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QPage 76: Q6: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q6 Solution: Can a process on an ideal gas be both adiabatic and isothermal?

⚠️ Common Exam Traps & Conceptual Pitfalls

Adiabatic means no heat exchange ($Delta Q=0$), not no work. For an ideal gas, an isothermal process gives $Delta U=0$, so the first law forces $Delta W=0$. Thus only a trivial (no volume change) process can satisfy both; a non‑trivial process cannot be both adiabatic and isothermal.

Can a process on an ideal gas be both adiabatic and isothermal?

Step-by-Step Verified Solution

**Answer:** No, a process on an ideal gas cannot be both adiabatic and isothermal. **Step-by-Step Explanation:** From the first law: ΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta W. For adiabatic, ΔQ=0\Delta Q = 0. For isothermal, ΔT=0⇒ΔU=0\Delta T = 0 \Rightarrow \Delta U = 0. This gives ΔW=0\Delta W = 0. But for a non-trivial process (volume change), work is nonzero. Hence no such process exists [citation:2].

All Questions in this Chapter

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