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

  • question_answer
    A gas expands with temperature according to the relation \[V=k{{T}^{2/3}}\]. Calculate work done when the temperature changes by 60 K?

    A) 10 R    

    B) 30 R

    C) 40 R    

    D) 20 R

    Correct Answer: C

    Solution :

    [c]\[dW=\,pdV=\,\frac{RT}{V}dV\]  …. (i)
    As,  \[V=\,k{{T}^{2/3}},\,dV=\,k\frac{2}{3}\,\,{{T}^{-2/3}}\,\,dT\]
    From Eq. (i), \[W=\int_{{{T}_{1}}}^{{{T}_{2}}}{RT}\,\frac{dV}{V}=\int_{{{T}_{1}}}^{{{T}_{2}}}{RT\,\frac{2}{3}\,\,\frac{dT}{T}}\]
    \[=\frac{2}{3}\,R\times \,60\,=\,40R\]

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