JEE Main & Advanced Physics Thermodynamical Processes Question Bank Topic Test - Thermodynamical Processes

  • question_answer
    A gas undergoes a process in which its pressure p and volume V are related as \[V{{p}^{n}}=\] constant the bulk modulus for the gas in the process is

    A) np

    B) \[{{p}^{1/n}}\]

    C) \[\frac{p}{n}\]

    D) \[{{p}^{n}}\]  

    Correct Answer: C

    Solution :

    \[V{{p}^{n}}=\,(V\,+\Delta V)\,{{(p+\,\Delta p)}^{n}}\]
    \[=V{{p}^{n}}\,\left( 1+\,\frac{\Delta V}{V} \right)\,\,\left( 1+\,n\,\frac{\Delta p}{p} \right)\]
    \[1=\,1+\frac{\Delta V}{V}+\,n\frac{\Delta p}{p}+\,\frac{n\,\Delta V}{V}\,\,.\,\frac{\Delta p}{p}\]
    \[\frac{\Delta V}{V}=-n\,\frac{\Delta p}{p}\]
    \[\therefore \]    \[k=\frac{-\Delta p}{\Delta V/V}\,\,=\,\frac{p}{n}\]

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