KTGMedium
Question
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: If the average kinetic energy of $H_{2}$ and $O_{2}$ molecules, kept in two different sized containers are same, then their temperatures will be same.
Reason R: The r.m.s. speed of $H_{2}$ and $O_{2}$ molecules are same at same temperature.
Choose the correct answer from the options given below
Options
A.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
B.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
C.$\mathbf{A}$ is true but $\mathbf{R}$ is false
D.$\mathbf{A}$ is false but $\mathbf{R}$ is true
Solution
Sol. [Key Concept: Equal average KE fixes equal temperature (A true); but $v_{rms} \propto \sqrt{1/M}$ differs, so R is false.]
Avg. kinetic energy of molecule will be $\frac{f}{2}KT$
But $v_{rms} = \sqrt{\frac{3RT}{M}}$
Molar mass $m$ different so $v_{rms}$ is different
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