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