Kinetic Theory

JEE Main level, single correct, medium

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Question 78 of 168

NN moles of a polyatomic gas(f=6)(f=6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of NN is:

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Answer: (C) 44

The equivalent degree of freedom feq{f}_{eq} of the mixture is
feq=n1f1+n2f2n1+n2{f}_{eq}=\dfrac{{n}_{1}{f}_{1}+{n}_{2}{f}_{2}}{{n}_{1}+{n}_{2}}
For diatomic gas feq=5{f}_{eq}=5.
⇒5=(n)(6)+(2)(3)n+2\Rightarrow 5=\dfrac{(n)(6)+(2)(3)}{n+2}
⇒5n+10=6n+6\Rightarrow 5n+10=6n+6
⇒n=4\Rightarrow n=4

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