence it'll cool down slower.

2. Dec 7, 2004

### Staff: Mentor

Right, because the rate of cooling is proportional to the temperature difference between the coffee surface and the surroundings (ignoring convection).

3. Dec 8, 2004

### kuba

I think that the real answer is: it depends.

If you add lots of milk, then for sure the change of rate of cooling due to lower absolute temperature will dominate.

But if you add just a bit of milk to change the color of coffee, you might actually get it to cool slightly slower. That depends of course how much heat (percentage-wise) is lost through radiation from cup's walls, how much is lost through conduction to the table, how much goes out via convection, and how much is radiated from the top surface :) If there's a significant amount of heat lost due to radiation from the top surface, then making the coffee lighter will decrease radiated heat flux.

Cheers

4. Dec 8, 2004

### KingNothing

I'd say if Youri's cofee was a few degrees less than it's boiling point, and Saku's was frozen at about 5 degrees kelvin, that Youri's would be hotter.