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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)


P1 V1 = P2V2(1b)


P1 / P2= V2/ V1 (1c)


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

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