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QPage 76: Q7: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Page 76: Q7 Solution: Show that the slope of the p-V diagram is greater for an…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently forget to include the adiabatic index $\gamma$ in the derivative, incorrectly concluding that both isothermal and adiabatic curves have the same slope magnitude $P/V$. Always differentiate $PV^\gamma = K$ to reveal the steeper $-\gamma P/V$ slope.

Show that the slope of the p-V diagram is greater for an adiabatic process compared to an isothermal process.

Step-by-Step Verified Solution

**Answer:** The slope of the

P

-

V

diagram is greater for an adiabatic process. **Step-by-Step Explanation:** For isothermal:

PV = k

, so slope

\frac{dP}{dV} = -\frac{P}{V}

. For adiabatic:

PV^\gamma = K

, so slope

\frac{dP}{dV} = -\gamma\frac{P}{V}

. Since

\gamma > 1

,

|slope_{adiabatic}| > |slope_{isothermal}|

[citation:2].

All Questions in this Chapter

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