JEE Main & Advanced Physics Kinetic Theory of Gases JEE PYQ-Kinetic Theory Of Gases

  • question_answer
    Two moles of an ideal gas with \[\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{5}{3}\] are mixed with 3 moles of another ideal gas with \[\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{4}{3}\]. The value of \[\frac{{{C}_{P}}}{{{C}_{V}}}\] for the mixture is:                                                                        [JEE MAIN Held on 07-01-2020 Morning]

    A)  1.47    

    B)       1.42

    C)  1.50                

    D)       1.45

    Correct Answer: B

    Solution :

    [b]
                \[\because \frac{{{n}_{1}}}{{{\gamma }_{1}}-1}+\frac{{{n}_{2}}}{{{\gamma }_{2}}-1}=\frac{{{n}_{1}}+{{n}_{2}}}{{{\gamma }_{m}}-1}\]
                \[\Rightarrow \frac{3}{\frac{4}{3}-1}+\frac{2}{\frac{5}{3}-1}=\frac{5}{\gamma m-1}\]
                \[\Rightarrow \frac{9}{1}+\frac{2\times 3}{2}=\frac{5}{{{\gamma }_{m}}-1}\]
                \[\Rightarrow {{\gamma }_{m}}-1=\frac{5}{12}\]
                \[\Rightarrow {{\gamma }_{m}}=\frac{17}{12}=1.42\]


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