The Combined Gas Equation

At this point, for each of the three gas laws, we have kept one aspect constant, but this is not a realistic representation of the real world. In order to fully explain the changes that occur within a gas in real life, the three separate formulae must be combined to give a combined Gas Equation.

Recap of the Three Gas Laws

Boyle's Law - Pressure v Volume

Charles' Law - Volume v Temperature

Gay-Lussac's Law - Pressure v Temperature

In order to generate the above formulae we had to set each to be equal to some constant in order to convert from a proportional relationship. This means that if we arrange each formula to be equal to this constant value, we can combine them all to form the combined formula:-

The above formula allows us to tackle any given problem covering any of the gas laws.

Example 1 -

In a car engine, air and fuel are drawn into a cylinder at atmospheric pressure ( 1.01x105 Pa ) at a temperature of 40°C. The volume of the cylinder is 200 cm3. During the compression, the air and fuel mixture is compressed into a volume of 20 cm3 at a pressure of 4.00x106 Pa. Find the temperature of the air / fuel mixture after compression.

P1 = 1.01x105 Pa

P2 = 4.00x106 Pa

V1 = 200 cm3

V2 = 20 cm3

T1 = 40°C = 40+273 = 313 K

T2 = ?

( P1 x V1 ) / T1 = ( P2 x V2 ) / T2

( 1.01x105 x 200 ) / 313 = ( 4.00x106 x 20 ) / T2

T2 = 1240 K