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QPage 76: Q1: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q1 Solution: Does a gas have just two specific heat capacities or more than…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat specific heat as a fixed property and assume only $C_p$ and $C_v$ exist; however $C$ is defined for any infinitesimal thermodynamic path, so each distinct $P$‑$V$ relation yields a different value, giving an uncountable family of heat capacities. Remember to specify the process (e.g., constant pressure, constant volume, or any other constraint) before assigning a numeric $C$.

Does a gas have just two specific heat capacities or more than two? Is the number of specific heat capacities of a gas countable?

Step-by-Step Verified Solution

**Answer:** No, a gas does not have just two specific heat capacities. The number of specific heat capacities is not countable. **Step-by-Step Explanation:** Specific heat capacity depends on the process followed. Since there are infinitely many possible processes (each with a different PP-VV relation), there are infinitely many specific heat capacities for a gas. CpC_p and CvC_v are just two special cases for isobaric and isochoric processes respectively [citation:2].

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