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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    If one mole of an monoatomic gas \[(\ell =5/3)\] is mixed with one mole of a diatomic gas \[(\ell =7/5)\], the value of \[\ell \] for the mixture is :

    A)  1.50         

    B)  1.40

    C)  1.53            

    D)  3.07

    Correct Answer: A

    Solution :

    \[{{\gamma }_{1}}=5/3,\] gas is monoatomic \[{{C}_{v1}}\,=\frac{3R}{2}\] \[{{\gamma }_{2}}=7/5,\] gas is diatomic \[{{C}_{v2}}\,=\frac{5R}{2}\] \[{{C}_{v}}\,=\frac{{{n}_{1}}{{C}_{v1}}\,+{{n}_{2}}{{C}_{{{v}_{2}}}}}{{{n}_{1}}+{{n}_{2}}}\] \[=\frac{(1)\left( \frac{3}{2}R \right)\,+(2)\,\left( \frac{5}{2}R \right)}{1+1}=2R\] \[{{C}_{P}}={{C}_{V}}+R=3R\] \[{{\gamma }_{mixture}}\,=\frac{{{C}_{p}}}{{{C}_{v}}}=1.5\]


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