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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
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
-
 All
particles have mass and their movement gives them kinetic energy and
momentum.
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The particles in a gas are in constant
random motion - random direction, variety of velocities and kinetic
energies.
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Although the collisions occur at random
in any direction, there is a resultant force acting at right angles to
any surface.
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There will always be a gas pressure,
unless a container is under vacuum, no particles - no collisions - no
pressure!
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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.
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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.
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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.
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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.
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pressure x volume = a constant
(at constant temperature)
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pV = constant
(known as Boyle's Law)
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p = pressure in pascals (Pa =
N/m2),
V = volume (m3)
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You can connect two pressure and
two volumes by the simple equation
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p1 x V1
= p2 x V2
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where 1 represent the original
conditions, and 2 the final situation if an enforced change of p1
or V1 is made.
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Examples of simple gas
calculations
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(i) 5 m3 volume of
a gas at a pressure 101 300 Pa was compressed to a volume of 2.8
m3.
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Calculate the final
pressure
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p1 x V1
= p2 x V2
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rearranging gives p2
= (p1 x V1) / V2
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p2 = (101 300
x 5) / 2.8 = 180893 Pa
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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INDEX of notes on Particle model theory
state changes and latent heat
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