It's day two of my training course, and as I contemplate my mug of decaf, I am suddenly flashing back to a question that was rumored to be part of the chemical engineering qualifying exam in my chemistry graduate program. As it's an intriguing problem, I thought I'd share it here:
In the dead of winter, a professor sends his grad student out into the cold to fetch him a hot beverage from the cafe. "Coffee with two creams, and make sure it's HOT when it gets to me!" the professor barks.
Shivering from fear as much as cold, the grad student procures a 12-ounce styrofoam cup of hot coffee and two little containers (maybe 20 mL each) of half and half at the cafe. To maximize the temperature of the coffee when it is delivered to the prof, should he add the half and half to the coffee before he walks it through the cold or after?
Feel free to work together on this problem, and please show your work in the comments.