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JEE Main & Advanced JEE Main Solved Paper-2015

  • 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 Solved Paper-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 :

    From given Informaiton \[P\propto u\]                                 \[\frac{T}{V}\propto {{T}^{4}}\] \[\frac{1}{V}\propto {{T}^{3}}\] \[{{T}^{3}}V=\]costant \[{{T}^{3}}{{R}^{3}}=\]costant TR= costant \[\]


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