Expert: Abe Mantell - 1/5/2008

Question
One of Julius Sumner Millar's physics questions was:
You have made a cup of coffee and the doorbell rings. To ensure you have the hottest coffee when you return, should you add the milk before answering the door, or should you add the milk afterwards. His reasoning was that the coffee lost temperature at a rate proportional to its temp above ambient. Therefore by adding the milk immediately you would have the hottest coffee by virtue of the reduced cooling rate. I have attempted to prove this mathematically but my calcs show that the temp ends up the same no matter when the milk is added. Adding the milk before results in a greater immediate drop in temp than adding milk after. This exactly cancels the greater cooling rate before the milk is added.
Am I wrong?

My derived expression for temp T at any time t is
T = 20 + 60exp -0.023t
assuming ambient = 20
initial coffee temp = 80
coffee cools to 50 in 30 minutes.


Answer
Interesting question!

Check these link for some answers.  The first link "does
the math," the second one "does the experiment"!
http://www.bottledcity.com/2007/02/26/when-to-add-milk-to-coffee/
http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/-0c2ee7e805/

Abe