Question

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is:

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
On a P-V (Pressure-Volume) diagram, the slope of different thermodynamic processes varies.
- Isochoric: Vertical line (Volume constant).
- Isobaric: Horizontal line (Pressure constant).
- Isothermal and Adiabatic: Curves with negative slopes.
Key Formula or Approach:
The slope of an Isothermal process (\(PV = \text{const}\)) is:
\[ \left(\frac{dP}{dV}\right)_{\text{iso}} = -\frac{P}{V} \]
The slope of an Adiabatic process (\(PV^\gamma = \text{const}\)) is:
\[ \left(\frac{dP}{dV}\right)_{\text{adia}} = -\gamma \frac{P}{V} \]
Since \(\gamma>1\), the adiabatic curve is steeper than the isothermal curve.
Step 2: Detailed Explanation:
Referring to the graph:
- Curve 4 is a horizontal line, so it is isobaric.
- Curve 1 is a vertical line, so it is isochoric.
- Curves 2 and 3 represent expansion. Since the adiabatic curve is steeper than the isothermal curve, the curve that drops more rapidly (the steeper one) is adiabatic.
- Curve 2 is steeper than Curve 3. Therefore, Curve 2 is adiabatic and Curve 3 is isothermal.
Step 3: Final Answer:
The curve representing the adiabatic process is 2.