Verified Solution • 2025–26 Session moderate

QPage 11: Q4: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Page 11: Q4 Solution: In defining the ideal gas temperature scale, it is assumed that …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat $P\propto T$ at constant volume as a theorem derived from kinetic theory, forgetting that it is an empirical postulate verified by gas‑thermometer experiments. The proportionality holds only for an ideal (or sufficiently dilute) gas; real gases must be tested at low pressure and fixed volume before the temperature scale can be defined.

In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature TT. How can we verify whether this is true or not? Do we have to apply the kinetic theory of gases? Do we have to depend on experimental result that the pressure is proportional to temperature?

Step-by-Step Verified Solution

**Answer:** We verify the proportionality by comparing different gas thermometers and other thermometers experimentally. We do not need kinetic theory, and we do depend on experimental results. **Step-by-Step Explanation:** The ideal gas temperature scale assumes P∝TP \propto T at constant volume. This is verified by comparing constant-volume gas thermometers filled with different gases (hydrogen, helium, nitrogen) at low pressure � they all agree. Further verification comes from comparing the gas scale with other independent scales (platinum resistance, thermocouples, radiation pyrometers). Kinetic theory provides a theoretical explanation for why P∝TP \propto T, but the verification is experimental.

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