Question

In the indicator diagram, AB is an isotherm and BC is an adiabat, because :

• A. AB and BC meet at B
• B. BC is shorter than AB
• C. slope of AB is less than slope of BC
• D. none of the above

Hint:

Adiabatic curves are always steeper than isothermal curves on P-V diagram.

Answer 1

The Correct Option is C

Concept: For isothermal process: \[ PV = \text{constant} \Rightarrow \left|\frac{dP}{dV}\right|_{\text{iso}} = \frac{P}{V} \] For adiabatic process: \[ PV^\gamma = \text{constant} \Rightarrow \left|\frac{dP}{dV}\right|_{\text{adi}} = \gamma \frac{P}{V} \]

Step 1: Compare slopes.
\[ \left|\frac{dP}{dV}\right|_{\text{adi}} = \gamma \left|\frac{dP}{dV}\right|_{\text{iso}} \] Since \( \gamma>1 \), adiabatic curve is steeper.

Step 2: Conclusion.
\[ \text{slope of AB (isotherm)<slope of BC (adiabat)} \]