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QPage 32: Q9: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Page 32: Q9 Solution: It is said that the assumptions of kinetic theory are good for…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often equate the kinetic energy of the lone molecule with a temperature using $\frac{3}{2}k_BT=\frac12mv^2$, but temperature is a statistical property defined for an ensemble of particles; with only one molecule the average kinetic energy is undefined, so a meaningful temperature cannot be assigned.

It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?

Step-by-Step Verified Solution

**Answer:** The assumption of a large number of molecules (statistical averaging) is not valid. We cannot assign a meaningful temperature to a single molecule. **Step-by-Step Explanation:** Kinetic theory assumes a large number of molecules so that statistical averages (like average kinetic energy) are well-defined. With only one molecule, concepts like average speed, temperature, and pressure lose their statistical meaning. Temperature is a macroscopic property.

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