Heat and Thermodynamics

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