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Thermal energy & particle theory: 4.9
Considering the
internal and external pressures of a container of gas e.g. a balloon and the
effect of changing the gas temperature on pressure
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
4.9
Considering the
internal and external pressures of a container of gas
Pressure in fluids
Fluids are materials that can flow
because the attractive forces between the particles are weak in liquids
and almost non-existent in gases.
Since the particles are free to move,
they collide with any surface they make contact with.
This produces a net resultant force
at 90o to the surface.
The basic formula for pressure is:
Pressure = Force normal to the
surface ÷ area of contact surface
P (Pa) = F (N)
÷ A (m2)
For more on liquid
fluid and atmospheric pressure see:
Pressure in liquid fluids and hydraulic
systems
Pressure &
upthrust in liquids, why
objects float/sink?, variation of atmospheric pressure with
height
However, here, I'm only concerned
with explaining more about gas pressure, using the model illustrated below
to describe, explain and quantify the behaviour of a gas.
The effects of changing
the amount or
temperature of a gas in a container
The particles in a gas are in constant
motion - flying around in all directions with frequent collisions (e.g.
in air the collision rate is 109/s !!!).
As already described, increasing the
temperature of a gas, increases the kinetic energy store of the gas
particles.
This is the kinetic energy of
movement from one place to another, its not vibrational kinetic energy.
In fact, the average kinetic energy of
the gas particles is directly related to the temperature.
The higher the gas temperature, the
greater the average kinetic energy of the particles,
and the cooler the gas the lower the
average kinetic energy of the particles.
As you increase temperature, the
average speed of the particles increases and the average kinetic
energy - remember the kinetic energy formula:
KE = ½mv2
(m = mass of particle, v = velocity of particle)
We can now discuss particular 'pressure'
situations and the starting point is the fact that ...
... gas pressure is caused by the
collision of particles with any surface ...
... because when particles collide
with a surface, the exert a force on that surface.
Pressure is related to the number or
force of particle impacts per unit area of the surface.
The more impacts or more forceful
impacts on the surface, the greater the pressure created.
Increasing temperature of a gas
actually increases both.
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(i) Consider a steel cylinder of gas -
a rigid containing wall
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When a gas is contained a rigid vessel
you can pump lots of gas in to a pressure much higher than the surrounding
atmospheric pressure.
-
Steel cylinders are used in industry to
store gaseous chemicals and in the home we used cylinders of hydrocarbon
gases for heating and cooking.
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The effect of increasing
the amount of gas in the cylinder
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The more gas you force in, the greater
the internal pressure because of the increase in the number of particle impacts per
unit area - a greater concentration of particles means more impacts on
the same surface area.
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For a given cylinder, the gas volume is
constant and the pressure is proportional to the amount of gas pumped in at
constant temperature.
-
Pressure and volume are inversely
proportional to each other.
-
P x V = constant, P =
pressure in Pa (pascals), V = volume in m3.
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At constant temperature, increasing the
volume decreases pressure because the collisions are more spread out over
the same area - less particle collisions per unit area.
-
At constant temperature, decreasing the
volume increases pressure because the collisions are more concentrated over
the same area - more particle collisions per unit area.
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See also
P-V-T pressure-volume-temperature gas
laws and calculations
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If the internal and external pressures are
not balanced, that's no problem with a strong steel walled cylinder!
-
The effect of increasing the
temperature of the gas in a cylinder
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If the cylinder is heated it will expand
a little, but this will not compensate for the increase in gas pressure as
the gas tries to expand.
-
If the cylinder and its contents increase
in temperature, then the thermal energy store is increased as the gas
particles gain kinetic energy.
-
This increase in the particle kinetic
energy store increases the rate of particle collision AND the force of the
particle impacts on the container surface - thus raising the pressure with
increase in temperature.
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This is quite a dangerous situation that
fire-fighters face when tackling a fire at a factory where gas cylinders are
used - the high temperatures and high pressures created in the gas cylinders
will cause them to explode violently.
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(ii) Consider a balloon of gas - a
flexible containing wall
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If the sides of a gas
container are 'flexible' (e.g. like a balloon), the volume will only
be constant when the internal and external pressures are equal.
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If the external pressure is greater than
the internal pressure the balloon will decrease in volume (size).
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If the internal pressure is greater than
the external pressure the balloon will increase in volume (inflate).
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To blow up the balloon you blow in
with a force greater than atmospheric pressure to create the volume of
trapped gas.
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The size of the balloon is then determined by how much air
you have blown in and the ambient atmospheric pressure.
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The pressure of a gas in a balloon produces a net outward force at right angles to the
container surface due to the internal gas particle impacts.
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BUT, as you observe with a blown-up
balloon, it doesn't seem to be expanding or contracting.
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The reason being that the external air
particle impacts on the outside surface of the balloon create an opposing
and equal balancing pressure.
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By blowing in air you increase the
internal pressure and force the balloon to expand, pushing the rubber skin
outwards, until the internal and external pressures are equal when expansion
will stop.
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When you blow in you are increasing the
number of particle impacts per unit area of the internal surface to create
the greater outward acting force.
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Remember, increasing the volume of a gas
at constant temperature decreases the pressure (pV = constant).
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The pressure you create initially when
blowing up the balloon, must decrease as it expands - less particle impacts
per unit area.
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If you let air out of the balloon, or it
leaks out, there are less particle impacts per unit area of surface and the
pressure is reduced, so the greater external pressure causes the balloon to
contract until the volume is reduced creating a pressure equal to the
external atmospheric pressure.
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If a balloon inflated with air is
heated, the gas particles inside will increase in kinetic energy
producing more collisions and more forceful collisions - increase in net
force acting on the surface.
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Therefore the pressure increases and the
balloon expands.
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BUT, the expansion spreads out the
collisions (which decreases pressure - less force per unit area), so the
balloon only expands until the internal pressure equals the external
pressure of the cooler air.
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When the balloon cools down it will
decrease in size, less forceful particle collisions, balloon shrinks until,
again, the internal and external pressures are equal.
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When helium weather balloons are
released, they rapidly rise up through the atmosphere and greatly expand
because atmospheric pressure significantly decreases with increase in
height above the earth's surface.
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As the external pressure decreases
(less particle impacts per unit area) the internal pressure is greater (more
impacts) and so the greater number of internal impacts per unit area force the volume of
the gas in the balloon to increase.
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The helium balloon will continue to
expand as long as the external pressure is less than the internal pressure.
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It will stop expanding when the internal
balloon pressure drops to the same as the external pressure.
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However, since it is filled with less
dense helium, it will continue to rise and rise!
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(iii) The same arguments apply to blowing
up a bicycle tyre or motor car tyre or anything else!
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Any increases in the external
pressure from a pump system will allow expansion of the tyre if it
exceeds the internal pressure inside the tyre - otherwise no further
inflation!
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When you seal the end of a gas
syringe (like you see in chemistry), with your hand and press the
plunger in.
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You can compress the air to create a greater gas pressure
than the external atmospheric pressure. BUT, although the pressures are
not initially balanced, as in the case of blowing up balloon, its your extra
muscle force that helps create the balancing force.
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internal pressure in syringe =
atmospheric pressure + pressure from muscle force
INDEX of notes on Particle model theory
state changes and latent heat
Keywords, phrases and learning objectives for particle models, internal and
external gas pressures and temperature
Be able to explain gas pressure in terms of a particle model and apply
the theory to explain various internal and external 'pressure'
contexts e.g. gas storage cylinders, inflated
balloon, a bicycle tyre.
Be able to explain the effect of changing the gas temperature on pressure
using the particle theory model.
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INDEX of notes on Particle model theory
state changes and latent heat
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