Energy and Temperature

First of all I am going to talk a bit about energy. It is not going to be a scientific analysis but is designed to give you a feel about how energy behaves.

We are going to do a Gedankenexperiment (thought experiment). Let us consider a pool table with no pockets. Also the pool table is perfect so the balls do not slow down due to friction and bounce off the sides without loosing energy. The balls continue bouncing about the table for ever.

First of all nothing is moving but I put a bit of energy in by hitting the que ball. Initially all the balls are moving to the left (Figure 1).

Figure 1

However, after a certain amount of time the balls are travelling in what seems to be random directions (Figure 2). If I did the same thing again and managed to hit the que ball with exactly the same energy in exactly the same place then the balls would end up with the same positions and velocities after the same amount of time.

Figure 2

The total energy is still the same as the amount of energy that I put into the system initially since there is no energy loss due to friction.

At some point the system may not look random. We may have a point when all the balls are travelling to the left again or we may have a point when only one ball is moving. (However, we can never have a point when no balls are moving since this would imply that we have lost all our energy.)

These special points are going to be extremely rare so when we look at the system it is highly likely that we will see the balls moving in random directions.

For the arrangement in Figure 1 we may be able to devise some way that we could harvest the energy since we know in which direction all the balls are travelling to the left. However, when the balls are moving in seemingly random directions it would not be possible to havest that energy. The energy of the system remains the same but we cannot use that energy since we have lost track of the direction of the individual balls.

What is Temperature

What we experience as temperature is a measure of the ‘average’ energy of the molecules about us. In air some of the molecules may be travelling very fast (i.e. with high energy). Others may not be moving much at all – what we experience is what the average energy is.

Molecules can also have other sorts of energy than just their kinetic energy due to them moving. They can spin and vibrate depending on what sorts of molecules they are.

To give another analogy consider three water containers connected with a small pipes as shown in Figure 3.

Figure 3

Since the containers are of different sizes they contain different amounts of water. However, the water will settle to the same height – it reaches what is called equlibrium. In our analogy this height is the ‘temperature’. Different types of molecule can have spin and rotate differently and therefore have different energy ‘containers’. The amount of energy that you need to put in to raise this level defines what is called the ‘heat capacity’ of the material. Different materials have different heat capacities since they are made up of different types of molecules.

In our water container analogy the water molecules are continually moving in random directions. There will therefore be very, very, small random changes in the level of the water in the containers.

Let us say that initially the containers where empty and that we filled the system up by putting water into the left hand side container.We could reach a point as shown in Figure 4. There is no level set since the system has not yet reached equilibrium. In our analogy there is no defined ‘temperature’ for the overall system.

Figure 4

Temperature is only truly defined for a system that has reached equilibrium.

If things are changing slowly we might think that the different parts of the system are at different levels – i.e. each part is at a different temperature. However we would have to be much more careful if things are changing very quickly.

We also have to be careful when we talk about the ‘temperature’ of an individual molecule or even a small groups of molecules. Some of the molecules may be moving, spinning or vibrating very fast others a lot slower. Temperature is only the average over a large number of molecules. Water changes from liquid state to a gas state at 100°C. However, some water molecules will have much higher energy than the average – that is why water evaporates.

Absolute Zero

What happens if we break off the container on the right from Figure 3. The containers empty and water spills out over the floor (Figure 5).

Figure 5

Eventually the water reaches the level of the bottom of the tubes and water stops flowing and the water reaches its lowest possible level.

This also happens with temperature. As we remove energy from the system we eventually reach a point where we cannot remove any more. There is some energy still left (called zero point energy) but it can never be removed. This lowest level is analogous to what is called absolute zero in temperature terms and is -273.15°C.

In physics and chemistry a different temperature scale is often used rather than Centigrade of Fahrenheit and is measured in kelvin(K). Absolute zero is 0K, water freezes at 273.15K and boils at 373.15K.

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