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QPage 60: Q2: HC Verma: Concepts of Physics - Volume 2 Laws of Thermodynamics Page 60: Q2 Solution: Should the internal energy of a system necessarily increase if…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume $U$ always rises with $T$ because $U=nC_vT$ for an ideal gas, forgetting that for real substances $U$ also depends on volume, phase and intermolecular forces. Remember that during phase changes or in non‑ideal systems temperature can stay constant while $U$ changes (latent heat), or $U$ can change without a temperature change.

Should the internal energy of a system necessarily increase if its temperature is increased?

Step-by-Step Verified Solution

**Answer:** No, the internal energy of a system does not necessarily increase if its temperature is increased (for systems other than ideal gases). **Step-by-Step Explanation:** For an **ideal gas**, internal energy depends only on temperature: U=nCvTU = nC_vT. So if TT increases, UU must increase. However, for **real systems** (e.g., during a phase change like melting), the temperature can remain constant while internal energy increases due to latent heat. Conversely, there are processes where internal energy can change without a temperature change. The statement is strictly valid only for ideal gases [citation:8][citation:10].

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