# Charles' Law

This illustration explores the relationship between the temperature and volume* of an ideal gas* in a container that adjusts to allow pressure to remain constant.

The molecules that make up a gas move in straight lines until they encounter another molecule or the walls of a container. 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 balloon, the force of individual molecules hitting the inside of the balloon keeps 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, creating pressure inside of the syringe.

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 a rigid 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 between temperature and volume at a fixed pressure.

This relationship allows changes in the volume of a fixed mass* of gas to be calculated given a change in temperature.

The equation describing Charles' Law is:

V1/T1 = V2/T2

Where V1 is the volume of the gas at one temperature (T1) and, V2 is the volume after a change to a new temperature (T2). For this relationship to hold, both the mass of the gas and its pressure are held constant, and the temperature must be reported in Kelvin.

The relationship is linear, if the temperature of a volume of gas doubles, the volume doubles.

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 gas' condensation point. Closer to the condensation point, the linear relationship does not hold up; volume decreases more rapidly than temperature.

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