 Objectives:

1. To understand that energy is stored inside a system by the particles (atoms and molecules) that make up the system. This is called internal energy.
2. To appreciate that internal energy is the total kinetic energy and potential energy of all the particles (atoms and molecules) that make up a system.
3. To comprehend that heating changes the energy stored within the system by increasing the energy of the particles that make up the system. Either the temperature of the system increases, or changes of state happen.

From the previous lessons you will have learnt how the particle model of matter is used to describe solids, liquids and gases. You will remember that solids have strong forces between them making strong intermolecular bonds, they have little energy and hence the particles cannot separate. Liquids have a greater amount of energy than solids and so can vibrate more, this results in weaker intermolecular bonds because there is less force holding them in place. Gases have a lot of energy and very weak intermolecular bonds, they vibrate and move around a lot and as such the forces between each particle are small.

Internal energy is a concept used to explain the amount of energy (shown in bold above) in each state. Which of the following two examples contains the most energy do you think and why?

The answer is the bathtub of water even though it is at about half the temperature compared to the hot cup of tea, what is the reason for this?

The reason for why the bath tub has more energy is actually quite simple and introduces the topic of internal energy. There are many more water particles in the bath tub than the cup and the total energy of each system has to take into consideration each and every particle.

Internal energy is the concept used to describe how much energy a system of particles contains. The internal energy is dependent on the particles kinetic energy and potential energy stores:

• If the particles in a system vibrate or move around, they have energy in their kinetic energy stores.
• The faster they move or vibrate, the greater the kinetic energy store.
• The particles also have energy in their potential energy stores.
• Potential energy of the particles is due to their positions relative to each other. There are forces of attraction between particles which must be overcome by putting energy into the system.
• So as the particles move further apart, their potential energy stores will increase (and vice versa).

The total energy that particles in a system have is equal to the sum of their kinetic and potential energy stores, we call this total energy the internal energy of the system. Where does the energy go when a substance is supplied with energy?

Naturally one would think that an input of energy would cause the temperature of a substance to increase, however this is only part of what happens. The following graph shows how an increase in energy of a system affects the temperature of it; The graph appears positive and linear through each state that the system is in, so when it is a solid, the temperature increases proportionally to the supplied energy. Similarly, when the system is a liquid the rise in temperature is proportional to the energy input and when the system is a gas the rise in temperature is proportional to the supplied energy.

By definition the temperature is proportional to the average kinetic energy of a system, this (along with temperature being proportional to the energy input as shown in the graph above) tells us that the input energy goes into raising the kinetic energy store of a system.

As you will notice in the graph above, between the points B and C the substance is between the two states of solid and liquid, the temperature does not increase even though  there is an increase in energy input. So energy is supplied… but the temperature does not rise, so where does the energy go (bearing in mind energy is always conserved and so is not created nor destroyed)? The same is said for between points D and E where the substance is between the two states of liquid and gas.

The input energy goes into the potential energy stores of the system, this is evident by bonds breaking and the structure of the substance changing (i.e. changing from a solid to a liquid).

To summarise:

• When a substance increases or decreases in temperature the systems kinetic energy store increases.
• Similarly, when a systems temperature decreases, its kinetic energy store decreases.
• When a substance melts or boils, the input energy goes into the potential energy stores whereby the bonds end up increasing in length and/ or break.
• Similarly, when a systems solidifies or condenses, the potential energy stores decrease, the particles get closer together and so their bonds become stronger.

The following graph shows the cooling effects on stearic acid, it began as a liquid at a high temperature and cooled down; You can see that at around the $42 \ ^{ \circ}C$ mark, the temperature became steady for several minutes. It was during these minutes that the stearic acid changed state and solidified. You may question why there is a very slight decrease in temperature in this period – this would be down to the fact that different parts of the system would have solidified before others.

Here is a video helping to explain the internal energy topic;