What does the law of conservation of energy state?

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Conservation of energy is one of the basic principles of physics. It has several different statements, which are all equivalent. Here's the definition of the law of conservation of energy from Encyclopedia Britannica:

Conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant.

There are no known exceptions to this law. In fact, it can be rigorously proven using Noether's theorem by only supposing that physical laws do not change over time. The law basically states that energy cannot be created or destroyed; it can only change from one form to another. Here are some examples of that change:

  • Potential to kinetic energy—a ball dropped from the top of a building loses its potential energy (energy of its position) but gains kinetic energy (energy of motion)
  • Kinetic to kinetic—on a pool table, one moving ball transfers its kinetic energy to another by hitting it
  • Chemical to kinetic—burning a chemical fuel (gas, gasoline, alcohol) releases chemical energy contained in covalent bonds and gives the car kinetic energy
  • Kinetic to electrical—the motion of a turbine in a hydro-plant moves magnets in an electric generator and "creates" electrical energy
  • Nuclear to heat—an exploding nuclear bomb creates huge amounts of heat, sound waves, light, and electromagnetic waves by either splitting (fission) or making new nuclear bonds (fusion).

None of the above mentioned transitions from one form of energy to another is perfect, and all of them are accompanied by some residual heat. Just remember how hot a car engine gets after a while. It should also be noted that in the last case, the nuclear energy we talk about is actually mass, which brings us to the one of the most famous equations in physics `E=mc^2`, which tells us that the energy of a body (kinetic, heat, potential, and other energies not included) is equal to its mass multiplied by the square of the speed of light. This tells us that the laws of conservation of energy and conservation of mass are actually one and the same.

One thing people often forget when talking about conservation of energy is that energy is conserved in any isolated system. This means we cannot apply the law to a system that is not completely isolated. For example, Earth may seem isolated in space on a first glance, but our planet actually receives huge amounts of energy from the Sun and loses some of that energy through infrared radiation.

Having the conservation of energy in mind, we should note that available energy is something entirely different. While energy cannot be created or destroyed, it can be in certain forms that are not readily available to human use. Examples of such energy include the heat energy of volcanoes, lightning, hurricanes, etc. All of these contain great amounts of energy, yet we have not yet found a way to exploit them. Energy is plentiful, but the energy available to us is very limited. Therefore, while energy cannot be destroyed, it doesn't mean we should waste it.

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