The combined gas law is the combination of three other gas laws, each of which relates two thermodynamic variables. By combining them into one equation, you can quantify the relationship between all three thermodynamics variables: pressure, temperature and volume. This is extremely useful in chemistry and physics for systems that involve the use of these three independent variables.
The combined gas law has many applications, especially in heating and cooling (like in the production of air conditioning units) and in meteorology (understanding the formation of clouds). It was created out of a combination of three earlier gas laws, that were realized as 18th century scientists began to better understand the relationships between pressure, volume and temperature in gases.
The first law included in the combined gas law is Boyle's law, which states that the product of the pressure and the volume of a gas system is held constant. To increase the pressure, the volume must be decreased. If the volume is increased, the pressure will decrease. It's a fairly straightforward observation that generally holds true.
Boyle's Law: P x V = k
The second law is Charles's law, which holds that the volume of a system is proportional to the temperature.
Charles's Law: V = k x T
The last law included in the combined gas law is Gay-Lussac's law, which relates pressure to temperature the same way that Charles's law related volume to temperature. The pressure of a system is proportional to the temperature.
Gay-Lussac's Law: P = k x T
Simple and careful algebra allows for the combining of these three equations into what is known as the combined gas law.
Combined Gas Law: P x V = K x T
Which can be rewritten as a combination of pressure, volume and temperature to give: (P x V) / T = k
It is worth noting the difference between the combined gas law and the ideal gas law. The combined gas law does not include Avogadro's law, which relates the total number of gas atoms in a container to the volume of the container. By including the relationship of moles to volume in the combined gas law, you get an even more complete understanding of gas physics, known as the ideal gas law.
Avogadro's Law: V = N x k
Ideal Gas Law: P x V = N x R x T
(Where R is an ideal gas constant for correcting units.)