Verified Solution • 2025–26 Session moderate

QPages 34-37: Q17: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q17 Solution: The mean speed of the molecules of a hydrogen sample equals the …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently invert the molar mass ratio when equating mean speeds, failing to recognize that temperature is directly proportional to molar mass ($T \propto M$) for a fixed speed. Always derive the proportionality $v_{av} = \sqrt{8RT/\pi M}$ to confirm that $T_H/T_{He} = M_H/M_{He}$, not the inverse.

The mean speed of the molecules of a hydrogen sample equals the mean speed of the molecules of a helium sample. Calculate the ratio of the temperature of the hydrogen sample to the temperature of the helium sample. Use

R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:**

T_H/T_{He} = 1/2

**Step-by-Step Explanation:** Mean speed

v_{av} \propto \sqrt{T/M}

. For equal mean speeds:

\frac{T_H}{M_H} = \frac{T_{He}}{M_{He}}

.

T_H/T_{He} = M_H/M_{He} = 2/4 = 1/2

All Questions in this Chapter

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