JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    One mole of an ideal monoatomic gas at temperature \[{{T}_{0}}\] expands slowly according to the law P/V = constant. If the final temperature is 2To, heat supplied to the gas is -

    A) \[2R{{T}_{0}}\]           

    B)        \[\frac{3}{2}R{{T}_{0}}\]

    C) \[R{{T}_{0}}\]             

    D)        \[\frac{1}{2}R{{T}_{0}}\]

    Correct Answer: A

    Solution :

    [a] \[\frac{P}{V}=\] constant, PV = RT \[W=\int{pdV}=C\int\limits_{{{V}_{1}}}^{{{V}_{2}}}{VdV}\] \[W=C\left[ \frac{{{V}^{2}}}{2} \right]\] \[=\frac{1}{2}{{P}_{2}}{{V}_{2}}-\frac{{{P}_{1}}{{V}_{1}}}{2}\] \[=\frac{1}{2}R({{T}_{2}}-{{T}_{1}})\] \[=\frac{1}{2}R{{T}_{0}}\] \[\Delta U=1\times \frac{3}{2}R\times {{T}_{0}}\] \[=\frac{3}{2}R{{T}_{0}}\] \[Q=W+\Delta U=2R{{T}_{0}}\]

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