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AIIMS 2004

Exam: AIIMS
Year: 2004
Subject: Physics
Chapter: Kinetic Theory of Gases

AIIMS 2004 · Physics · Kinetic Theory of Gases

v_ r m s , v_ a v and v_ m p are root mean square, average and most...

v_{r m s}, v_{a v}

and

v_{m p}

are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

Options

A $v_{m s} < v_{a v} < v_{m p}$
B $v_{r m s}>v_{a v}>v_{m p}$
C $v_{m p} < v_{r m s} < v_{a v}$
D $v_{m p}>v_{r m s}>v_{\alpha v}$ .

Correct answer

B. $v_{r m s}>v_{a v}>v_{m p}$

Step-by-step solution

\begin{aligned}& v_{r m s}=\sqrt{\frac{3 K_B T}{m}}=1.73 \sqrt{\frac{K_B T}{m}}\\ & v_{a v}=\sqrt{\frac{8 K_B T}{\pi m}}=1.60 \sqrt{\frac{K_B T}{m}}\\ & v_{m p}=\sqrt{\frac{2 K_B T}{m}}=1.41 \sqrt{\frac{K_B T}{m}} \end{aligned}

From these equations,

v_{r m s} \gt v_{a v} \gt v_{m p}

.

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