Kinetic Theory

JEE Main level, single correct, medium

42 of 168

Question 42 of 168

Given below are two statements:
Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is vv. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2v2v.
In the light of the above statements, choose the correct answer from the options given below :

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Answer: (D) Statement I is false but Statement II is true

Momentum is a vector quantity and average momentum of molecules of a sample is zero due to random motion.
Pavg=0{P}_{avg}=0
RMS speed of a molecule is given by
vrms=3RTM{v}_{rms}=\sqrt{\dfrac{3RT}{M}}
Now the temperature is doubled Tnew=2T{T}_{new}=2T and due to dissociation Mnew=M2{M}_{new}=\dfrac{M}{2}.
⇒vnewv=2TM2TM\Rightarrow \dfrac{{v}_{new}}{v}=\dfrac{\sqrt{\dfrac{2T}{\dfrac{M}{2}}}}{\sqrt{\dfrac{T}{M}}}
⇒vnew=2v\Rightarrow {v}_{new}=2v

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