Kinetic Theory

JEE Main level, single correct, medium

137 of 168

Question 137 of 168

A flask contains argon and oxygen in the ratio of 3:23:2 in mass and the mixture is kept at 27∘C27^{\circ}C. The ratio of their average kinetic energy per molecule respectively

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Answer: (A) 3:53:5

Given here, mArmO=32\dfrac{{m}_{Ar}}{{m}_{O}}=\dfrac{3}{2}.
As argon is monoatomic gas, so it has three degree of freedom (f)\left(f\right) and oxygen is a diatomic gas, so its degree of freedom is five.
We know that average kinetic energy per molecule is given by KE=f2kTKE=\dfrac{f}{2}kT, where, kk is Boltzmann's constant and TT is temperature.
Here, T=27∘CT=27^{\circ}C is fixed for both gas.
So, (KE)Ar(KE)O=32kT52kT=35\dfrac{{\left(KE\right)}_{Ar}}{{\left(KE\right)}_{O}}=\dfrac{\dfrac{3}{2}kT}{\dfrac{5}{2}kT}=\dfrac{3}{5}

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