Consider two friends who meet at a coffee shop. Both order hot coffee and both w
ID: 1487396 • Letter: C
Question
Consider two friends who meet at a coffee shop. Both order hot coffee and both want to add some almond-flavored creamer (which is at room temperature) to their hot coffee. They know that they will be so busy talking that they probably will not drink their coffees for half an hour, but they would like the coffee to still be as hot as possible when they drink it. One friend decides to add the creamer to her coffee immediately, figuring that, if she cools the coffee right away, it will lose heat at a slower rate during the half-hour of chatting, and thus will be hotter in the end. The other friend decides to wait until just before she drinks the coffee to add the creamer, figuring that adding cool creamer to cooler coffee will make less of a temperature change in the coffee, and thus it will be hotter in the end. Which friend is right? Which coffee will be hotter when they quit talking and start drinking? Clearly and completely explain the logic behind your answer.
Explanation / Answer
Resons:
1) black coffee is darker, so it emits heat faster than lighter-colored coffee with cream.
2) Stefan-Boltzmann law, which says that hotter surfaces radiate heat faster.
3) More viscous liquids — like coffee with cream added — evaporate more slowly, so there is slower heat loss through evaporation.
The first one is right because he pour cream in cup #1 and the coffee drops in temperature immediately. But the rate at which it loses heat also drops. Meanwhile, the hotter black coffee in cup #2 cools so rapidly that within few minutes the two coffees are at about the same temperature. But he still haven't added the cream to coffee #2! When he do, it cools even more; cup #1 is now the hotter of the two.