Conservation of energy

The conservation of energy states that the total energy of an isolated system does not change with time. While energy can be converted between different types of energy such as kinetic energy into thermal energy. However, it is not possible to produce within a closed system energy or to destroy: the energy is conserved.

Energy conservation is considered an important principle of all science, which states:

In a closed system refers to a system without energy, information or material exchange and without interaction with the environment.

The energy conservation law can be derived from the fact that valid for the system laws of physics do not depend on the time using the Noether theorem.

Colloquial aspects

In the physical sense of energy conservation, a loss of energy is not possible. If it is still colloquially spoken of energy consumption, waste of energy, energy saving and energy loss, it is because the earth on the one hand not a closed system, the human and other life forms on Earth other hand, can only use energy in some form. There the loss of commercially readily usable or biologically usable forms of energy is described by these terms thus.

For most nowadays common types of energy conversion of energy are converted into forms with higher entropy with a small or specific entropy, which are no longer available for technical and / or biological processes. A motor vehicle for example, converts chemical energy that originates from crude oil or rapeseed oil, into kinetic energy and thermal energy. Since oil can not be regenerated, one speaks of a loss of energy in the sense that this particular form of chemical energy with low entropy is lost for future generations or for other purposes.

From Waste is often spoken of, when raw materials are used for the production of luxury goods, while at the same time there is a shortage of food. In each of the kinds of conversion which are in use today, only a part of the energy present in the energy into useful energy is converted. From energy conservation we speak, therefore, if increasing the efficiency of the power generation process or a device by technical progress, so that less raw material more usable energy supplies or with less energy, more power is achieved through reduced energy loss.

History

The first of the physician Julius Robert von Mayer (1814-1878) formulated the principle of energy conservation. He has in 1842 established the value of the mechanical equivalent of heat by tests and so demonstrated that kinetic energy can be completely converted into heat. Regardless of Mayer did so in 1843 James Prescott Joule, whose works were widely known at the time, but also more physicists and engineers such as Ludwig August Colding in Denmark ( also 1843). Was formulated definitively the energy conservation law in 1847 by Hermann von Helmholtz. In Berlin, he gave a lecture on 23 July 1847 the constancy of the force and underscored the principle of energy conservation.

The energy conservation law has not always been controversial in the history of physics. The most famous example is Niels Bohr, the only statistical ( averaged ) conservation of energy in quantum processes advocated on several occasions. First, to bring in 1924 in the so-called BKS theory with John C. Slater and Hendrik Anthony Kramers, when it came to the older quantum theory interacting with a classical electromagnetic field in line with Bohr in particular against the idea of ​​the particle character of the radiation ( photon concept of Albert Einstein, then confirmed recently experimentally Compton effect ) opposed it. A little later this theory was also Hans Geiger and Walther Bothe disproved by experiments of Arthur Holly Compton itself, but confirming the validity of the conservation of energy also at the quantum level. Also, on a later occasion Bohr tried only a statistical validity of conservation of energy to explain initially puzzling quantum mechanical phenomena to use, so during beta decay, where the missing energy of the decay products but shortly afterwards by the postulate of a new, weakly interacting particle, the neutrino, by Wolfgang Pauli was declared.

Today, the energy conservation law in the vast majority of physicists as established and is even often used to define the energy.

Conservation of energy in Newtonian mechanics

Upon movement of particles in a force field, the sum of conservative kinetic energy and potential energy is obtained, the total energy. The force of the negative gradient of the potential energy ( in the jargon often referred to simply as potential)

A particle moves with time in such a force field on any routes from a starting point to a destination, then, for the work that is being done here on the particles, the way irrelevant. Regardless of the way the work done is the difference of the potential energies at the start and finish.

For a particle with constant mass and the potential energy of the Newtonian equations of motion are:

And also:

An integration with respect to time now gives the work required along any ( piecewise smooth ) physical path with the respective potential energy at the start and at the finish:

Was identified as being temporally derived kinetic energy, which is increased by the work done on the particles work.

One arranges the terms in order, one obtains:

The sum of kinetic and potential energy, according to a displacement of the body still the same. This is the energy conservation law.

May, for example a pendulum, the friction can be neglected, then the sum of the potential and kinetic energy does not change with time. Deflecting the pendulum, it swings between two reversal points and reaches its highest velocity at the location of the potential minimum. At the turning points, the kinetic energy is zero and the potential energy is at a maximum. Regardless of the position of the pendulum is the sum of kinetic and potential energy is given by the initial displacement value.

Conservation of energy in thermodynamics

Each thermodynamic system has a certain " reserve " of energy. This is composed of an outer portion and an inner portion (internal energy ). The sum of the two fractions gives the total energy of the thermodynamic system, whereby the change in the external portion is equal to zero in the chemical thermodynamics (). Under this assumption leads to the first law of thermodynamics:

" The internal energy is a characteristic of the material components of a system and can not be created or destroyed. The internal energy is a state variable. "

Therefore applies to closed systems, that the internal energy therefore their change is constant and equal to zero. For closed systems is the first law of thermodynamics:

• U - internal energy
• Q - heat
• W - Work

Conservation of energy in electrodynamics

The set of Poynting describes the conservation of energy in electrodynamics.

Conservation of energy in relativity theory

A relativistic particle of ( rest) mass that moves with the speed, has the power

Wherein the speed of light. At rest, the energy is

For small velocities (Taylor development ) comes to rest energy added to the Newtonian kinetic energy

When high-energy particles, this approximation can be measured incorrectly. Only the sum of the relativistic energies is preserved in particle interactions.

Conservation of energy in quantum mechanics

The energy quantum mechanical states is obtained when the Hamiltonian does not depend on time. However, many quantum mechanical states, namely all that change with time measurable, no energy eigenstates. In them, but the expectation value of the energy is at least maintained.

Energy exchange

Can a system exchange energy with another system, for example, by radiation or conduction, then we speak of an energetically open system. The conservation of energy states here is that the energy that flows into a system minus the energy that it leaves, is the change in energy of the system. By considering the energy flows of the system can be inferred processes within the system, even if they can not be observed even.

The energy of a system can not be measured directly at: apart from the gravitational effect of energy, so only energy differences affect measurable.

Noether 's theorem

In Lagrangian mechanics, energy conservation follows from the Noether theorem, if the action is invariant under time shifts.