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

Step 1: Understanding the Concept:
For an ideal gas, the slope of an adiabatic process on a P-V diagram is steeper than the slope of an isothermal process starting from the same point.
: Key Formula or Approach:
1. Isothermal slope \( \left( \frac{dP}{dV} \right)_{\text{iso}} = -\frac{P}{V} \).
2. Adiabatic slope \( \left( \frac{dP}{dV} \right)_{\text{adia}} = -\gamma \frac{P}{V} \).
3. Since \( \gamma>1 \), the adiabatic slope is \( \gamma \) times the isothermal slope.
Step 2: Detailed Explanation:
- In the P-V indicator diagram, both curves generally look like hyperbolas.
- To distinguish them, we compare their slopes.
- The adiabatic curve drops more rapidly than the isothermal curve because work is done at the expense of internal energy, leading to a faster decrease in pressure for a given volume expansion.
- Therefore, the slope of the adiabat (BC) is greater than the slope of the isotherm (AB).
Step 3: Final Answer:
The slope of AB is less than the slope of BC.