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# 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

P 1 V 1 = P 2 V 2 (1b)

or

P 1 / P 2 = V 2 / V 1 (1c)

where

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

V = volume (m 3 , ft 3 ...)

### Example - Final Pressure when Compressing an Air Volume

A gas with volume 1 m 3 and initial pressure 2 MPa is compressed to final volume 0.5 m 3 . With constant temperature the required final pressure can be calculated as

P 2 = P 1 V 1 / V 2

= (2 MPa) (1 m 3 ) / (0.5 m 3 )

= 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:

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

= 0.09 ft 3

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

V 2 = P 1 V 1 / P 2

= (114.7 psia) (0.09 ft 3 ) /  (14.7 psia)

= 0.7 ft 3

## Related Topics

### • Gases and Compressed Air

Air, LNG, LPG and other common gas properties, pipeline capacities, sizing of relief valves.

## Related Documents

### Charles' Law

Volume of an ideal gas vs. temperature.

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