Verified Solution • 2025–26 Session moderate

QPage 32: Q5: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Page 32: Q5 Solution: Comment on the following statement: the temperature of all the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake temperature for the kinetic energy of a single molecule, assuming every molecule has the same temperature. Remember that temperature is a macroscopic, statistical quantity proportional to the *average* kinetic energy ($\langle KE\rangle = \tfrac32 k_B T$) of the ensemble, while individual molecules follow the Maxwell‑Boltzmann speed distribution and have varied energies.

Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.

Step-by-Step Verified Solution

**Answer:** The statement is incorrect. The molecules in a gas sample do not all have the same temperature; temperature is a property of the entire sample, not of individual molecules. Molecules have a distribution of speeds (and hence kinetic energies) given by the Maxwell-Boltzmann distribution. **Step-by-Step Explanation:** Temperature is a macroscopic, statistical quantity. It is related to the average kinetic energy of the molecules, not the kinetic energy of each individual molecule. Individual molecules have a wide range of speeds.

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