In physics, a system is simply a collection of objects. It abstracts properties in order to simplify the problem, and treats most objects as if they have very few useful properties. Usually, we also define an environment, which is basically anything that isn’t the system.
Open
An open system is one that allows the exchange of both energy and matter between the system and the environment. A good example of an open system is water boiling in a kettle on a stove. If we consider just the kettle and the water within to be a system, then external energy is given to the system from the environment (stove). The system also releases both energy and matter in the form of steam.
Closed
A closed system is one that only allows the exchange of energy, but not matter. Because energy and force are inter-related, a closed system also can have external forces acting on bodies in the system from the environment. An example of a closed system could be a cart being pushed. If we define the system to be just the cart, then we have an external force (a person) doing work on the system. However, the cart does not gain any additional mass, nor does it lose it. So the system can be defined as closed. The conservation of mass applies to a closed system, meaning the net amount of mass can never change.
Isolated
Finally, an isolated system is one that restricts the flow of both energy and matter between the system and the environment. Such a system is mostly hypothetical, as energy generally ‘leaks’ out of any system, but the energy lost can sometimes be negligible, so an isolated system is useful in calculations. Most importantly, the conservation of energy applies in an isolated system. An example would be a system of a falling ball and the Earth. The system does not have any external forces, since the force of gravity is a direct effect of the existence of the bodies in the system.
In an isolated system, the conservation of energy applies (as well as the conservation of mass!):
Configurations
A configuration of a system is essentially a ‘snapshot’ of all the objects in the system, with some properties being changed. The easiest example of two configurations is a ball being dropped from the earth. Configuration 1 could be when the ball is metres above the Earth, while configuration 2 is when the ball is on the Earth ().
Total Energy in a System
The total energy in a system is given as the sum of the kinetic energies possessed by objects within the system, plus the total potential energy in the system.
Kinetic energy is solely possessed by a body within the system, and as such the total kinetic energy within a system is simply the net sum of the kinetic energies of bodies within the system.
Potential Energy is possessed by the system, and not the bodies. However, there are various types of potential energies, so the net total is a sum of the various types.
Formula
Net Energy in a System
E_{sys} = K_{sys} + U_{sys} = \sum K_{obj} + \sum U_{type}
Energy Transfer (Work) in Systems
Let’s start with a really, really abstract concept, a system entirely viewed in terms of energy. Let’s say the energy in the system, , is joules.
Adding energy to this system externally means we have increased the energy of this system. If is the extra energy added to the system, we know that: . In other words, .
This can be generalised to show that the sum of all energy transfers into and out of the system is equal to the change in energy of the system: