Vapour pressure of the liquid (a) increases with increase in temperature. (b) decreases with increase in temperature. (c) is independent of temperature. (d) either increases or decreases with the increase in temperature, depending on the nature of liquid.

When exploring the concept of vapor pressure, it's crucial to understand thermodynamic equilibrium. This state of balance occurs when a liquid and its vapor are in a closed container, and the rates of evaporation and condensation are equal, resulting in no net change over time. At this point, the system's properties, such as vapor pressure, temperature, and density, remain constant.

In the context of vapor pressure, thermodynamic equilibrium refers to the dynamic but balanced process where the liquid molecules evaporate to form vapor and, at the same time, vapor molecules condense back into the liquid. The vapor pressure is the pressure exerted by the vapor in this equilibrium state. As temperature increases, this equilibrium is affected because the added heat provides energy for more molecules of the liquid to overcome intermolecular forces and become gas, which leads to increased vapor pressure.

The kinetic energy of molecules plays a pivotal role in understanding how temperature affects vapor pressure. Kinetic energy is the energy that molecules possess due to their motion. At higher temperatures, molecules move more vigorously because they have more kinetic energy. This heightened movement means that a greater number of molecules have sufficient energy to escape from the liquid's surface and turn into vapor. The heightened escape rate results in increased vapor pressure.

To simplify, imagine a pot of water boiling on the stove; as the temperature climbs, the water bubbles more intensely. This bubbling is a macroscopic view of the increased kinetic energy at the molecular level, with more water molecules transitioning to steam as the temperature rises. Therefore, the relationship between temperature and vapor pressure can be understood as a direct consequence of changes in the kinetic energy of the molecules.

Phase transition of liquids is another integral concept related to vapor pressure. When a liquid undergoes a phase transition into a gas, it's called evaporation or vaporization. This transformation happens at the surface of the liquid and is influenced by temperature. At the boiling point, the liquid's vapor pressure equals the surrounding atmospheric pressure, and the liquid swiftly transitions to gas throughout the entire volume.

However, below the boiling point, evaporation still occurs at a less competitive rate, notably at the surface where the liquid and air meet. When conditions allow more molecules to vaporize than condense, the liquid will eventually evaporate completely. In essence, as temperature increases, the increased kinetic energy promotes the phase transition of more liquid into vapor, thus increasing vapor pressure.