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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

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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.

  • (i) Consider a steel cylinder of gas - a rigid containing wall

    • 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.

    • The effect of increasing the amount of gas in the cylinder

    • 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.

      • 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.

      • 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.

      • See also P-V-T pressure-volume-temperature gas laws and calculations

    • If the internal and external pressures are not balanced, that's no problem with a strong steel walled cylinder!

      • After all, we store gases at high pressure in steel cylinders e.g. butane gas for heating.

    • The effect of increasing the temperature of the gas in a cylinder

    • 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.

    • 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.

  • (ii) Consider a balloon of gas - a flexible containing wall

    • 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.

      • If the external pressure is greater than the internal pressure the balloon will decrease in volume (size).

      • If the internal pressure is greater than the external pressure the balloon will increase in volume (inflate).

    • To blow up the balloon you blow in with a force greater than atmospheric pressure to create the volume of trapped gas.

    • The size of the balloon is then determined by how much air you have blown in and the ambient atmospheric pressure.

    • 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.

    • BUT, as you observe with a blown-up balloon, it doesn't seem to be expanding or contracting.

    • The reason being that the external air particle impacts on the outside surface of the balloon create an opposing and equal balancing pressure.

    • 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.

      • 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.

      • Remember, increasing the volume of a gas at constant temperature decreases the pressure (pV = constant).

      • The pressure you create initially when blowing up the balloon, must decrease as it expands - less particle impacts per unit area.

      • 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.

    • 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.

      • Therefore the pressure increases and the balloon expands.

      • 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.

      • 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.

    • 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.

      • 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.

      • The helium balloon will continue to expand as long as the external pressure is less than the internal pressure.

      • It will stop expanding when the internal balloon pressure drops to the same as the external pressure.

      • However, since it is filled with less dense helium, it will continue to rise and rise!

  • (iii) The same arguments apply to blowing up a bicycle tyre or motor car tyre or anything else!

    • 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!

      • More on compression and work done in the next section.

    • When you seal the end of a gas syringe (like you see in chemistry), with your hand  and press the plunger in.

      • 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.

      • 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