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QPage 76: Q9: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q9 Solution: Can two states of an ideal gas be connected by an isothermal…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume two different states can satisfy both $PV=\text{const}$ (isothermal) and $PV^{\gamma}=\text{const}$ (adiabatic) simultaneously, but dividing the two relations gives $V^{\gamma-1}=\text{const}$, which forces $V_1=V_2$ and thus identical states; only the trivial case where the states coincide satisfies both processes.

Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?

Step-by-Step Verified Solution

**Answer:** Yes, two states of an ideal gas can be connected by both an isothermal and an adiabatic process, but only if

V_1 = V_2

(trivial case). **Step-by-Step Explanation:** For both processes:

P_1V_1 = P_2V_2

and

P_1V_1^\gamma = P_2V_2^\gamma

. Dividing:

V_1^{\gamma-1} = V_2^{\gamma-1}

, which gives

V_1 = V_2

. This is the trivial case where the two states are identical [citation:14].

All Questions in this Chapter

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