# Charles' Law

The Ideal Gas* Laws describe the relationship between pressure, volume* and temperature in a fixed mass* of gas. Charles' law describes the relationship between temperature and volume at a constant pressure.

The ability to visualize the behavior of individual gas particles in an enclosed space helps in understanding the mechanism underlying Charles’ Law. The molecules that make up a gas are moving in straight lines until they encounter another molecule, or a wall. When a molecule encounters a wall, it bounces off and moves off in a different direction. When this happens, Newton's Third Law of motion says that both the molecule and the wall will experience a force. In a flexible container such as a balloon, molecules hitting the inside of the of the balloon are what keep the balloon inflated. In a rigid, but adjustable container such as a sealed syringe, the collisions of the moving gas molecules with the syringe walls provide the force that resists efforts to move the syringe plunger.

Increasing the temperature of a volume of gas causes individual gas molecules to move faster. As the molecules move faster, they encounter the walls of the container more often and with more force. In an inflexible container, the more frequent and forceful collisions result in higher pressure. However, if the container volume is adjustable, the volume will increase, and the pressure will remain the same. Charles’ Law is the formal description of this relationship, allowing change in volume to be calculated if the temperature change is known.

The equation describing Charles’ Law is:

V1/T1 = V2/T2

assuming no change in pressure.

The relationship is linear, if the temperature of a volume of gas doubles, the volume doubles. Temperature has to be measured in Kelvin, the absolute* temperature scale, for the relationship to hold.

While Charles’ Law describes the behavior of ideal gases, not real ones, the law does have real world applications. Real gas*es behave in accordance with Charles' Law at temperatures well above the gases condensation point. Closer to the condensation point, the linear relationship does not hold up; volume decreases more rapidly than temperature.

The following illustration explores the relationship between the temperature and volume of an ideal gas in a container that can adjust to allow pressure to remain constant. This is done by observing changes in the volume of a sealed syringe as the temperature varies. A video demonstrating the illustration can be found at the bottom of the post.

Video demonstration:

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