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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Self Evaluation Test - Thermodynamics

  • question_answer
    A monatomic ideal gas, initially at temperature \[{{T}_{1}}\] is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \[{{T}_{2}}\,\] by releasing the piston suddenly. If \[{{L}_{1}}\] and \[{{L}_{2}}\] are the length of the gas column before and after expansion respectively, then \[\frac{{{T}_{1}}}{{{T}_{2}}}\] is given by

    A) \[{{\left( \frac{{{L}_{1}}}{{{L}_{2}}} \right)}^{2/3}}\]

    B) \[\frac{{{L}_{1}}}{{{L}_{2}}}\]

    C) \[\frac{{{L}_{2}}}{{{L}_{1}}}\]

    D) \[{{\left( \frac{{{L}_{2}}}{{{L}_{1}}} \right)}^{2/3}}\]

    Correct Answer: D

    Solution :

    [d] Here \[T{{V}^{^{\gamma -1}}}=\text{constant}\] As \[\gamma =\frac{5}{3},\] hence \[T{{V}^{2/3}}=\text{constant}\] Now\[{{T}_{1}}L_{1}^{2/3}={{T}_{2}}L_{2}^{2/3}\text{      (}\therefore V\propto L\text{)}\]; Hence, \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left( \frac{{{L}_{2}}}{{{L}_{1}}} \right)}^{2/3}}\]


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