Verified Solution • 2025–26 Session moderate

QPages 34-37: Q20: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q20 Solution: Figure shows a vessel partitioned by a fixed diathermic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often use the wrong expression for the mean speed of an ideal gas. The correct formulas are $v_{ ext{rms}}=sqrt{3kT/m}$ and $v_{ ext{av}}=sqrt{8kT/(pi m)}$. When equating them, square both sides to eliminate the square roots, then solve for the mass ratio: $rac{3}{m_1}=rac{8}{pi m_2}Rightarrow rac{m_1}{m_2}=rac{3pi}{8}$. Using the wrong mean‑speed expression or forgetting to square the equation leads to an incorrect ratio such as $3/pi$.

Figure shows a vessel partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part equals the mean speed of the molecules in the right part. Calculate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.

Step-by-Step Verified Solution

**Answer:**

m_1/m_2 = 3/\pi

**Step-by-Step Explanation:** For left part:

v_{rms} = \sqrt{3kT/m_1}

. For right part:

v_{av} = \sqrt{8kT/\pi m_2}

. Setting equal:

\frac{3}{m_1} = \frac{8}{\pi m_2} \Rightarrow \frac{m_1}{m_2} = \frac{3\pi}{8}

.

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