JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    If one mole of an ideal monotonic gas \[(\gamma =5\text{/}3)\] is mixed with one mole of ideal diatomic gas \[(\gamma =7\text{/5}),\], the value of \[\gamma \] for the mixture will be

    A)  1.4                                        

    B)  1.5

    C)  1.53                                      

    D)  3.07

    Correct Answer: B

    Solution :

    \[{{\text{U}}_{\text{mixture}}}\text{=}{{\text{U}}_{\text{monoatomic}}}\text{+}{{\text{U}}_{\text{diatomic}}}\] \[\therefore \]\[\frac{({{n}_{1}}+{{n}_{2}})}{{{\gamma }_{mix}}-1}=\frac{{{n}_{1}}RT}{{{\gamma }_{1}}-1}+\frac{{{n}_{2}}RT}{{{\gamma }_{2}}-1}\] \[\therefore \]\[\frac{2}{\gamma {{ & }_{mix}}^{-1}}=\frac{1}{\left( \frac{5}{3}-1 \right)}+\frac{1}{\left( \frac{7}{5}-1 \right)}\] \[\therefore \]\[{{\gamma }_{mix}}=1.5\]


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