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QPage 60: Q8: HC Verma: Concepts of Physics - Volume 2 Laws of Thermodynamics Page 60: Q8 Solution: The final volume of a system is equal to the initial volume in…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat $W=\int P\,dV$ as a state function and conclude $W=0$ whenever $V_f=V_i$, forgetting that the integral depends on the entire path. Emphasize that $P$ may vary during the process, so a cyclic or non‑isobaric path can yield non‑zero work even though the volume returns to its initial value.

The final volume of a system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?

Step-by-Step Verified Solution

**Answer:** Work done is **not necessarily zero**, and **not necessarily nonzero**. **Step-by-Step Explanation:** - If the process is **isobaric** and Vf=ViV_f = V_i, then W=PΔV=0W = P\Delta V = 0. - In a **cyclic process**, the system returns to its initial state, so Vf=ViV_f = V_i, but the net work done can be **nonzero** (it equals the area enclosed by the cycle on a PP-VV diagram). Thus, equal initial and final volumes do not guarantee zero work [citation:8][citation:10].

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