Objectives:

• To review the concept that work is the transfer of energy by a force.
• To understand that doing work on a gas increases the internal energy on the particles and can cause an increase in the temperature of the gas.
• To be able to explain how, in a given situation e.g. a bicycle pump, doing work on an enclosed gas leads to an increase in the temperature of the gas.

A recap of work done?

Work done is a term used by physicists to explain how much energy is required to do something. In order to push a boulder up a hill you have to put energy in. This energy comes from your own chemical potential store (from consuming food). The reason you have to put this energy into the boulder is because gravity is pulling the boulder down to the lowest part of the hill, therefore you have to oppose gravity which you can do by exerting force on the boulder against gravity.

You are working on the boulder to get it up the hill… hence ‘work done on the boulder’

Work done is the defined as the force you apply on an object multiplied by the distance you push (or pull) that object through:

$W = Fd$

where;
$W$ is the work done, measured in joules, $J$
$F$ is the force, measured in newtons, $N$
$d$ is the distance the object moves through against the force, measured in metre, $m$

Linking work done to the particles in a system

Whenever work is done on a single particle, a force is applied to it to overcome fictional force. In the case of a gas, this force is continuously required to move it through a distance because of all the other gas particles in its way (air resistance). As you know however, energy is never created or destroyed.

Imagine that you were ridiculously small and had to push a single air particle through a volume of gas, you give it a little push and it moves but then slows down and comes to a stop (because of the friction/ air resistance). You realise you need to constantly exert a force of lets say $10 N$ to prevent it from slowing down. You manage to push the particle through a distance of a metre. Well the energy you personally have supplied is; $W = Fd$ and so $W = 10 \times 1 = 10 \ J$.

After your achievement of pushing this particle, you have lost $10 J of energy$, the particle however is no longer moving so have no kinetic energy, so where has this $10 J$ disappeared to?

The answer is in the potential energy stores of all the particles that collided with the one you were moving. Since the substance is a gas, this results in them all having increased kinetic energy stores. As mentioned on the previous page (the motion of particles in a gas), The temperature of the gas is related to the average energy in the kinetic energy stores of the gas particles. Therefore as work is done on a particle (or a system of particles) the average kinetic energy rises and as a result the overall temperature increases too.

The next video is something you will hopefully have seen in class (otherwise you can prove it by doing it at home). Place a balloon over the top of a glass bottle, if the bottle is then placed in cold or room temperature water, nothing happens. If instead the bottle is placed in hot water, the thermal energy conducts through the glass and to the air particles, this makes them heat up and increases their kinetic energy store. This results in the balloon inflating.

What do you think would happen if you kept swapping the balloon from the hot water to the cold water?

Would the balloon just keep inflating, then deflating and vice versa?

Using the knowledge learnt from above, you should now consider what the individual particles are doing as they flow into the balloon and then out of it again (as it keeps inflating and deflating). They will constantly be colliding with other gas particles and will inevitably increase their kinetic energy stores. In other words, if the process if repeated over and over, eventually the pure act of repetition will cause the balloon to eventually stay inflated due to the increase in the average kinetic energy. Watch the following video to see if this checks out:

The fact that work done on a gas can ultimately cause an increase in internal energy of a substance can be a real problem. Below are some questions, the answers to these are further down:

1. Explain how doing work on an enclosed gas in a given situation, eg a car tyre, leads to an increase in temperature of the gas.
2. Find out why gas cylinders may freeze if they are opened and the gas inside is allowed to escape too quickly.