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QPage 76: Q5: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q5 Solution: In a real gas, the internal energy depends on temperature and…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that because a real gas’s internal energy depends on volume, the difference $C_p-C_v$ must exceed $R$. In reality, the correct identity is $C_p-C_v=-T rac{(partial P/partial T)_V^2}{(partial P/partial V)_T}$, which can be larger, smaller, or equal to $R$ depending on the gas and state. Always derive from the thermodynamic relation rather than extrapolating the ideal‑gas formula.

In a real gas, the internal energy depends on temperature and also on volume. The energy increases when the gas expands isothermally. Examining the derivation of Cp−Cv=RC_p - C_v = R, find whether Cp−CvC_p - C_v will be more than R, less than R or equal to R for a real gas.

Step-by-Step Verified Solution

**Answer:** For a real gas, Cp−Cv>RC_p - C_v > R. **Step-by-Step Explanation:** For an ideal gas, Cp−Cv=RC_p - C_v = R. For a real gas, the internal energy depends on volume as well as temperature. When the gas expands at constant pressure, some heat is used to overcome intermolecular attractions (doing internal work against these forces). So Cp−Cv=R+kdTdtC_p - C_v = R + k\frac{dT}{dt} where k>0k > 0, giving Cp−Cv>RC_p - C_v > R [citation:2].

All Questions in this Chapter

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