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A solid copper cube and a solid copper sphere have the same mass and the same emissivity. They are heated to the same initial temperature and then left to cool under identical surroundings. Find the ratio of the cube's initial rate of temperature fall to that of the sphere.

1. (6/pi)^(1/3): 1 (about 1.24: 1)
2. 1: 1
3. 1: (6/pi)^(1/3) (about 1: 1.24)
4. (pi/6)^(1/3): 1 (about 0.81: 1)

Correct answer: (6/pi)^(1/3): 1 (about 1.24: 1)

Solution

Since mass and specific heat are equal, the cooling-rate ratio equals the surface-area ratio at equal volume; the cube has the larger area, giving (6/pi)^(1/3): 1, about 1.24: 1.

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