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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is(\[\frac{{{C}_{P}}}{{{C}_{V}}}=\gamma ,\]universal gas constant =R)

    A)  \[\frac{pV}{\gamma }\]               

    B)                         \[\frac{pV}{(2\gamma -1)}\]

    C)  \[\frac{pV}{2(\gamma -1)}\]     

    D)         \[\frac{R}{(\gamma -1)}\]

    E)  \[\frac{pV}{(\gamma -1)}\]

    Correct Answer: E

    Solution :

    In case of gases whatever be the process \[\Delta U=n{{C}_{V}}\Delta T\] or            \[\Delta U=n\Delta T\left( \frac{R}{\gamma -1} \right)\]                ?. (i)                 \[pV=nR{{T}_{1}}\]                 \[2pV=nR{{T}_{2}}\] \[\Rightarrow \]               \[pV=nR({{T}_{2}}-{{T}_{1}})\] \[\frac{pV}{R}=n\Delta T\]                           \[[{{T}_{2}}-{{T}_{1}}=\Delta T]\] Substituting in Eq. (i)                 \[\Delta U=\frac{pV}{(\gamma -1)}\]


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