For the assignment in TMA4101 Mathematics 1, I picked a problem I actually have. The best beer is as cold as it can be without freezing. A Dahls pilsner freezes at about −2 °C, so I set the target at −1 °C. My fridge is set to 3 °C and my freezer to −21 °C.
Newton’s law of cooling gives the beer’s temperature over time, and solving it for time tells you how long to leave it in the freezer. The catch is the cooling constant α. To find it you’d have to time how long the beer takes to reach −1 °C, which risks freezing it.
The way around it is a shorter, safer measurement:
- The beer actually started at 5.0 °C, and the freezer held −22.2 °C (my thermometer disagreed with the dials).
- After 10 minutes with a thermometer in the can, the beer was at 1.7 °C. That gives α.
- The model then predicts 19.2 minutes to reach −1 °C.
- Measured: almost exactly 20 minutes.
Out of curiosity I left it in to see when it would actually freeze. About 26 minutes.