Kinetic Theory

JEE Main level, single correct, medium

76 of 168

Question 76 of 168

If three moles of monoatomic gas (γ=53)\left(\gamma =\dfrac{5}{3}\right) is mixed with two moles of a diatomic gas (γ=75)\left(\gamma =\dfrac{7}{5}\right), the value of adiabatic exponent γ\gamma for the mixture is:

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Answer: (C) 1.521.52

Given:
f1=3,f2=5n1=3,n2=2\begin{matrix}{f}_{1}=3, & {f}_{2}=5 \\ {n}_{1}=3, & {n}_{2}=2\end{matrix}
Now, for mixture

fmixture=n1f1+n2f2n1+n2=9+105=195{f}_{\text{mixture}}=\dfrac{{n}_{1}{f}_{1}+{n}_{2}{f}_{2}}{{n}_{1}+{n}_{2}}=\dfrac{9+10}{5}=\dfrac{19}{5}
Therefore,
γmixture=1+2fmixture=1+2×519=2919=1.52{\gamma }_{\text{mixture}}=1+\dfrac{2}{{f}_{\text{mixture}}}=1+\dfrac{2\times 5}{19}=\dfrac{29}{19}=1.52

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