What Is the Formula for Charles' Law?

Charles' Law Formula and Explanation

Charles's Law: Liquid nitrogen is added to a beaker. When air-filled balloons are placed in liquid nitrogen at 77K the volume of air is greatly reduced. When out of the nitrogen and warmed to air temperature, they re-inflate to original volume.
Charles's Law: Liquid nitrogen is added to a beaker. When air-filled balloons are placed in liquid nitrogen at 77K the volume of air is greatly reduced. When out of the nitrogen and warmed to air temperature, they re-inflate to original volume. Matt Meadows / Getty Images

Charles' Law is a special case of the ideal gas law. It states that the volume of a fixed mass of a gas is directly proportional to the temperature. This law applies to ideal gases held at a constant pressure, where only the volume and temperature are allowed to change.

Charles' Law is expressed as:

Vi/Ti = Vf/Tf

where
Vi = initial volume
Ti = initial absolute temperature
Vf = final volume
Tf = final absolute temperature

It is extremely important to remember the temperatures are absolute temperatures measured in Kelvin, NOT °C or °F.

Charles Law Example Problems

A gas occupies 221 cm3 at a temperature of 0 C and pressure of 760 mm Hg. What will its volume be at 100 C?

Since the pressure is constant and the mass of gas doesn't change, you know you can apply Charles' law. The temperatures are given in Celsius, so they must first be converted into absolute temperature (Kelvin) to apply the formula:

V1 = 221cm3; T1 = 273K (0 + 273); T2 = 373K (100 + 273)

Now the values can be plugged into the formula to solve for final volume:

Vi/Ti = Vf/Tf
221cm3 / 273K = V/ 373K

Rearranging the equation to solve for final volume:

V = (221 cm3)(373K) / 273K

V = 302 cm3

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Helmenstine, Todd. "What Is the Formula for Charles' Law?" ThoughtCo, Feb. 13, 2017, thoughtco.com/formula-for-charles-law-604281. Helmenstine, Todd. (2017, February 13). What Is the Formula for Charles' Law? Retrieved from https://www.thoughtco.com/formula-for-charles-law-604281 Helmenstine, Todd. "What Is the Formula for Charles' Law?" ThoughtCo. https://www.thoughtco.com/formula-for-charles-law-604281 (accessed November 22, 2017).