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4.8 The particle model of a gas - particle motion and gas pressure calculations

Great animation, BUT in reality ...

this happens 10⁹ times faster than this animation (from Wikipedia)

• All particles have mass and their movement gives them kinetic energy and momentum.

• The particles in a gas are in constant random motion - random direction, variety of velocities and kinetic energies.

• Although the collisions occur at random in any direction, there is a resultant force acting at right angles to any surface.

• There will always be a gas pressure, unless a container is under vacuum, no particles - no collisions - no pressure!

• When the fast moving gas particles collide with a surface, their millions of impacts create a force that we measure as gas pressure - the total force of impacts per unit area.

• The particles collide with the container surface completely at random and impact at every angle, BUT, the effect is to create a net force at right angles to the surface - gas pressure!

• The more forceful the collisions on a surface or the greater the number of collisions per unit area of surface, the greater the pressure, assuming the gas volume keeps constant.

  • If the temperature is kept constant and the volume increased, the impacts are more spread out and less frequent per unit area, so the gas pressure decreases.

  • Conversely, if a gas is compressed into a smaller volume at constant temperature, the number of impacts per unit area increases, so the pressure increases.

  • If the sides of a gas container are 'flexible' (e.g. balloon), the volume will only be constant when the internal and external pressures are equal.

  • From measurements of volumes and pressure of gases at constant pressure, a numerical inverse law can be formulated - see graph on right.

  • pressure x volume = a constant (at constant temperature)

  • pV = constant (known as Boyle's Law)

  • p = pressure in pascals (Pa = N/m²), V = volume (m³)

  • You can connect two pressure and two volumes by the simple equation

  • p₁ x V₁ = p₂ x V₂

  • where 1 represent the original conditions, and 2 the final situation if an enforced change of p₁ or V₁ is made.

  • Examples of simple gas calculations

  • (i) 5 m³ volume of a gas at a pressure 101 300 Pa was compressed to a volume of 2.8 m³.

    • Calculate the final pressure

    • p₁ x V₁ = p₂ x V₂

    • rearranging gives p₂ = (p₁ x V₁) / V₂

    • p₂ = (101 300 x 5) / 2.8 = 180893 Pa

  • (ii) 10m³ of gas at a pressure of 100 000 Pa was compressed to a pressure of 300 000 Pa.

    • Calculate the final volume of the gas

    • p₁ x V₁ = p₂ x V₂

    • rearranging gives V₂ = (p₁ x V₁) / p₂

    • V₂ = (100 000 x 10) / 300 000 = 3.33 m³

You can use other units for P and V, but make sure the units used are the same for the two P values of V values!

For more gas calculation see P-V-T pressure-volume-temperature gas laws and calculations

INDEX of notes on Particle model theory state changes and latent heat

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Key points Thermal energy & particle models - gas pressure and Boyle's law calculations

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

A comprehensive set of summary revision notes on Gas Pressure and Boyle’s Law Calculations, explained using particle theory, and tailored to the GCSE/IGCSE Physics specifications for WJEC, CCEA, CIE, AQA, Edexcel, and OCR.

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Gas Pressure Explained by Particle Theory

Particle Theory Basics

• Gases consist of particles in constant, random motion.
• These particles collide with the walls of their container.
• Each collision exerts a tiny force; the total force per unit area is the gas pressure.

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Factors Affecting Gas Pressure

Factor	Effect on Pressure	Explanation
Temperature ↑	Pressure ↑ (if volume constant)	Particles move faster → more frequent and forceful collisions
Volume ↓	Pressure ↑ (if temperature constant)	Particles have less space → more frequent collisions
Number of Particles ↑	Pressure ↑	More particles → more collisions

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Boyle’s Law: Pressure–Volume Relationship

Statement

For a fixed mass of gas at constant temperature, the pressure is inversely proportional to volume.

Formula

• p₁ x V₁ = p₂ x V₂

• 1 = indicates initial pressure and volume
• 2 = indicates final pressure and volume
• Units: Pressure in Pa, Volume in m³

Rearranging the Formula

To find e.g. P₂:

p₂ = (p₁ x V₁) / V₂

Example

A gas at 100 kPa occupies 2.0 m³. What is the pressure when compressed to 1.0 m³?

P = 100 x 2.0 / 1.0} = 200 kPa

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Required Practicals (varies by board)

• Investigate how pressure changes with volume using a syringe and pressure sensor.
• Plot pressure versus volume graph → curve shows inverse relationship.

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Exam Tips about gas pressure and calculations

• Use consistent units (Pa, m³).
• Check assumptions: mass and temperature must remain constant.
• Expect curved graph for pressure versus volume.
• Know that Boyle’s Law only applies to gases.
• Be ready to rearrange and apply the gas pressure formula.

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Common Misconceptions about gas pressure and calculations

• Pressure and volume are directly proportional → They’re inversely proportional.
• Boyle’s Law applies when temperature changes → It only applies at constant temperature.
• Particles slow down when compressed → They don’t unless temperature changes.
• Pressure is caused by particle size → It’s caused by collisions, not size.

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Keywords, phrases and learning objectives for particle models and gas pressure.

Be able to use the particle model of a gas to explain gas pressure and the relationship between pressure-volume.

Be able to calculations using Boyle's Law equation using the appropriate units.

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WHAT NEXT?

TOP of page

INDEX for physics notes on particle model theory, state changes,  latent heat, heating/cooling curves

INDEX of all my THERMAL ENERGY notes

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