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 prop1/R`
B. `T prop1/R^3`
C. `T prop e^-R`
D. `T prop e^(-3R)`

Answer

A

Explanation

(a) As, `P=1/3(U/V)`
But `U/V=KT^4`
So, `P=1/3KT^4`
or `(uRT)/V=1/3KT^4 [As PV=uRT]`
`4/3piR^3T^3=constant`
Therefore, `T prop1/R`