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Thermal energy & particle theory: 4.8 Using the particle model of a gas to explain gas pressure and pressure-volume calculations

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


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

  • (c) doc bAll 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.

    • Boyle's Law, P versus V graphFrom 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


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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