Boyle's Law (Mariotte's Law)

Boyle's law (Mariotte's Law) states that in a perfect gas where mass and temperature are kept constant - the volume of the gas varies inversely with the absolute pressure.

Boyle's law can be expressed as

PV = constant                                   (1)

or

P₁ V₁ = P₂V₂(1b)

or

P₁ / P₂= V₂/ V₁ (1c)

where

P = absolute pressure (Pa, psi...)

V = volume (m³, ft³ ...)

Example - Final Pressure when Compressing an Air Volume

A gas with volume 1 m³ and initial pressure 2 MPa is compressed to final volume 0.5 m³ . With constant temperature the required final pressure can be calculated as

P₂= P₁ V₁ / V₂

= (2 MPa) (1 m³ ) / (0.5 m³ )

= 4 MPa

Example - Final Volume when Compressed Air is Expanded to Standard Conditions

Air is compressed to 114.7 psia in a 4 inches schedule 40 steel pipe . Inside diameter of the pipe is 4.03 inches and the compressed air volume in one foot of the pipe can be calculated as:

V₁ = π (((4.03 in) / (12 in/ft)) / 2)²(1 ft)

= 0.09 ft³

Expansion of the compressed air to a normal pressure of 14.7 psia can be calculated by rearranging Boyle's law:

V₂= P₁ V₁ / P₂

= (114.7 psia) (0.09 ft³ ) /  (14.7 psia)

= 0.7 ft³