Energy (science)

Energy is a word with several connotations. The word goes back to the natural philosophy of Aristotle, ενέργεια (energeia), where it means roughly "efficacy". In the early nineteenth century the word was incorporated into science by Thomas Young. In science, the concept energy has a clear meaning, which, however, is not easy to explain because of the many forms in which energy manifests itself. The word energy is also very commonly used outside science, where it means physical or mental power to achieve something. "Negative energy" is a mental power that is in the way of achieving things.

In this article we will restrict attention to the scientific meaning of energy. In science, energy is a measurable property of a physical or chemical system, i.e., the energy of a system may be given by a single real number. Roughly speaking, the energy of a system is a measure of the amount of work that the system is able to perform on its environment. As stated, energy has many manifestations, be it chemical energy of a certain amount of gasoline, the kinetic energy of a moving cannon ball, the heat stored in a steam boiler, the potential energy of water in a reservoir, the fusion energy contained in a hydrogen bomb, the electricity in a battery. All these manifestations obey the same very important law: energy is conserved in conversion from one form of energy to the other. This law of conservation of energy is known as the first law of thermodynamics. This law pervades all of science, and is probably science's most important principle.

Let us consider an example. Assume we use a pump, running on gasoline, to pump water up to a reservoir, and when the reservoir is filled, we let the water flow down to drive an electrical generator. Doing this, we convert the chemical energy stored in the gasoline, to the mechanical energy of the pump, to the potential energy of the water in the reservoir, to the kinetic energy of the falling water, and finally to the electric energy generated by the generator. If we use the generated electric current for lighting, then the light bulbs convert the electric current to yet another form of energy, namely light (electromagnetic radiation). During all these energy conversion processes, the law of conservation of energy assures us that no energy is lost. To non-scientists the contrary may seem the case sometimes, because heat is generated (especially in burning the gasoline to drive the pump), and the heat will escape to the environment without any useful, or directly noticeable, effect. However, since heat is also a form of energy, it must be included in the energy balance of the first law.

Energy in classical mechanics

To keep the discussion simple we will consider a point mass m in one-dimensional space. That is the position of m at time t is given by x(t). For more details and extension to the three-dimensional case see classical mechanics.