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QPage 76: Q4: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q4 Solution: Does a solid also have two kinds of molar heat capacities and ? …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the ideal‑gas identity $C_p-C_v=R$ holds for all substances, including solids. In reality, the correct thermodynamic relation is $C_p-C_v=dfrac{T,V,alpha^2}{kappa_T}$, where $alpha$ is the thermal expansion coefficient and $kappa_T$ the isothermal compressibility. For solids both $alpha$ and $kappa_T$ are small, so $C_p-C_v$ is much less than $R$ and must be computed from the material’s elastic and thermal properties, not taken as $R$.

Does a solid also have two kinds of molar heat capacities CpC_p and CvC_v? If yes, is Cp>CvC_p > C_v? Or is Cp−Cv=RC_p - C_v = R?

Step-by-Step Verified Solution

**Answer:** Yes, a solid also has two molar heat capacities CpC_p and CvC_v. Cp>CvC_p > C_v, but Cp−Cv≠RC_p - C_v \neq R. **Step-by-Step Explanation:** For a solid, the expansion coefficient is very small, so the work done during expansion at constant pressure is negligible compared to the heat supplied. Hence CpC_p is only slightly greater than CvC_v, and the difference is much less than RR [citation:2].

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