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Consider a spherical shell of radius \( \mathrm{R} \) at temperature \( \mathrm{T} \). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume \( \mathrm{u}=\frac{\mathrm{U}}{\mathrm{V}} \propto \mathrm{T}^{4} \) and pressure
\( \mathrm{P} \) \( \mathrm{P}=\frac{1}{3}\left(\frac{\mathrm{U}}{\mathrm{V}}\right) \). If the shell now undergoes an adiabatic expansion the relation between \( \mathrm{T} \) and \( \mathrm{R} \) is :
(A) \( \mathrm{T} \propto \frac{1}{\mathrm{R}} \)
(B) \( \mathrm{T} \propto \frac{1}{\mathrm{R}^{3}} \)
(C) \( \mathrm{T} \propto \mathrm{e}^{-\mathrm{R}} \)
(D) \( \mathrm{T} \propto \mathrm{e}^{-3 R} \)
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