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Boyle's Law (Mariotte's Law)

The volume of an ideal gas vs. pressure.

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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)


P1V1 = 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 = 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

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