Combined Gas Law Formula, Definition with Examples

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In the first place, what is the combined gas law anyway? Well, as the name goes, it combines the three special cases of an ideal gas law i.e Boyles Law, Charles Law, and Gay-Lussac Law. In other words, it’s just a mere unification of three cases of Ideal Gas Laws.

On the other hand, when the three special cases i.e  Boyles Law, Charles Law, and Gay-Lussac Law are further blended with Avogadro’s Law; the final result becomes the Ideal Gas Law Of Thermodynamics.

Not to mention, there is no official founder of this law. However, the official statement of this gas law states

The ratio of the product of pressure-volume and the absolute temperature (in kelvins) of a system remains constant, as long as the amount of substance of gas remain unchanged


Unification Process for Combined Gas Law

Relationships between Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, combined and ideal gas law, with the Boltzmann constant kB = R / NA = n R / N (in each law, properties circled are constant and properties not circled are variable)/Credit: Wikimedia Commons

As I said above, this law is merely an alliance of three other gas laws that works when everything held constant, except temperature, pressure, and volume.

  • Boyles Law states that at a given temperature, the pressure of a given mass of a gas is inversely proportional to its volume.
  • Charles Law states that when the pressure of sample gas is held constant, the temperature and the volume will be directly related.
  • Gay Lussac Law states that when the volume of the sample gas is held constant, the temperature and pressure will be directly related.

Finally, when you fuse together Boyle’s, Charle’s, and Gay Lussac Law, we get the Combined Gas Law. In addition, when Combined Gas Law is further substituted with Avogadro’s Law; yields Ideal Gas Law.


Combined Gas Law Formula

According to the Combined gas law definition, the combined gas law formula can be represented in two different forms i.e Normal Form and Special Form. Let us take a look at both equations one by one:

Normal Form

Mathematically, We can represent this gas law as:

qquad {frac {PV}{T}}=k


P = Pressure of Gas
V = Volume of Gas
T = Temperature of Gas (in Kelvin)
k = Constant

Special Form

If we have to compare the same substance under two different conditions, then the combined gas law formula can be stated as:

qquad {frac {P_{1}V_{1}}{T_{1}}}={frac {P_{2}V_{2}}{T_{2}}}

P1 = Initial Pressure of Gas
V1 = Initial Volume of Gas
T1 = Initial Temperature of Gas
P2 = Final Pressure of Gas
V2 =Final Volume of Gas
T2 = Final Temperature of Gas


Combined Gas Law Example Problem

The initial volume of the gas is 10L and the final volume is 5L. Calculate the final pressure of the gas. Given that the initial temperature is 300K, the final temperature is 250k, and the initial pressure is 30K Pa.

Here, we will use the special form of the combined gas law formula i.e

qquad {frac {P_{1}V_{1}}{T_{1}}}={frac {P_{2}V_{2}}{T_{2}}}


P1 = 30 k pa
V1 = 10 L
T1 = 300 k
V2 = 5 L
T2 = 250 k
P2 =?

Now, putting all the given values in the above equation we get,

30 x 10/300 = P2 x 5/250

on solving,

Final pressure P2 = 50 k pa.

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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my career, and therefore I did my postgraduate degree in physics. Right now I am a loner (as ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every aspect of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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