Systems and boundaries

1. In physics, a system is the object or group of objects you choose to study, such as a falling ball and the Earth, or a kettle and the water inside it.
2. Everything outside the system is called the surroundings, and the imaginary line that separates the two is the boundary of the system.
3. Energy can cross the boundary in either direction, for example when a mug of hot tea transfers energy to the cooler air in the room.
4. A closed system is one where no energy crosses the boundary, so no energy enters from the surroundings and none escapes to them.
5. Very few single objects form a closed system on their own, because almost every object exchanges some energy with the air, the ground or whatever is supporting it.
6. You can still make a system closed by drawing the boundary wide enough to include every object that the energy reaches, such as a ball, the Earth and the air around them.
7. The whole Universe can be treated as the largest closed system, because there is nothing outside it for energy to be transferred to.

Conservation of energy

1. The law of conservation of energy states that energy cannot be created or destroyed.
2. Energy can only be transferred, either from one energy store to another or from one place to another.
3. For example, a moving object holds energy in its kinetic store, and an object raised above the ground holds energy in its gravitational potential energy store.
4. Whenever a system changes, the energy in at least one store goes down while the energy in one or more other stores goes up.
5. In a closed system the total decrease is always exactly equal to the total increase, because no energy has left the system and no new energy has appeared.
6. This means there is no net change in the total energy of a closed system, however many transfers happen inside it.
7. A net change is the overall change once every increase and every decrease has been added together, so a rise of $30J$ in one store and a fall of $30J$ in another give a net change of zero.
8. Individual stores can change by large amounts, so conservation of energy never means that each separate store stays the same.
9. It is the sum of all the stores in the closed system that stays constant from the start of a process to the end.

Choosing the boundary

1. Whether a system counts as closed depends entirely on where you draw its boundary.
2. If the boundary surrounds only a ball rolling across a carpet, the total energy of the ball falls as it slows down.
3. This happens because friction and air resistance transfer energy out of the ball to the thermal stores of the carpet and the air.
4. The ball on its own is therefore not a closed system, even though no energy has been destroyed.
5. If the boundary is widened to include the carpet and the air, every joule that leaves the ball stays inside the system.
6. The wider system is closed, so its total energy stays constant while the energy moves from the kinetic store of the ball to the thermal stores of its surroundings.
7. In the end, much of the energy is spread thinly through the thermal stores of the surroundings, but every joule of it still exists.
8. Always state the system you are describing, because the claim that total energy stays constant is only true for a closed system.