Boyle's Law (Mariotte's Law)
The volume of an ideal gas vs. pressure.
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
P1V1 = 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 = P1V1 / 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
