consider a spherical shell of radius R at temparature T.  The black body radiation inside it can be considered as an ideal gas of photon with internal energy per unit volume u=u/V is directly proportional to T4 and pressure P=1/3×U/V .  If the shell now undergoes an adiabatic expansion the relation between T and  R is

Arun
25758 Points
2 years ago
Dear student

P = U/3V
nRT/V = U/3V

nRT/V = T4 /3

4/3 pi R^3 T^3 = constant

hence $T \alpha 1/R$

Hope it helps

Regards
Arun