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JCECE Engineering JCECE Engineering Solved Paper-2010

  • question_answer
    The equation of state of some gases can be expressed as\[\left( p+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\]where, \[p\] is the pressure, \[V\] the volume, \[T\] the absolute temperature and \[a\] and \[b\] are constants. The dimensional formula of \[a\] is

    A) \[[M{{L}^{5}}{{T}^{-2}}]\]                            

    B) \[[{{M}^{-1}}{{L}^{5}}{{T}^{-2}}]\]

    C) \[[M{{L}^{-1}}{{T}^{-2}}]\]                          

    D)  \[[M{{L}^{-5}}{{T}^{-2}}]\]

    Correct Answer: A

    Solution :

    In the equation \[p,\,\,\,V\] and \[T\] are pressure, volume and temperature respectively.                 \[\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=RT\] Dimensions of \[\frac{a}{{{V}^{2}}}\] will be same as that of\[p\]pressure. \[\therefore \]Dimensions of\[\frac{a}{{{V}^{2}}}=\]dimensions of\[p\] \[\Rightarrow \]               Dimensions of\[a=\]dimensions of \[p\times \]dimensions of\[{{V}^{2}}\]                 \[=[M{{L}^{-1}}{{T}^{-2}}][{{L}^{6}}]\]                 \[=[M{{L}^{5}}{{T}^{-2}}]\]


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