Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be consider as an ideal gas of photons with internal energy per unit volume $u= \large\frac{U}{V}$$ \alpha T^4$ and pressure $P= \large\frac{1}{3} \bigg( \frac{U}{V} \bigg) $. If the shell now undergoes an adiabatic expansion the relation between T and R is :

Question

$\begin{array}{1 1} T \alpha \frac{1}{R^3} \\ T \alpha e^{-R} \\ T \alpha e^{-3R} \\ T \alpha \frac{1}{R} \end{array} $