Which Equation Is Charles' Law?

History of Charles' Law

• Influenced by the rise in popularity of hot-air balloons, Jacques Charles investigated the compressibility of gases in the 1780s. His experiments were built on Robert Boyle's work nearly a century earlier that defined the relationship between the volume and pressure of a gas. However, Charles was interested in the relationship between the volume and temperature of a gas. While Charles performed the original work, it was another French scientist, Joseph-Louis Gay-Lussac, who verified Charles' unpublished results and published his findings in 1802.

Charles' Law

• Charles Law states that, at a constant mass and pressure, the volume of a gas is directly proportional to its absolute temperature. In other words, if the temperature of a gas rises, so will its volume. Conversely, if the temperature of a gas decreases, so will its volume. Charles' Law can be stated as volume equals temperature times a constant: V=Tk.

  The constant represents the slope of the relationship and is different for each gas. The law applies only to ideal gases, which conform to it at all temperatures and pressures. However, real gases also conform to the law at most temperatures and pressures. The only difference is a noticeable deviation as the real gas cools and approaches its condensation point.

Using Charles' Law

• Charles' Law is typically used in terms of a ratio, allowing you to solve for an unknown variable. In this form, the gas's initial volume divided by its initial temperature is equal to the gas's final volume divided by its final temperature: Vi/Ti=Vf/Tf. If three variables are known, you can cross multiply to solve for the fourth.

  For example, if a gas has an initial volume of 3.0 gallons and an initial temperature of 350 degrees Kelvin, you can determine its final volume if it is cooled to 250 degrees Kelvin: 3G/350K=X/250K. By solving for "X," you can determine that the gas's final volume would be 2.14 gallons.

Basis for Charles' Law

• Temperature is simply a measure of speed at which an object's molecules vibrate. The hotter an object is, the faster its molecules will vibrate. Therefore, as the temperature of a gas rises, so does the speed at which its molecules are vibrating. As the molecules vibrate faster, they strike the walls of the container more frequently, raising the pressure. To keep this pressure constant, the volume of the gas must be expanded. This expansion provides more room for the molecules to move, thus bringing the frequency of collisions back to its initial level.