Definition
Work done on a gas
Work done on a gas is the energy transferred to the gas when an external force pushes a surface inwards and reduces the volume of the gas.
Definition
Internal energy
Internal energy is the total kinetic energy and potential energy of all the particles in a system.
- Work is done whenever a force moves an object in the direction of that force, and the work done equals the energy transferred.
- Pushing a piston inwards against the pressure of a trapped gas moves the piston in the direction of the applied force, so work is done on the gas.
- This transfers energy mechanically rather than by heating, so the gas gains energy without ever being placed next to anything hotter than itself.
- The energy transferred is added to the internal energy of the gas, so the internal energy increases.
- The piston is moving towards the particles while this happens, so a particle that collides with it is struck by a surface coming to meet it.
- Each such particle therefore rebounds faster than it arrived, in the same way that a tennis ball leaves a moving racket faster than it leaves a stationary one.
- The average kinetic energy of the particles rises as a result, so the temperature of the gas rises.
- Compressing a gas quickly produces the largest temperature rise, because there is little time for energy to escape from the gas to its surroundings.
- Compressing the same gas very slowly gives almost no temperature rise, because the energy transferred leaks away to the surroundings as fast as it is supplied.
The bicycle pump
- Pushing the handle of a bicycle pump down applies a force to the piston and moves it along the barrel, so work is done on the air inside.
- The air is compressed into a smaller volume, and the energy transferred mechanically increases its internal energy.
- The average kinetic energy of the air particles increases, so the temperature of the air in the barrel rises.
- Energy is then transferred by conduction from the warm air to the metal barrel, which is why the pump feels noticeably warm after use.
- Pumping rapidly makes the barrel much warmer than pumping gently, because energy is being supplied faster than it escapes.
- Friction between the piston seal and the barrel adds a little to the warming, but the main cause is the work done in compressing the air.
- The same effect is used deliberately in a diesel engine, where air is compressed so sharply that it becomes hot enough to ignite the fuel without a spark.
When a gas does the work
- An expanding gas pushes a surface outwards and moves it, so the gas does work on its surroundings.
- The energy for that work comes out of the internal energy of the gas, so the internal energy falls.
- Particles bouncing off a surface that is moving away from them rebound more slowly than they arrived.
- The average kinetic energy of the particles therefore falls, so a rapidly expanding gas cools.
- Gas released from an aerosol can or from a bicycle tyre valve feels cold on the skin for exactly this reason.
- Both directions are mechanical energy transfers, so neither of them involves heating the gas or cooling it with a colder object.
Example
Why the pump barrel gets warm
- A cyclist pumps hard for thirty seconds and then finds that the barrel of the pump is warm to the touch.
- Each downstroke applies a force to the piston and moves it, so work is done on the air trapped in the barrel.
- That work transfers energy mechanically into the internal energy of the air.
- The average kinetic energy of the air particles increases, so the temperature of the air rises.
- The warm air is in contact with the metal barrel, so energy is transferred to the barrel by conduction and the barrel warms up.
- Pumping quickly rather than slowly makes the barrel hotter, because the energy is supplied faster than it can escape to the surroundings.
Exam technique
Building the explanation
- Use the phrase work is done on the gas, because this topic is about a mechanical transfer and the wording is credited.
- Follow the chain in order: work done on the gas, internal energy increases, average kinetic energy increases, temperature rises.
- Mention the conduction step when a question asks why the pump itself feels warm, since the barrel is warmed by the air rather than directly by the work.
- Say that the transfer is not by heating when a question contrasts this with warming something on a hob.
- Reverse every step of the same chain if the question is about an expanding gas cooling down.
Common Mistake
- Do not write that the gas is heated by the pump, because the energy is transferred by doing work rather than by heating.
- Do not put friction forward as the main reason the barrel warms, because the work done compressing the air is the larger effect.
- Do not say the particles get hotter, because temperature is a property of the gas as a whole rather than of one particle.
- Do not leave out the internal energy step, because the link from work done to temperature runs through it.
- Do not assume every compression raises the temperature noticeably, because a very slow compression lets the energy escape as fast as it arrives.
Self review
- Explain what is meant by doing work on a gas.
- Explain why doing work on a gas raises its temperature.
- Describe the full chain of energy transfer that makes a bicycle pump barrel warm.
- Explain why a fast compression warms a gas more than a slow one.
- Explain why gas released from an aerosol can feels cold.
- State the difference between transferring energy by heating and transferring it by doing work.
