the law of conservation of energy.

[Mandalay University Family 2006]

 the law of conservation of energy

James Prescott Joule

Joule's apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.

states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can be neither created nor be destroyed, but it transforms from one form to another, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite.

A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist. That is to say, no system without an external energy supply can deliver an unlimited amount of energy to its

Contents

• 1 History
  • 1.1 Mechanical equivalent of heat
  • 1.2 Mass–energy equivalence
  • 1.3 Conservation of energy in beta decay
• 2 First law of thermodynamics
• 3 Noether's theorem
• 4 Relativity
• 5 Quantum theory
• 6 See also
• 7 Footnotes
• 8 References
  • 8.1 Modern accounts
  • 8.2 History of ideas
• 9 External links
  
  

  First law of thermodynamics

  Main article: First law of thermodynamics

  For a closed thermodynamic system, the first law of thermodynamics may be stated as:

  , or equivalently,

  where is the amount of energy added to the system by a heating process, is the amount of energy lost by the system due to work done by the system on its surroundings and is the change in the internal energy of the system.

  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 increment of internal energy (see Inexact differential). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energy is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for 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 means "that amount of energy lost as the result of work". Thus one can state the amount of internal energy possessed by a thermodynamic system that one knows is presently in a given state, but one cannot tell, just from knowledge of the given present state, how much energy has in the past 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.

  
  Entropy is a function of the state of a system which tells of the possibility of conversion of heat into work.
  
  

  For a simple compressible system, the work performed by the system may be written:

  

  where is the pressure and is a small change in the volume of the system, each of which are system variables. The heat energy may be written
  
  

  

  where is the temperature and is a small change in the entropy of the system. Temperature and entropy are variables of state of a system.

  For a simple open system (in which mass may be exchanged with the environment), containing a single type of particle, the first law is written:^[11]

  

  where is the added mass and is the internal energy per unit mass of the added mass. The addition of mass may be accompanied by a volume change which is not associated with work (e.g. for a liquid-vapor system, the volume of the vapor system may increase due to volume lost by the evaporating liquid). In the reversible case, the work will be given by where v is the specific volume of the added mass.

  
  
  

  Relativity

  With the discovery of special relativity by Albert Einstein, energy was proposed to be 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 across time, in any closed system, as seen from any given inertial reference frame. Also conserved is the vector length (Minkowski norm), which is the rest mass for single particles, and the invariant mass for systems of particles (where momenta and energy are separately summed before the length is calculated—see the article on invariant 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 a massive particle; or else in the center of momentum frame for objects or systems which retain kinetic energy, the total energy of particle or object (including internal kinetic energy in systems) is related to its rest mass or its invariant mass via the famous equation
  
  .
  
  

  Thus, the rule of conservation of energy over time in special relativity continues to hold, so long as the reference frame of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the invariant mass, which is the minimal system mass and energy that can be seen by any observer, and which is defined by the energy–momentum relation.

  In general relativity conservation of energy-momentum is expressed with the aid of a stress-energy-momentum pseudotensor. The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.

  
  

Quantum theory

In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the

Hilbert space (or a space of wave functions ) of the system. If the Hamiltonian is a time independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Note that due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position-momentum uncertainty principle, and merely holds in specific cases (see Uncertainty principle). Energy at each fixed time can in principle be exactly measured without any trade-off in precision forced by the time-energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.

It was 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, m_i each with velocity v_i ),

was conserved so long as the masses did not interact. He called this quantity the vis viva or living force of the system. The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction. Many physicists at that time held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:

was the conserved vis viva. It was later shown that both quantities are conserved simultaneously, given the proper conditions such as an elastic collision.

[Mandalay University Family 2006]

https://en.wikipedia.org/wiki/Conservation_of_energy#First_law_of_thermodynamics

 the law of conservation of energy

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Conservation of energy in beta decay

Main article: Beta decay § Neutrinos in beta decay

The discovery in 1911 that electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. This problem was eventually resolved in 1933 by Enrico Fermi who proposed the correct description of beta-decay as the emission of both an electron and an antineutrino, which carries away the apparently missing energy.

On Sunday, June 21, 2015 at 2:46:44 AM UTC+6:30, Mandalay University Family 2006 wrote: