2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    An ideal monatomic gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure \[{{P}_{i}}.\] If the same gas is expanded adiabatically to a volume 2V, the final pressure is \[{{P}_{a}}.\]The ratio \[\frac{{{P}_{a}}}{{{P}_{i}}}\]is.   JEE Main Online Paper (Held On 26-May-2012)  

    A) \[{{2}^{-1/3}}\]                                

    B) \[{{2}^{1/3}}\]

    C) \[{{2}^{2/3}}\]                                  

    D) \[{{2}^{-2/3}}\]

    Correct Answer: D

    Solution :

    For isothermal process: \[PV={{P}_{i}}2V\] \[P=2{{P}_{i}}\] ...(i) For adiabatic process \[P{{V}^{\gamma }}={{P}_{a}}{{(2V)}^{\gamma }}\] (\[\because \] for monatomic gas \[\gamma =5/3\]) or,\[2{{P}_{i}}{{V}^{\frac{5}{3}}}={{P}_{a}}{{(2V)}^{\frac{5}{3}}}\]                             [From (i)] \[\Rightarrow \]\[\frac{{{P}_{a}}}{{{P}_{i}}}=\frac{2}{{{2}^{\frac{5}{3}}}}\]\[\Rightarrow \]\[\frac{{{P}_{a}}}{{{P}_{i}}}={{2}^{\frac{-2}{3}}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner