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 propT^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 e^(-R)`
B. `T prop e^(-3R)`
C. `T prop (1)/(R )`
D. `T prop (1)/(R^(3))`

Answer

C

Explanation

`p = (1)/(3)(U)/(V)`
`(nRT)/(V) prop (1)/(3)T^(4)`
`VT^(3) = const`
`(4)/(3)piR^(3)T^(3) = const`
`T R = const`
`T prop (1)/(R )`