Pressure & Volume (OCR GCSE Physics A (Gateway))

Pressure Changes in a Gas

• If the temperature of a gas remains constant, the pressure of the gas changes when it is:

  • Compressed – decreases the volume which increases the pressure

  • Expanded – increases the volume which decreases the pressure

Pressure increases when a gas is compressed

• Similarly, a change in pressure can cause a change in volume

• A vacuum pump can be used to remove the air from a sealed container

• The diagram below shows the change in volume to a tied up balloon when the pressure of the air around it decreases:

• Therefore, if the gas is compressed, the molecules will hit the walls of the container more frequently

• This creates a larger overall net force on the walls which increases the pressure

Pressure on a Surface

• As the gas particles move about randomly they collide with the walls of their containers

• These collisions produce a net force at right angles to the wall of the gas container (or any surface)

• Therefore, a gas at high pressure has more frequent collisions with the container walls and a greater force

  • Hence the higher the pressure, the higher the force exerted per unit area

Gas molecules bouncing off the walls of a container

• It is possible for someone to experience this force by closing their mouth and forcing air into their cheeks

• The strain on the cheeks is due to the force of the gas particles pushing at right angles to the cheeks

Pressure & Volume

• In a gas, the molecules are widely spread

• This makes the gas easy to expand and compress

• Changing the pressure acting on the gas will compress it or allow it to expand if the temperature is kept constant

• When a gas is compressed, the volume is decreased

  • The density of the gas increases, since the size of the container has decreased but the number of molecules has remained the same

  • This allows more frequent collisions of the molecules on the container wall

  • This means they hit the walls with a greater force and therefore increases the pressure

• When a gas expands, the volume is increased

  • This causes a decrease in pressure

Decreasing the volume increases the pressure of molecules at the same temperature

• Therefore, in summary:

  • When the volume decreases (compression), the pressure increases

  • When the volume increases (expansion), the pressure decreases

• The key assumption is that the temperature and the mass (and number) of the particles remains the same

Calculating Changes in Pressure & Volume

• For a fixed mass of a gas held at a constant temperature:

pV = constant

• Where:

  • p = pressure in pascals (Pa)

  • V = volume in metres cubed (m³)

• This means that the pressure and volume are inversely proportional to each other

  • When the volume decreases (compression), the pressure increases

  • When the volume increases (expansion), the pressure decreases

• This is because when the volume decreases, the same number of particles collide with the walls of a container but more frequently as there is less space

  • However, the particles still collide with the same amount of force meaning greater force per unit area (pressure)

• The key assumption is that the temperature and the mass (and number) of the particles remains the same

• This equation can also be rewritten for comparing the pressure and volume before and after a change in a gas:

P₁V₁ = P₂V₂

• Where:

  • P₁ = initial pressure in pascals (Pa)

  • V₁ = initial volume in metres cubed (m³)

  • P₂ = final pressure in pascals (Pa)

  • V₂ = final volume in metres cubed (m³)

Initial pressure and volume, P₁ and V₁, and final pressure and volume, P₂ and V₂