What Is the Formula for the Combined Gas Law?

Relating Pressure, Volume, and Temperature of a Gas

One practical application of the combined gas law is predicting cloud formation under conditions of changing pressure, temperature, and volume.
One practical application of the combined gas law is predicting cloud formation under conditions of changing pressure, temperature, and volume. Yagi Studio / Getty Images

The combined gas law ties together Boyle's law, Charles' law, and Gay-Lussac's law. Basically, it states that as long as the amount of gas doesn't change, the ratio between the pressure-volume and temperature of a system is a constant. There is no "discoverer" of the law as it simply puts together concepts from other cases of the ideal gas law.

The Combined Gas Law Formula

The combined gas law examines the behavior of a constant amount of gas when pressure, volume and/or temperature is allowed to change.

The simplest mathematical formula for the combined gas law is:

k = PV/T

In words, the product of pressure multiplied by volume and divided by temperature is a constant.

However, the law is usually used to compare before/after conditions. The combined gas law is expressed as:

PiVi/Ti = PfVf/Tf

where Pi = initial pressure
Vi = initial volume
Ti = initial absolute temperature
Pf = final pressure
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.

It is also important to keep your units constant. Do not use pounds per square inch for pressures initially to find Pascals in the final solution.

Uses of the Combined Gas Law

The combined gas law has practical applications in situations where pressure, volume, or temperature can change. It is used in engineering, thermodynamics, fluid mechanics, and meteorology.

For example, it can be used to predict cloud formation and the behavior of refrigerants in air conditioners and refrigerators.