SITEMAP   School-college Physics Notes: Thermal energy 4.8 Explaining gas pressure

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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

Doc Brown's Physics exam study revision notes

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

• 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

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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