Temperature can be measured using the Celsius and Kelvin scales. Gas pressure increases with temperature. Equations explain the relationship between pressure, temperature and volume in gases.

Decreasing the volume of a gas increases the pressure of the gas. An example of this is when a gas is trapped in a cylinder by a piston. If the piston is pushed in, the gas particles will have less room to move as the volume the gas occupies has been decreased.

Because the volume has decreased, the particles will collide more frequently with the walls of the container. Each time they collide with the walls they exert a force on them. More collisions mean more force, so the pressure will increase.

When the volume decreases, the pressure increases. This shows that the pressure of a gas is inversely proportional to its volume.

This is shown by the following equation - which is often called **Boyle’s law**. It is named after 17th century scientist
Robert Boyle.

P_{1}V_{1} = P_{2}V_{2}

where:

P_{1} is the initial pressure

V_{1} is the initial volume

P_{2} is the final pressure

V_{2} is the final volume

It can also be written as:

pressure_{1} × volume_{1} = pressure_{2} × volume_{2}

Note that volume is measured in metres cubed (m^{3}) and temperature in kelvin (K).

It means that for a gas at a constant temperature, pressure × volume is also constant. So increasing pressure from pressure_{1} to pressure_{2} means that volume_{1} will change to volume_{2}, providing the temperature remains constant.

- Question
A sealed syringe contains 10 × 10

^{-6}m^{3}of air at 1 × 10^{5}Pa. The plunger is pushed until the volume of trapped air is 4 × 10^{-6}m^{3}. If there is no change in temperature what is the new pressure of the gas?P

_{1}= 1 × 10^{5}PaV

_{1}= 10 × 10^{-6}m^{3}V

_{2}= 4 x 10^{-6}m^{3}P

_{1}V_{1}= P_{2}V_{2}Therefore:

\[p_{2} = \frac{p_{1}{V_{1}}}{V_{2}}\]

\[p_{2} = \frac{{1 \times 10^{5} \times 10 \times 10^{-6}}}{4 \times 10^{-6}}\]

P

_{2}= 2.5 × 10^{5}PaThe new pressure in the syringe is 2.5 × 10

^{5}Pa

Charles’ law describes the effect of changing temperature on the volume of a gas at constant pressure. It states that:

\[volume_{1} = volume_{2} \times \frac{temperature_{1}}{temperature_{2}}\]

\[V_{1} = V_{2} \times \frac{T_{1}}{T_{2}}\]

where:

V_{1} is the initial volume

V_{2} is the final volume

T_{1} is the initial temperature

T_{2} is the final temperature

Note that volume is measured in metres cubed (m^{3}) and temperature in kelvin (K).

This means that if a gas is heated up and the pressure does not change, the volume will. So for a fixed mass of gas at a constant pressure, volume ÷ temperature remains the same.