• question_answer If one mole of monoatomic gas $\gamma =\frac{5}{3}$ is mixed with one mole of diatomic gas $\gamma =\frac{7}{5}$. The value of $\gamma$ for the mixtures is:                                   A)  $2.5$                         B)  $1.5$C)  $1.8$                         D)  none of these

Solution :

To find the value of $\gamma ,$ for mixture we take average value of $\gamma =\left( \frac{{{C}_{p}}}{{{C}_{\upsilon }}} \right){{\alpha }_{\upsilon }}$ ${{C}_{\upsilon }}$ for monoatomic gas $=\frac{3}{2}R$            ?..(i) ${{C}_{\upsilon }}$ for diatomic gas $=\frac{5}{2}R$ So,     average ${{C}_{\upsilon }}=\frac{\frac{3}{2}R+\frac{5}{2}R}{2}=2R$ Thus ${{C}_{p}}$ for mixture or average ${{C}_{p}}$                 $={{C}_{\upsilon }}+R=2R+R$                 $=3R$                                             ?..(ii) Therefore the value of y for the mixture is given by $\gamma =\left( \frac{{{C}_{p}}}{{{C}_{\upsilon }}} \right){{a}_{\upsilon }}=\frac{3R}{2R}$ (from (0 and (ii))

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