Physics

4.2 - Pressure, Volume & Temperature

6 min

Compressing a gas

Filling a dive cylinder

note 1 of 2

Boyle's Law and the combined gas relationship

For a fixed mass of gas:

$\frac{p V}{T} = constant$

Where:

$p$ = Pressure, in pascals (Pa)
$V$ = Volume, in cubic metres (m³)
$T$ = Temperature, in kelvin (K)

Temperature must be in kelvin (K). To convert from degrees Celsius to kelvin, add 273. At constant temperature, $p V = constant$ (Boyle's Law), so pressure and volume are inversely proportional.

note 2 of 2

Worked example - Using pV/T = constant

A fixed mass of gas has a volume of 0.0030 m³ at a pressure of 100,000 Pa and a temperature of 300 K. It's compressed to a volume of 0.0020 m³ and heated to 400 K. Calculate its new pressure.

Step 1 - Write the relationship as a before-and-after comparison

$\frac{p_{1} V_{1}}{T_{1}} = \frac{p_{2} V_{2}}{T_{2}}$

Step 2 - Rearrange for the new pressure

$p_{2} = \frac{p_{1} V_{1} T_{2}}{T_{1} V_{2}}$

Step 3 - Substitute the values and calculate

$\begin{matrix} p_{2} & = \frac{100,000 \times 0.0030 \times 400}{300 \times 0.0020} \\ = 200,000 Pa \end{matrix}$

key terms

TermDefinition

Boyle's lawFor a fixed mass of gas at a constant temperature, the pressure and volume are inversely proportional.

Inversely proportionalA relationship between two quantities where their product stays constant, so doubling one halves the other.

end of notes

Key points to remember

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4.3 - Changes of StateNext up