Combined gas law

The combined gas law is a gas law that combines Charles's law, Boyle's law, and Gay-Lussac's law. There is no official founder for this law; it is merely an amalgamation of the three previously discovered laws. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other as long as pressure is held constant. Boyle's law asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally, Gay-Lussac's law introduces a direct proportionality between temperature and pressure as long as it is at a constant volume. The inter-dependence of these variables is shown in the combined gas law, which clearly states that:

This can be stated mathematically as:

where:

For comparing the same substance under two different sets of conditions, the law can be written as:

The addition of Avogadro's law to the combined gas law yields the ideal gas law.

Boyle's Law states that the pressure-volume product is constant:

Charles's Law shows that the volume is proportional to the absolute temperature:

Gay-Lussac's Law says that the pressure is proportional to the absolute temperature:

where P is the pressure, V the volume and T the absolute temperature of an ideal gas.

By combining (1) and either of (2) or (3), we can gain a new equation with P, V and T. If we divide equation (1) by temperature and multiply equation (2) by pressure we will get:

As the left-hand side of both equations is the same, we arrive at

which means that

Substituting in Avogadro's Law yields the ideal gas equation.

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