Consider a spherical shell of radius R at temperature T . black body radiation inside it can be cons

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11.Thermodynamics

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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$E=$ $\frac{U}{V} \propto {T^4}$ 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

$T \propto {e^{ - 3R}}\;\;\;\;\;\;\;\;\;\;\;\;$

B

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

C

$\;T \propto \frac{1}{{{R^3}}}$

D

$\;T \propto {e^{ - R}}$

(JEE MAIN-2015)

Solution

$As,\,P = \frac{1}{3}\left( {\frac{U}{V}} \right)$

$But\frac{U}{V} = K{T^4}$

$So,P = \frac{1}{3}K{T^4}$

$or\,\frac{{uRT}}{V} = \frac{1}{3}K{T^4}\,\,\,\left[ {As\,PV = u\,RT} \right]$

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

$Therfore,T \propto \frac{1}{R}$

Standard 11

Physics

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