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.

When a gas is trapped inside a container which has a fixed size (its volume cannot change) and the gas is heated, the particles will gain kinetic energy which will make them move faster.

The temperature of the gas is proportional to the average kinetic energy of its molecules. Faster moving particles will collide with the container walls more frequently and with greater force. This causes the force on the walls of the container to increase and so the pressure increases.

If the temperature of the gas is measured on the Kelvin scale, the pressure is proportional to the temperature.

From this we can derive the equation

\[\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\]

where:

P_{1} is the initial pressure

T_{1} is the initial temperature

P_{2} is the final pressure

T_{2} is the final temperature

All the temperatures are measured on the Kelvin scale of temperature.

This equation is true as long as the volume and mass of the gas are constant

- Question
A car tyre contains air at 1.25 × 10

^{5}Pa when at a temperature of 27°C. Once the car has been running for a while, the temperature of the air in the tyre rises to 42°C. If the volume of the tyre does not change, what is the new pressure of the air in the tyre?First convert the temperatures into kelvin.

T

_{1}= 27 + 273 = 300 KT

_{2}= 42 + 273 = 315 KNow calculate the new pressure

T

_{1}= 300 KT

_{2}= 315 KP

_{1}= 1.25 × 10^{5}Pa\[\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\]

Therefore

\[P_{2} = \frac{P_{1}T_{2}}{T_{1}}\]

\[P_{2} = \frac{(1.25 \times 10^5 \times 315)}{300}\]

The new pressure is 1.31 × 10

^{5}Pa.