Jun 10, 2012

In order to answer that we need a formula that describes the surface area of an object, how much energy it has, and what it’s thermodynamic temperature, or ‘absolute’ temperature. In simpler terms… how big its surface is, and how cool it can get, in how much time. Since coffee is mostly water, we’ll just use plain water in our calculation.

So, say we have a liter of water, and 100º C. The surface area of the thermos (or just any container, it doesn’t need to be insulated, because we already have the vacuum of space) is about 50cm square. We know it takes about 4180 joules to heat a liter of water up to 1º C. So we’ll just reverse that to -4180 Joules (because we’re cooling) and multiply by 100 because we’re going from the boiling point down to 0º C. Giving us -418 kJ of energy, or 418000 Joules. S

tefan Boltzmann came up with a formula that handles all those variables so we plug all that into Stefan’s Law and we come up with an average loss of about 31 joules/second. So your coffee would go from about 100º C to close to 0º C in about 3 or 4 hours. But there is more than meets the eye with this. At the end, the cooling slows down considerably as you approach 0º C, so it would take an additional 7-8 hours to freeze solid.