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Coffee temperature and time of milk addition

  1. Dec 7, 2004 #1
    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. jcsd
  3. Dec 7, 2004 #2

    Doc Al

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    Staff: Mentor

    Right, because the rate of cooling is proportional to the temperature difference between the coffee surface and the surroundings (ignoring convection).
  4. Dec 8, 2004 #3
    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.

  5. Dec 8, 2004 #4
    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.
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