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. `Tae^(-R)`
B. `Talphae^(-3)R`
C. `T=(1)/(R)`
D. `T alpha(1)/(R^(3))`

Answer

C

Explanation

`P=(1)/(3)((U)/(V))=(1)/(3)kT^(4)`
PV=mRT
`(muRT)/(V)=(1)/(3)kT^(4)`
`VpropT^(3)`
`Rprop(1)/(T)`