Physics

1.8 - Pressure & Volume

5 min

Compressing a gas

Filling a dive cylinder

note 1 of 2

The pressure-volume formula (pV = constant)

For a fixed mass of gas at a constant temperature:

$p V = constant$

This can be written to compare starting and final states:

$p_{1} V_{1} = p_{2} V_{2}$

Where:

$p_{1}, p_{2}$ = Pressure, in pascals (Pa)
$V_{1}, V_{2}$ = Volume, in cubic metres (m³)

Pressure-volume graph

A graph of pressure against volume is a curve that falls steeply at first and levels off ( $p \propto \frac{1}{V}$ ).
This formula only holds for a fixed mass of gas at a constant temperature.

note 2 of 2

Worked example - New pressure with pV = constant

A fixed mass of gas has a volume of 0.50 m³ at a pressure of 200,000 Pa. It's slowly compressed to a volume of 0.20 m³ at constant temperature. Calculate its new pressure.

Step 1 - Find the constant from the starting values

$p V = 200,000 \times 0.50 = 100,000$

Step 2 - Rearrange $p_{1} V_{1} = p_{2} V_{2}$ for the new pressure

$p_{2} = \frac{p_{1} V_{1}}{V_{2}} = \frac{100,000}{0.20}$

Step 3 - Calculate

$p_{2} = 500,000 Pa$

end of notes

Key points to remember

The pressure-volume formula (pV = constant)

For a fixed mass of gas at a constant temperature:

p V = constant

This can be written to compare starting and final states:

$p_{1} V_{1} = p_{2} V_{2}$

Where:

p_{1}, p_{2}

= Pressure, in pascals (Pa)

V_{1}, V_{2}

= Volume, in cubic metres (m³)

Pressure-volume graph

A graph of pressure against volume is a curve that falls steeply at first and levels off (

p \propto \frac{1}{V}

This formula only holds for a fixed mass of gas at a constant temperature.

Worked example - New pressure with pV = constant

A fixed mass of gas has a volume of 0.50 m³ at a pressure of 200,000 Pa. It's slowly compressed to a volume of 0.20 m³ at constant temperature. Calculate its new pressure.

Step 1 - Find the constant from the starting values

$p V = 200,000 \times 0.50 = 100,000$

Step 2 - Rearrange $p_{1} V_{1} = p_{2} V_{2}$ for the new pressure

$p_{2} = \frac{p_{1} V_{1}}{V_{2}} = \frac{100,000}{0.20}$

Step 3 - Calculate

$p_{2} = 500,000 Pa$

1.8 - Pressure & Volume

The pressure-volume formula (pV = constant)

Where:

Pressure-volume graph

Worked example - New pressure with pV = constant

Step 1 - Find the constant from the starting values

Step 2 - Rearrange p1V1=p2V2 for the new pressure

Step 3 - Calculate

Key points to remember

1.8 - Pressure & Volume

The pressure-volume formula (pV = constant)

Where:

Pressure-volume graph

Worked example - New pressure with pV = constant

Step 1 - Find the constant from the starting values

Step 2 - Rearrange p1V1=p2V2 for the new pressure

Step 3 - Calculate

Key points to remember

Step 2 - Rearrange $p_{1} V_{1} = p_{2} V_{2}$ for the new pressure

Step 2 - Rearrange $p_{1} V_{1} = p_{2} V_{2}$ for the new pressure