When the pressure of a gas is kept constant, the volume of the gas is directly proportional to its absolute temperature. This means that as the temperature of the gas increases, the volume of the gas also increases, and vice versa.

This relationship can be explained using the particle theory. The particles in a gas are in constant random motion. Increasing the temperature means the particles gain more kinetic energy and move faster. This increased motion causes the particles to collide more forcefully with the walls of the container. To maintain a constant pressure, the volume of the container must increase to allow the particles to move further and the collisions to occur at the same rate. Essentially, the particles need more space to maintain the same rate of collisions per unit time. This is described by Charles's Law.

Gay-Lussac's Law states that the pressure of a gas is directly proportional to its absolute temperature, provided the volume and the number of moles of gas remain constant. Mathematically, this is expressed as P ∝ T (at constant volume and moles).

This law is consistent with kinetic theory because it directly reflects the relationship between temperature and the kinetic energy of the gas particles. As explained earlier, increasing the temperature increases the average kinetic energy of the particles, causing them to move faster and collide more frequently and with greater force against the container walls. This increased collision frequency and force translates directly into an increase in pressure.

Example of a practical application: Scuba diving. As a diver descends deeper, the pressure increases. Without proper regulation, the increased pressure would cause the air in the diver's lungs to expand, potentially leading to serious health problems. Therefore, divers must use specialized equipment (regulators) to maintain a constant volume of air in their lungs, ensuring that the pressure remains safe and prevents lung damage. The regulator maintains a constant volume, so the pressure is directly proportional to the temperature of the air in the lungs.

Kinetic Molecular Theory and Compressibility:

The Kinetic Molecular Theory states that gas particles are in constant, random motion. These particles are widely separated and have relatively low intermolecular forces. This means there is a significant amount of empty space between the particles. When pressure is applied, the gas particles are forced closer together, and the empty space is reduced. Because of the large spaces between the particles, gases can be easily compressed – a relatively small pressure change results in a significant volume change.

Liquids vs. Gases:

In liquids, the particles are much closer together than in gases. They are held together by stronger intermolecular forces. This means there is less empty space between the particles. When pressure is applied to a liquid, the particles are already relatively close together, so there is less space for them to move. Therefore, liquids are less compressible than gases. While liquids can be compressed to some extent, the compressibility is significantly less than that of gases.

Table summarizing compressibility: