# 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

P_{1}V_{1}= P_{2}V_{2}(1b)

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}*