Solution to 1992 Problem 14

Recall the Stefan-Boltzmann formula:
\begin{align*}\frac{\Delta Q}{\Delta t} = \sigma A T^4\end{align*}
Here \Delta Q/\Delta t is the rate at which energy is radiated from the blackbody, \sigma is the Stefan-Boltzmann constant, A is the area of the blackbody, and T is the temperature of the blackbody in ^{\circ}\mbox{K}. So, doubling T increases the power radiated by the blackbody by a factor of 16. Assuming the heat capacity of the water is constant over the relevant temperature range, this means that the temperature would increase 8 ^{\circ}\mbox{K} instead of 0.5 ^{\circ}\mbox{K}. Therefore, answer (C) is correct.

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