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NEET Sample Paper NEET Sample Test Paper-64

  • question_answer
    Suppose ideal gas equation follows \[V{{P}^{3}}=\]constant. Initial temperature and volume of the gas are T and V respectively. If gas expand to 27 V then its temperature will become

    A) T                                 

    B) 9T

    C) 27T                              

    D) T/9

    Correct Answer: B

    Solution :

    \[V{{P}^{3}}= constant\,\,=\, k\,\,\Rightarrow \,\,P=\,\,\frac{k}{{{V}^{1/3}}}\] Also \[PV=\mu RT\,\,\Rightarrow \,\,\frac{k}{{{V}^{1/3}}}\,.V\,\,=\,\,\mu RT\] \[\Rightarrow \,\,\,\,{{V}^{2/3}}\,=\,\,\frac{\mu RT}{k}\] Hence \[\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right){{\,}^{2/3}}\,=\,\,\frac{{{T}_{1}}}{{{T}_{2}}}\,\,\,\Rightarrow \,\,{{\left( \frac{V}{27V} \right)}^{2/3}}\,\,=\,\,\,\frac{T}{{{T}_{2}}}\] \[\Rightarrow \,\,\,\,{{T}_{2}}\,=\,\,9\,T\]


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