To match the processes with their corresponding P-V diagram curves, we apply the characteristics of thermodynamic processes for an ideal gas:

1. Isochoric Process (Constant Volume): The work done is zero, and the volume ($V$) remains constant while pressure ($P$) changes. On a P-V graph, this corresponds to a vertical line. Thus, Process I matches with (c) Isochoric.

2. Isobaric Process (Constant Pressure): The pressure ($P$) remains constant while volume changes. On a P-V graph, this corresponds to a horizontal line. Thus, Process IV matches with (b) Isobaric.

3. Isothermal vs. Adiabatic (Expansion): Both processes represent curves with negative slopes. However, the magnitude of the slope for an adiabatic process ($|\frac{dP}{dV}| = \gamma \frac{P}{V}$) is greater than that for an isothermal process ($|\frac{dP}{dV}| = \frac{P}{V}$) because the heat capacity ratio $\gamma$ (gamma) is greater than 1. Therefore, the adiabatic curve is steeper (falls more rapidly) than the isothermal curve.

• Process II: Being the steeper curve in standard representations of expansion, it corresponds to (a) Adiabatic.
• Process III: Being the less steep curve, it corresponds to (d) Isothermal.

Matching: P (Process I) → c (Isochoric) Q (Process II) → a (Adiabatic) R (Process III) → d (Isothermal) S (Process IV) → b (Isobaric)

This sequence corresponds to Option 1 .