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
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
- [JEE MAIN 2015]
- A
$T \propto {e^{ - 3R}}\;\;\;\;\;\;\;\;\;\;\;\;$
- B
$\;T \propto \frac{1}{R}$
- C
$\;T \propto \frac{1}{{{R^3}}}$
- D
$\;T \propto {e^{ - R}}$
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- [JEE MAIN 2024]
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