Discussion Forum



1)

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


A) $T\propto e^{-R}$

B) $T\propto e^{-3R}$

C) $T\propto \frac{1}{R}$

D) $T\propto \frac{1}{R^{3}}$

Answer:

Option C

Explanation:

According to question

 $p=\frac{1}{3}\left(\frac{U}{V}\right)$

    $\Rightarrow$ $\frac{nRT}{V}=\frac{1}{3}\left(\frac{U}{V}\right)$                 [ $\because$  pV=nRT]

   or    $\frac{nRT}{V}\propto\frac{1}{3}T^{4}$

   or     $VT^{3}$  = constant

   or    $\frac{4}{3}\pi R^{3} T^{3}= constant$

  or      TR= constant

   $\Rightarrow$    $T\propto\frac{1}{R}$