1,mole of a gas having gamma = frac {7}{5} is mixed with 1,mole of a gas having gamma&nb

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12.Kinetic Theory of Gases

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$1\,mole$ of a gas having $\gamma = \frac {7}{5}$ is mixed with $1\,mole$ of a gas having $\gamma = \frac {4}{3}$ . What will be the $\gamma $ for the mixture ?

A

$\frac{5}{{11}}$

B

$\frac{15}{{13}}$

C

$\frac{15}{{11}}$

D

$\frac{5}{{13}}$

Solution

for $\mathrm{y}=\frac{7}{5} ; \mathrm{C}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$

for $\mathrm{y}=\frac{4}{3} ; \mathrm{C}_{\mathrm{v}}=3 \mathrm{R}$

Hence $C_{v\,mix}=\frac{\mu_{1} C_{v_{1}}+\mu_{2} C_{v_{2}}}{\mu_{1}+\mu_{2}}$

$=\frac{\frac{5}{2} R+3 R}{2}=\frac{11}{4} R$

$\mathrm{C}_{\mathrm{p} \operatorname{mix}}=\frac{15}{4} \mathrm{R}=\mathrm{C}_{\mathrm{v} \operatorname{mix}}+\mathrm{R}$

$\mathrm{y}_{\operatorname{mix}}=\frac{\mathrm{C}_{\mathrm{pmix}}}{\mathrm{C}_{\mathrm{vmix}}}=\frac{15}{11}$

Standard 11

Physics

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