# 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*. With constant temperature the required final pressure can be calculated as

^{ 3 }

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.