question_answer

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\[u=\frac{U}{V}\propto {{T}^{4}}\]and pressure\[p=\frac{1}{3}\left( \frac{U}{V} \right).\]If the shell now undergoes an adiabatic expansion the relation between T and R is:                                                            [JEE MAIN 2015]

A)  \[T\propto \frac{1}{R}\]

B)       \[T\propto \frac{1}{{{R}^{3}}}\]

C)  \[T\propto {{e}^{-R}}\]           

D)       \[T\propto {{e}^{-3R}}\]

Correct Answer: A

Solution :

[a] From given Information

constant

constant

TR= constant