Discussion
If the temperature T of photon gas in equilibrium in a radiation cavity is doubled, the equilibrium number of photons will increase by the factor of :
Answer: C
The number of photons increases by a factor of 8.
The equilibrium photon number density in a cavity is obtained by integrating the Planck distribution:
\[ \begin{aligned} n &= \frac{2\zeta(3)}{\pi^{2}}\left(\frac{kT}{\hbar c}\right)^{3} \\ &\propto T^{3} \end{aligned} \]
Doubling T multiplies the number by \(2^{3} = 8\). The energy density goes as \(T^{4}\) and would rise 16 times; 2, 6 and 9 do not come from either law.
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