Physics Thermodynamics PMDC Conceptual Practice
PMDC Verified Question 2 of 54
According to the kinetic theory of gases, the root-mean-square (RMS) velocity of a gas molecule having pressure \( P \) and density \( \rho \) is given by which of the following expressions?
A
\( \sqrt{3P/\rho} \)
B
\( 3 P \rho \)
C
\( 3 \rho / P \)
D
\( \sqrt{3\rho / P} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( \sqrt{3P/\rho} \)
Concept:

The kinetic theory relates the macroscopic pressure of a gas to the microscopic kinetic energy (and thus velocity) of its individual molecules.

Formula:

$$ P = \frac{1}{3} \rho v_{\text{rms}}^2 $$

Solution:

  • Isolate the squared velocity term: \( v_{\text{rms}}^2 = \frac{3P}{\rho} \).
  • Take the square root of both sides to find the RMS velocity.
  • \( v_{\text{rms}} = \sqrt{\frac{3P}{\rho}} \).


Why other options are incorrect:

Option D mistakenly inverts the fraction inside the square root. Options B and C entirely omit the square root, physically breaking dimensional consistency.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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