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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    For an ideal gas, \[\frac{{{C}_{p}},\,m}{{{C}_{V}},\,m}=r.\]The molecular mass of the gas is M, its specific heat capacity at constant volume is

    A)  \[\frac{rR}{M(r-1)}\]                     

    B)  \[\frac{rRM}{r-1}\]

    C)  \[\frac{M}{R(r-1)}\]                      

    D)  \[\frac{R}{M(r-1)}\]

    E)  \[\frac{R}{M(1-r)}\]

    Correct Answer: D

    Solution :

                    As \[\frac{{{C}_{p}},\,m}{{{C}_{V}},\,m}=r\] and \[{{C}_{p,\,m}}-{{C}_{V,\,m}}=R\] \[\therefore \]  \[{{C}_{V,m}}=\frac{R}{r-1}\] \[{{C}_{V,\,m}}=\frac{{{C}_{V}}}{n}\] and \[{{C}_{V}}=m\cdot {{C}_{V}}\] \[\therefore \]  \[\frac{R}{r-1}=\frac{m\cdot {{C}_{V}}}{m}\times M\] \[\therefore \]  \[{{C}_{V}}=\frac{R}{(r-1)\,M}\]


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