Conservation of energy
Encyclopedia : C : CO : CON : Conservation of energy
- This article is about the physics principle. For information on using energy resources sustainably, see Energy conservation.
The energy conservation law is possibly the most important, and certainly the most practically useful, of several conservation laws in physics. The main reason is that energy, as defined via mechanical work, is force times distance, and civilization needs to exchange by goods and build various structures and machines - both required to transport matter over distance against dissipating forces (friction, air or other medium resistance, etc).
In thermodynamics, the first law of thermodynamics is a statement of the conservation of energy for thermodynamic systems.
The energy conservation law is a mathematical consequence of shift symmetry of time. It is connected with the fact that physical laws remain the same over time.
Historical development
Ancient philosophers as far back as Thales of Miletus had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify this with what we know today as "mass-energy" (for example, Thales thought it was water). In 1638, Galileo published his analysis of several situations -- including the celebrated "interrupted pendulum" -- which can be described (in modernized language) as conservatively converting potential energy to kinetic energy and back again. However, Galileo did not state the process in modern terms and again cannot be credited with the crucial insight. It was the German Gottfried Wilhelm Leibniz during 1676-1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion (kinetic energy). Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi ),
- [\sum_ m_i v_i^2]
- [\,\!\sum_ m_i v_i]
Members of the academic establishment such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the heat inevitably generated by motion under friction, was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloricLavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", Académie Royal des Sciences pp4-355. Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat, and (as importantly) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). Vis viva now started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.
The recalibration of vis viva to
- [\frac \sum_ m_i v_i^2]
In a paper Über die Natur der Wärme, published in the Zeitschrift für Physik in 1837, Karl Friedrich Mohr gave one of the earliest general statements of the doctrine of the conservation of energy in the words: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called Kraft [energy or work]. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others."
A key stage in the development of the modern conservation principle was the demonstration of the mechanical equivalent of heat. The caloric theory maintained that heat could neither be created nor destroyed but conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.
The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer.von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in Annalen der Chemie und Pharmacie, 43, 233 Mayer reached his conclusion on a voyage to the Dutch East Indies, where he found that his patients' blood was a deeper red because they were consuming less oxygen, and therefore less energy, to maintain their body temperature in the hotter climate. He had discovered that heat and mechanical work were both forms of energy, and later, after improving his knowledge of physics, he calculated a quantitative relationship between them.
Meanwhile, in 1843 James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. In the most famous, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy (heat) gained by the water by friction with the paddle.
Over the period 1840-1843, similar work was carried out by engineer Ludwig A. Colding though it was little-known outside his native Denmark.
Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that, perhaps unjustly, eventually drew the wider recognition.
- For the dispute between Joule and Mayer over priority, see Mechanical equivalent of heat: Priority
In 1877, Peter Guthrie Tait claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the Philosophiae Naturalis Principia Mathematica. This is now generally regarded as nothing more than an example of Whig history.
Modern physics
With the discovery of special relativity by Albert Einstein, it was found that energy is one component of an energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved, as well as the vector length (Minkowski norm). The latter is associated with invariant mass and rest mass. The relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the rest frame of the massive particle, or the center-of-momentum frame for objects or systems), the total energy of particle or object (including internal kinetic energy in systems) is related to its rest mass via the famous equation [E=mc^2]. Thus, the rule of conservation of energy was shown to be a special case of a more general rule, alternatively called the conservation of mass and energy, the conservation of mass-energy, the conservation of energy-momentum, the conservation of invariant mass or now usually just referred to as conservation of energy.
The conservation of energy is a common feature in many physical theories. It is understood as a consequence of Noether's theorem which states that any theory whose description is not sensitive to a starting time will have constant energy. In other words, if the theory is invariant under the continuous symmetry of time translation its energy is conserved. Conversely, theories which are not invariant under shifts in time (for example, systems with time dependent potential energy) do not exhibit conservation of energy.
In quantum mechanics energy is defined as a time derivative of the wave function. Lack of commutation of the time derivative operator with time itself mathematically results in an uncertainty principle for energy definition: the longer the period of time, the more precisely energy can be defined (energy and time become a conjugate Fourier pair).
Thus uncertainty principle should not be confused with energy conservation violation (as laymen or philosophers often imply).
The first law of thermodynamics
| Laws of thermodynamics |
|---|
| Zeroth law of thermodynamics |
| First law of thermodynamics |
| Second law of thermodynamics |
| Third law of thermodynamics |
|
|}
For a thermodynamic system with a fixed number of particles, the first law of thermodynamics may be stated as:
The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the [\mathrmU] increment of internal energy. Work and heat are processes which add or subtract energy, while the internal energy [U] is a particular form of energy associated with the system. Thus the term "heat energy" for [\delta Q] means "that amount of energy added as the result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for [\delta W] means "that amount of energy lost as the result of work". The most significant result of this distinction is the fact that one can clearly state the amount of internal energy possessed by a thermodynamic system, but one cannot tell how much energy has flowed into or out of the system as a result of its being heated or cooled, nor as the result of work being performed on or by the system. The first law can be written exclusively in terms of system variables. The work done by the system may be written
Notes
See also
ReferencesModern accounts
History of ideas
Classic accounts
External links
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating. |