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A tiny body sits at the centre of a large evacuated hollow spherical shell whose walls are held at 0 K. At t = 0 the body is at 200 K. It cools to 100 K at time t1 and to 50 K at time t2. Treating both the body and the shell as ideal black bodies and taking the body's heat capacity to be temperature-independent, find the ratio t2/t1.

1. 7
2. 9
3. 3
4. 21/4

Correct answer: 9

Solution

Radiative cooling into a 0 K enclosure follows Stefan's law with no incoming radiation, so the temperature obeys an inverse-cube relation in time. The time to cool depends on the difference of 1/T³ between initial and final temperatures, which lets us compare the two cooling intervals.

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