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 colume `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. `Tprope^(-3R)`
B. `Tprop(1)/(R )`
C. `Tprop(1)/(R^(3))`
D. `Tprope^(-R)`

Answer

B

Explanation

`P=(1)/(3)((U)/(V))=1/3kT^(4)` . . . (i)
`PV=muRT` . . . (ii)
`(muRT)/(V)=(1)/(3)kT^(4)`
`rArrVpropT^(-3)`
`Rprop(1)/(T)`.
So correct is (b)