2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Thermodynamical Processes

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

  • question_answer
    A monoatomic ideal gas goes through a process \[p={{p}_{0}}-\alpha V\] where \[{{p}_{0}}\] and \[\alpha \] are positive constants and V is its volume. At what volume will the entropy of gas be maximum?

    A) \[\frac{5{{p}_{0}}}{6\alpha }\]

    B) \[\frac{{{p}_{0}}}{2\alpha }\]

    C) \[\frac{{{p}_{0}}}{4\alpha }\]   

    D) \[\frac{5{{p}_{0}}}{8\alpha }\]

    Correct Answer: D

    Solution :

    [d] \[ds=n{{C}_{v}}dT+PdV=0\] \[nR\frac{dT}{dV}+\left( {{p}_{0}}-\alpha V \right)=0\] \[pV=nRT\] \[{{p}_{0}}V-\alpha {{V}^{2}}=nRT\] \[{{p}_{0}}-2\alpha V=nR\frac{dT}{dV}\] \[-\left( {{p}_{0}}-\alpha V \right)\left( \gamma -1 \right)={{p}_{0}}-2\alpha V\] \[-{{p}_{0}}(\gamma -1)+\alpha (\gamma -1)\,V={{p}_{0}}-2\alpha V\] \[{{p}_{0}}V=\alpha V(\gamma +1)\]  \[V=\frac{{{p}_{0}}\gamma }{\alpha \left( \gamma +1 \right)}\] \[V=\frac{{{p}_{0}}\times \frac{5}{3}}{\alpha \left( \frac{5}{3}+1 \right)}=\frac{5{{p}_{0}}}{8\alpha }\]


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