Discussion
The temperature T of a blackbody enclosure is doubled, then the total number of photons inside the enclosure increases by a factor of :
Answer: C
The number of photons increases by a factor of 8.
Integrating the Planck distribution over all frequencies gives the photon number density in a blackbody cavity:
\[ \begin{aligned} n &= \frac{2\zeta(3)}{\pi^{2}}\left(\frac{k_{B}T}{\hbar c}\right)^{3} \\ &\propto T^{3} \end{aligned} \]
Doubling T multiplies n by \(2^{3} = 8\).
The factor 16 is the Stefan-Boltzmann result for the energy density, which goes as \(T^{4}\): the photons become both more numerous and more energetic on average. Factors of 2 and 4 would correspond to linear and quadratic dependences that do not apply to blackbody radiation.
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