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 $u=\frac{U}{V}\propto T^4$ 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:

• A

  $T\propto \frac{1}{R^3}$
• B

  $T\propto e^{-R}$
• C

  $T\propto e^{-3R}$
• Correct answer
  D

  $T\propto \frac{1}{R}$

Hence, the correct answer is option: 'D'.