In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. These properties are sometimes called “constants of the motion“. These quantities are said to be “conserved” and the conservation laws which result can be considered to be the most fundamental principles of mechanics. In mechanics, examples of conserved quantities are energy, momentum, and angular momentum. The laws of conservation are exact for an isolated system.

The law of conservation of matter or principle of matter conservation states that the mass of an object or collection of objects never changes over time, no matter how the constituent parts rearrange themselves.

The mass can neither be created nor destroyed.

The law requires that during any nuclear reaction, radioactive decay or chemical reaction in an isolated system, the total mass of the reactants or starting materials must be equal to the mass of the products.

Historically, already the ancient Greeks proposed the idea that the total amount of matter in the universe is constant. The principle of conservation of mass was first outlined by Mikhail Lomonosov in 1748. However, the law of conservation of matter (or the principle of mass/matter conservation) as a fundamental principle of physics was discovered in by Antoine Lavoisier in the late 18th century. It was of great importance in progressing from alchemy to modern chemistry. Before this discovery, there were questions like:

• Why a piece of wood weighs less after burning?
• Can a matter or some of its part disappear?

In the case of burned wood the problem was the measurement of the weight of released gases. Measurements of the weight of released gases was complicated, because of the buoyancy effect of the Earth’s atmosphere on the weight of gases. Once understood, the conservation of matter was of crucial importance in the progress from alchemy to the modern natural science of chemistry.

The law of conservation of energy is one of the basic laws of physics along with the conservation of mass and the conservation of momentum. The law of conservation of energy states that energy can change from one form into another, but it cannot be created or destroyed. Or the general definition is:

The total energy of an isolated system remains constant over time.

Newton’s cradle. A device that demonstrates the Law of Conservation of Mechanical Energy and Momentum.

Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another in hundreds of ways.

For example, burning gasoline to power cars is an energy conversion process we rely on. The chemical energy in gasoline is converted to thermal energy, which is then converted to mechanical energy that makes the car move. The mechanical energy has been converted to kinetic energy. When we use the brakes to stop a car, that kinetic energy is converted by friction back to heat, or thermal energy.

A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind, which produces work without the input of energy, cannot exist.

The concept of energy conservation is widely used in many fields. In this article the following fields are discussed:

• Conservation of Mechanical Energy
• Conservation of Energy in Fluid Mechanics
• Conservation of Energy in Thermodynamics
• Conservation of Energy in Electrical Circuits
• Conservation of Energy in Chemical Reactions
• Conservation of Energy in Special Relativity Theory
• Conservation of Energy in Nuclear Reactions

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². In words, energy equals mass multiplied by the speed of light squared. Because the speed of light is a very large number, the formula implies that any small amount of matter contains a very large amount of energy. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light. The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by increase in kinetic energy.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc²) this binding energy is proportional to this mass difference and it is known as the mass defect.

Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

During the nuclear splitting or nuclear fusion, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. The nuclear binding energies are enormous, they are of the order of a million times greater than the electron binding energies of atoms.

Generally, in both chemical and nuclear reactions, some conversion between rest mass and energy occurs, so that the products generally have smaller or greater mass than the reactants. Therefore the new conservation principle is the conservation of mass-energy.

See also: Energy Release from Fission