Internal Energy of a System

What do we mean by "system"?
A system is simply any thing or things.
So, a glass of water is a system; a potatoe is a system; a block of ice is a system.

The internal energy of a system is the energy inside the system, eg inside the glass of water or inside the potatoe etc.

How can a system such as a glass of water have energy inside it?
All things are made from atoms and molecules (let's just call them "particles"). These particles are always moving in some way, either vibrating (if the thing is a solid) or moving freely (if the thing is a liquid or a gas).
So, since they are moving they have some Kinetic Energy.
Also, there are bonds between the particles if the thing is a solid or a liquid, so the forces that arise from these bonds give the particles some Potential Energy.
The combination of these two energies, Kinetic and Potential, is known as the Internal Energy of the system.

Internal Energy = K.E + P.E of the particles inside a "system".

The following diagrams illustrate the Internal Energy of a Solid, a Liquid and a Gas.

So, in a Solid and in a Liquid the Internal Energy is a combination of some Kinetic energy and some Potential energy, but in a Gas the Internal Energy is purely Kinetic because the particles are so far apart that there are NO forces between them and hence, no Potential energy.

How to increase the Internal Energy of a System

All you have to do is transfer (or "add") Thermal Energy to the system by Heating it, eg heat water in a saucepan or heat water in a kettle from 20°C to 50°C.
What we find is that, as the Heating takes place, the temperature of the system (eg the water) rises.
If we could look inside at the particles whilst we were doing this we would notice that their speed of movement increases in line with the temperature.
So the Kinetic energy of the particles increases as Temperature increases.
But we would see no change to the forces between the particles and so no change in their Potential energy.
From outside, all we would see is the steady rise in temperature of the water as Heating continues.

If we keep supplying Thermal Energy we would see the Temperature steadily rise, but as we reach 100° we would notice that the Temperature stops rising even if we keep adding more Thermal Energy!

As we watch our water, we would see it changing into a gas, becoming steam.

So, what is going on here inside the liquid?
If we could look inside at the particles we would Not see any further increase in their speed (so no further increase in their kinetic energy and hence no further rise in Temperature) but we would see the particles moving further and further apart, increasing their Potential Energy.
Eventually when sufficient energy has been added to completely break the bonds, the change of state occurs and the liquid becomes a gas.
The energy that needs to be added to do this (to turn all of the available liquid into a gas,the "flatline" section on the graph) is known as Latent Heat, but more on that below.

Summary
To increase the internal energy of a system you add thermal energy.
This may increase the kinetic energy of the particles within the system and so raise its temperature.
Or it might increase the potential energy of the particles and so bring about a change of state.

Specific Heat Capacity and Specific Latent Heat

The exact slope (gradient) of the line in the above graph, where the temperature is changing, depends on the mass of the substance and on a quantity known as the Specific Heat Capacity of the substance.

The width of the flatline part in the above graph, where the temperature is not changing, depends on the mass of the substance and on a quantity known as the Specific Latent Heat of the substance.

We will consider both of these new terms in the following two sections, starting with Specific Heat Capacity.

Temperature Change and Specific Heat Capacity

As indicated in the paragraph above, the temperature change of a substance, when adding thermal energy, depends on two physical factors related to the substance itself; these are:

• Its mass, m
• Its Specific Heat Capacity, c.

Before we continue to explain how these factors affect temperature change we need to say a little bit about Specific Heat Capacity.

Now let's continue to explain how mass and S.H.C affect the temperature change of a substance:

The temperature change will be:
1. proportional to the amount of thermal energy added (this should be obvious).
But it will be:
2. inversely proportional to the mass of the substance (ie a more bulky substance will rise in temperature less than a lighter substance, for the same added energy.)
and from what we now know about S.H.C, it will be inversely proportional to the Specific Heat Capacity of the substance.

We can now use this equation to do some calculations concerning temperature change and thermal energy change for certain masses of materials.

As you can see, water stores far more thermal energy than copper for the same mass when raised by the same temperature.
This makes water good at holding its temperature and carrying thermal energy from place to place eg in a house central heating system.
The copper (and other metals), on the other hand will lose its energy and its temperature will fall much faster than the water. This makes metals useful as cooling fins around the back of fridges or behind room radiators.

Change of state and Specific Latent Heat

We now come to the second of the two new terms that we mentioned earlier.

Here we are concerned with the flatline part of the graph shown above and repeated below.

We have already described what is going on at a particle level during this "flatline".
But, to recap - during this period, the supplied thermal energy is NOT going towards raising the temperature of the substance (as you can see) but is going towards changing its state, eg in the case shown, the water is boiling, from liquid to gas. So, it is not raising the kinetic energy of the particles but it is raising their potential energy.
Finally for this recap, the width of this flatline is an amount of energy which we call "Latent Heat" or Specific Latent Heat if we refer to 1kg of a substance. And there we have the new term that we need to define.

Substances will have two values of specific latent heat, one for when they change from solid to liquid and one for when they change from liquid to gas.
The first is known as the "specific latent heat of fusion", L_f, (because it is when particles fuse together to make a solid or unfuse to make a liquid) and the second is known as the "specific latent heat of vaporisation", L_v, (because it is when the substance vaporises or becomes a gas).

Here are some typical values for specific latent heat.

As you can see, the amount of Latent energy needed to change the state of just 1Kg of any of these materials is very large.

If more than 1Kg of the material is involved then you just multiply by the mass to find the exact size of the Latent energy needed for a change of state, or use the following simple equation:

Now its time for you to have a go at a few calculations by yourself: