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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Critical Thinking

  • question_answer
    A monoatomic 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 lengths of the gas column before and after expansion respectively, then \[{{T}_{1}}/{{T}_{2}}\] is given by [IIT-JEE (Screening) 2000]

    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 :

               \[{{T}_{1}}{{V}_{1}}^{\gamma -1}={{T}_{2}}{{V}_{2}}^{\gamma -1}\]\[\Rightarrow \frac{{{T}_{1}}}{{{T}_{2}}}={{\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)}^{\,\gamma -1}}\]\[={{\left( \frac{{{L}_{2}}A}{{{L}_{1}}A} \right)}^{\,\frac{5}{3}-1}}={{\left( \frac{{{L}_{2}}}{{{L}_{1}}} \right)}^{\,\frac{2}{3}}}\]


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