Office Physics: Coffee Thermos

There are few worse feelings than when you come back to your coffee only to find out that it's luke warm. Sure you could microwave it, but something weird goes on there and makes the coffee less tasty than it would if it had never cooled in the first place (don't ask me why). Since I've never had a coffee maker at work, I've often solved this problem by putting my coffee in a thermos. They're wonderful inventions. They keep your coffee nice and hot for several hours if you have a good one. But how does it work?

It uses insulation. This is the exact same idea as when you put insulation in your attic. It's also the same idea as wearing ear muffs. Insulation is a barrier between a "hot reservoir" and a "cold reservoir." So when you put your coffee in the thermos, it is the hot reservoir and the air outside of the thermos is the cold reservoir.

When I say that insulation is a barrier, what I mean is that it slows down the transfer of heat. In the case of hot coffee, heat transfer is bad bad bad! I want my coffee to stay at the exact same perfect temperature until I've finished my last sip of coffee, gosh darn it! Sadly that's impossible. And sadly no thermos works perfectly. So if you leave coffee in a thermos long enough, it will eventually get to room temperature.

So why does heat have to transfer from a hot thing to a cold thing? It would make winter more enjoyable for me if all that cold air didn't suck all the heat out of my body. I think there are different ways to answer the question. You need to understand what temperature is first.

Temperature is (for our purposes) a measurement of how fast the molecules are moving around randomly. If the air around you is hot, the air molecules are moving around very rapidly, bouncing off one another in a random way. If the air around you is cold, then the air molecules are still bouncing around off one another randomly, but much slower.

So when your energetic warm skin molecules come into contact with the slow, cold air molecules, the energy is transferred to the air molecules, warming them up and cooling you down. Same idea as billiard balls. The energy in the cue ball is transferred to the other balls when it runs into them.

That's heat conduction, which is part of the reason your coffee gets cool. The coffee heats up the air it's in contact with. But the second form of heat transfer, called convection, is probably the most important reason your coffee gets cool.

Heat conducts more slowly when the temperature difference between the two reservoirs is small. So as your coffee heats up a particular group of air molecules, it has a harder and harder time dumping the heat into them. But the problem is that the air that's been heated up will get out of the way and make room for fresh, cool air to absorb the heat. So conduction and convection work together to cool down your coffee.

Air molecules are actually really bad at conducting heat, which is the same thing as saying that air is a good insulator. So it turns out that you could solve most of the problem by eliminating convection--to figure out a way to keep the air from moving around a whole lot. So for coffee thermoses, a metal shell is placed around the core so that there is a thin layer of air between the two metal cylinders. This keeps the air from moving around too much and slows down the heat transfer.

So that solves the problem. Now we can enjoy our hot coffee.