The vapour pressure?

Analysis

The question asks for the relationship between the vapour pressure of a liquid and its temperature. To answer this, we need to understand the kinetic theory of matter and how temperature affects the evaporation process.

Concept Explanation

Vapour pressure is the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.

1. Kinetic Energy: As temperature increases, the average kinetic energy of the molecules in the liquid increases.
2. Evaporation: More molecules gain enough energy to overcome the intermolecular forces holding them in the liquid phase and escape into the gas phase.
3. Pressure: As more molecules enter the vapour phase, the number of collisions with the walls of the container increases, thereby increasing the vapour pressure.
4. The Curve: This relationship is not a straight line (linear). It follows an exponential growth pattern described by the Clausius-Clapeyron equation. Because the rate of increase accelerates as the temperature rises, the graph of vapour pressure versus temperature is a curve that bends upwards.

Step-by-Step Solution

• Step 1: Evaluate the relationship. We know that as temperature increases, vapour pressure increases. This immediately eliminates options C and D.
• Step 2: Determine the nature of the increase. Because the relationship follows an exponential curve (as defined by the Clausius-Clapeyron relation), the increase is non-linear.
• Step 3: Compare with options. Option A states it "increases non-linearly," which perfectly matches the physical behavior of vapour pressure. Option B is incorrect because the relationship is not a straight line.

Conclusion

The vapour pressure of a liquid increases non-linearly as the temperature increases. This is a fundamental concept in thermodynamics often tested in JAMB Physics.

Exam Tip: Whenever you see a relationship involving "pressure" and "temperature" in a closed system (like vapour pressure or gas laws), always check if the relationship is linear or exponential. Most thermodynamic processes involving phase changes are non-linear!