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Consider a spherical shell of radius \( R \) at temperature \( T \). The black body radiation inside it can be considered as an
\( \mathrm{P} \) ideal gas of photons with internal energy per unit volume

W \( u=\frac{U}{V} \propto T^{4} \) and pressure \( P=\frac{1}{3}\left(\frac{U}{V}\right) \). If the shell now undergoes an adiabatic expansion the relation between \( T \) and \( R \) is
[JEE (Main) 2015]
(a) \( T \propto e^{-R} \)
(b) \( T \propto e^{-3 R} \)
(c) \( T \propto \frac{1}{R} \)
(d) \( T \propto \frac{1}{R^{3}} \)
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