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A solid copper sphere (density rho, specific heat c) of radius r, initially at 200 K, hangs in a chamber whose walls are at nearly 0 K. Treating the sphere as a black body, find the time for its temperature to fall to 100 K.

1.7 rho c
2.7 rho c
3.3 rho c
4.2 rho c

Correct answer: 1.7 rho c

Solution

m c dT/dt = -sigma A T⁴ leads to t = (rho r c/(9 sigma))[1/100³ - 1/200³] ~ 1.7 rho c (per unit r).

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