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/V prop T^(4)` and pressure `p = 1/3(U/V)`. If the shell now undergoes an adiabatic expansion the relation between T and R is :

Options

A. `T prop s^(-R)`
B. `T prop S^(-3 R)`
C. ` T prop 1/R`
D. `T prop 1/R^3`

Answer

C

Explanation

According to equestion,
`p=(1)/(3)(U/V) implies (nRT)/(V)=(1)/(3)(U/V)" "[:. Pv=nRT]`
or `(nRT)/(V) propto (1)/(3)T_4 " or " VT^3=` constant or `(4)/(3)pi R^3T^3`= constant or TR= constant `implies T propto (1)/(R )`.