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

Answer

A

Explanation

`P= (1)/(3)((U)/(V))`
`P alpha T^(4) "using" PV = nRT`
`(1)/(V) alpha T^(3)`
`implies T alpha(1)/(R)`