Pressure in liquids and gases - Cambridge OCR 21st CenturyGases

The particles in a gas are moving very quickly in random directions. The speeds of the particles vary but, on average, they move quicker than they do in liquids or solids.

This means that it does not take long for a gas to spread out to fill its entire container. The smell of an air freshener can spread all around a room very quickly.

Gas pressure

Since the particles in a gas are moving fast and randomly, collisions occur frequently. These collisions may be between two particles, between a particle and the wall of the container, or between a particle and something else in the container.

The force acting on the container due to these collisions is at right angles to the container.

For example, the collisions caused by a gas trapped inside a balloon cause forces to act outwards in all directions, giving the balloon its shape.

A person standing in a room full of air is constantly being hit by the particles of the gases that make up the air.

The pressure from gas molecules may increase if there are more molecules colliding each second or if the molecules are moving faster.

Pressure and volume

If a balloon is squeezed, it will get smaller. If the pressure squeezing the balloon is increased, the volume will decrease.

The Irish scientist, Robert Boyle, originally investigated this relationship in the 17th Century. Boyle carried out an experiment that gave one of the first pieces of experimental evidence for the particle theory.

By pouring mercury into a J-shaped tube that was sealed at one end, Boyle was able to trap a bubble of air. He then poured more mercury in slowly and watched what happened to the volume of the air bubble.

The higher the column of mercury in the left hand side of the tube, the greater the pressure the trapped air was experiencing and the smaller the bubble became.

For a fixed mass of gas at a constant temperature:

pressure × volume = constant

This is when:

• pressure (p) is measured in pascals (Pa)
• volume (V) is measured in metres cubed (m³)

If the temperature of a gas stays the same, the pressure of the gas increases as the volume of its container decreases. This is because the same number of particles collides with the walls of the container more frequently as there is less space. However, the particles still collide with the same amount of force.

The change in volume or pressure for gas at a constant temperature can be calculated using the equation:

p₁ and V₁ are the pressure and volume before either are changed, p₂ and V₂ are the pressure and volume after the change.

Example

A gas occupies a volume of 0.50 m³ at a pressure of 100 Pa. Calculate the pressure exerted by the gas if it is compressed to a volume of 0.25 m³. Assume that the temperature and mass of the gas stay the same.