Question

Consider a gas in a container that can adjust its volume to maintain constant pressure. Suppose the gas is cooled. What happens to the gas particles with the decrease in temperature? What happens to the volume of the container?

Short answer

When the gas is cooled, the gas particles slow down and their collisions become less frequent and less violent. As a result, to maintain the constant pressure, the volume of the container decreases.

Step-by-step solution

Effect on Gas Particles

When a gas is cooled, the average kinetic energy of the gas particles decreases. This is because temperature is a measure of the average kinetic energy of the particles in a substance. As the gas cools, the particles slow down and the collisions between particles become less frequent and less violent.

Constant Pressure Condition

In this scenario, the pressure is kept constant. Pressure is a force exerted by gas per unit area, caused by collisions of the gas particles with the walls of the container. As the temperature decreases, the kinetic energy of the particles decreases, and so does the force of the collisions. However, because the pressure is kept constant, the system must adjust.

Effect on Volume of the Container

To maintain the constant pressure condition as the force of the gas' collisions decrease, the volume of the container decreases as well. This is according to Boyle's law, which states that the volume of a gas is inversely proportional to its pressure, when the amount of gas and the temperature are kept constant. In this case, as the pressure is kept constant but the force of collisions decreases, the volume must decrease to compensate and keep the pressure constant.

Key concepts

Kinetic Theory of Gases

The kinetic theory of gases helps us understand the behavior of gas molecules. It explains how gas particles move and interact with each other and their surroundings. Gas particles are in constant random motion, colliding with each other and the walls of their container.
One of the key aspects of this theory is that the temperature of a gas is directly related to the average kinetic energy of its particles. When the temperature increases, the kinetic energy of the particles also increases, causing them to move faster. Conversely, when the temperature decreases, the particles slow down, indicating a decrease in kinetic energy.
This decrease in energy affects how often and how forcefully particles collide with each other and the container walls. With a decrease in temperature, these collisions become less frequent and less forceful.

Boyle's Law

Boyle's Law is a fundamental principle in understanding gas behaviors. It states that the volume of a gas is inversely proportional to its pressure, as long as the temperature and the number of gas particles remain constant.
In practical terms, if you increase the volume of the container holding a gas and the temperature stays the same, the pressure will decrease because the gas particles are more spread out and collide less often with the container walls. Conversely, if the volume is reduced, the pressure increases due to more frequent collisions.
It’s important to note that this inverse relationship works perfectly only under ideal conditions. Real gases may slightly deviate due to molecular interactions, but Boyle's Law provides an excellent approximation for understanding gas dynamics in everyday situations.

Temperature and Volume Relationship

The relationship between temperature and volume is another key concept in understanding how gases behave. According to Charles's Law, which deals with this relationship, the volume of a gas is directly proportional to its temperature when pressure is held constant.
This means that when the temperature of a gas increases, the volume will also increase, as long as the pressure doesn’t change. Similarly, when the temperature decreases, the volume decreases as well.

• Higher temperatures mean more kinetic energy and more vigorous particle movement.
• Higher volume allows gas particles more space to move.

In scenarios like the one in the exercise, where pressure is maintained constant, the volume will have to adjust to compensate for temperature changes, thereby demonstrating the direct relationship between temperature and volume.