\textbf{Step 1: Understand Physical Equilibrium}
Physical equilibrium occurs when two phases of a substance coexist in dynamic equilibrium, meaning there is no net change in the amount of each phase over time. Examples include:
Solid–liquid equilibrium (e.g., ice and water),
Liquid–vapor equilibrium (e.g., water and steam).
Chemical equilibrium, on the other hand, involves reversible chemical reactions where reactants and products are present simultaneously.
Step 2: Analyze Each Option
Option (1): $ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g) $
This is a chemical equilibrium because it involves a reversible chemical reaction between two different molecular species ($ \text{N}_2\text{O}_4 $ and $ \text{NO}_2 $).
Not a physical equilibrium.
Option (2): $ \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) $
This is a chemical equilibrium involving the reversible synthesis of ammonia from nitrogen and hydrogen gases.
Not a physical equilibrium.
Option (3): $ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) $
This is a chemical equilibrium involving the decomposition of calcium carbonate into solid calcium oxide and gaseous carbon dioxide.
Not a physical equilibrium.
Option (4): $ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) $
This represents the phase equilibrium between liquid water ($ \text{H}_2\text{O}(l) $) and water vapor ($ \text{H}_2\text{O}(g) $). At a given temperature and pressure, the rates of evaporation and condensation are equal, maintaining a constant concentration of both phases.
This is a physical equilibrium.
Step 3: Identify the Correct Option
From the analysis, Option (4) is the only example of physical equilibrium.