Step 1:
Statement I is correct. Adsorption of gases on a surface is indeed an exothermic process, as the gas molecules lose energy while being adsorbed onto the surface.
Step 2:
Statement II is incorrect. When a gas is adsorbed on charcoal, it leads to a decrease in pressure, not an increase. This happens because the molecules move from the gas phase to the surface, reducing the volume of the gas phase and therefore lowering the pressure in the vessel. Hence, the pressure \( P' \) should be less than \( P \), not greater.
Thus, the correct answer is option (3).