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ENERGY COMPOSITION OF MATTER

By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
This web page reviews the energy composition of matter.
 

PHOTON:
A photon is a packet of energy Ep that propagates at the speed of light as an electromagnetic wave. The frequency Fp of the wave is proportional to Ep via the relationship:
Ep = h Fp
where h is known as the Planck Constant.

A photon of sufficient energy can transform into a particle and and anti-particle. Similarly a particle and an anti-particle can annihilate to form a photon.
 

PARTICLES:
A particle is a concentration of energy in space. Stable charged atomic particles consist of quantized charge that is uniformly distributed along and moves along a stable closed spiral path at the speed of light and thus forms a stable non-propagating solution to the electromagnetic equations that determine the evolution of the universe. This solution is known as a spheromak. The potential (rest) energy of each stable particle consists of internal field energy + external magnetic field energy + external electric field energy + gravitational field energy. Total particle energy consists of potential (rest) energy plus kinetic energy.
 

RADIATION:
Random motion of particles with quantized charge causes local changes in the spacial charge density which correspond to emission or absorption of electromagnetic radiation photons. When quantized charge follows a stable closed path the charge is uniformly distributed along the path and there is no emission of radiation. However, an electron following a stable closed path can adopt another stable closed path with a different energy by absorption or emission of an electromagnetic radiation photon that provides the appropriate difference in energy.
 

PARTICLE AGGREGATION:
When particles aggregate together there is usually radiation emission, so that the total aggregated energy is less than the sum of the energies of the individual isolated particles. Most energy aggregation processes emit radiation to their surroundings and are termed exothermic. A few energy aggregation processes absorb radiation from their surroundings and are termed endothermic.
 

BINDING ENERGY:
As particles approach each other their field overlap can cause a reduction in potential energy and a corresponding increase in kinetic energy. Initially the kinetic energy of free particles is sufficient to allow the particles to escape from the mutual potential energy well that results from overlap of the particle's fields. However, in a low radiation density environment the random kinetic energy tends to convert to photons which radiate away into space. When photons are emitted and there is no off setting photon absorption the average kinetic energy of the remaining particles decreases. These particles are then trapped together in a mutual potential energy well. The additional average kinetic energy per particle required to allow a particle to escape from this mutual potential energy well is known as the particle binding energy. Atomic nuclei, atoms, molecules and solids all form by radiative emission of binding energy.
 

RADIO ISOTOPES:
A multi-particle nucleus with a relatively small binding energy per particle may be unstable. The particles composing the nucleus may randomly exchange energy until one of them acquires enough kinetic energy to escape from the mutual potential energy well. The remaining particles will then be in a lower energy state which is likely more stable. Alternatively the nucleus may over time discharge a succession of particles. Each particle discharge seeks to lower the nuclear energy and improve the nuclear stability. The more stable a nucleus the longer its half life. The particle types that are normally discharged are photons, electrons, positrons, neutrons and He-4 nuclei. Occasionally discrete protons are discharged.
 

MATTER:
Matter is a general name applied to an assembly of particles that has rest energy in the frame of reference of an inertial observer. Most atomic nuclei are the result of aggregation of the highly stable atomic particles known as protons and electrons. In a suitable high radiation density environment such as the center of a star electrons and protons can aggregate to form neutrons and atomic nuclei. An atom is an ordered aggregation of atomic particles. A molecule is an ordered aggregation of atoms. Matter is usually an aggregation of molecules. In a neutral gas there is no molecular order. In a liquid there is short range molecular order. In a crystaline solid there is long range molecular order. Matter at temperatures above zero degrees K also contains radiation photons. Total matter energy consists of potential (rest) energy + kinetic energy + contained photon energy. There are additional usually insignificant amounts of gravitational and neutrino energy.
 

STEADY STATE CONDITION:
When the total rate of radiant energy absorption by matter equals the total rate of radiant energy emission by that matter the matter is said to be in a Steady State Condition.
 

THERMAL EQUILIBRIUM CONDITION:
When the rate of radiant energy absorption as a function of frequency by matter equals the rate of radiant energy emission as a function of frequency by that same matter the matter is in a Thermal Equilibrium Condition. At Thermal Equilibrium no work can be done because there is no means of achieving net emission of the heat resulting from doing work.

The center of the Earth is in a near Thermal Equilibrium Condition. The center of the Earth is surrounded by other material of similar composition and equal temperature. Hence across the electromagnetic spectrum absorbed radiation equals emitted radiation and no work is done.
 

RANDOM KINETIC ENERGY AND CM KINETIC ENERGY:
The total energy consists of random thermal kinetic energy arising from particle motion with respect to the matter Center of Momentum (CM) plus CM kinetic and potential energy in the observers frame of reference. For most matter at room temperature the CM kinetic energy is small compared to the random thermal kinetic energy, which in turn is very much smaller than the CM potential (rest mass) energy. Hence, in most practical situations the CM kinetic energy is only a microscopic ripple in the total energy.
 

UNSTABLE PARTICLES:
Some particles are unstable energy states that eventually randomly decay into stable particles. From a practical engineering perspective the decay of unstable atomic particles is dealt with using tables which show the half life and decay products along each decay path.
 

STABLE PARTICLES:
The stable particles that have rest energy are the electron, proton and various stable atomic nuclei. In the absence of interactions with anti-matter these particles have half lives in excess of tens of billions of years. Antimatter particles are believed to be equally stable as long as they do not interact with normal matter.

Stable particles located in an external magnetic field exhibit quantized energy states known as spin states. However, for many approximate practical calculations stable particles are treated as simple singularities.
 

STABLE PARTICLES:
Stable particles have quantized charge Q and a characteristic natural frequency F. The natural frequency is related to the particle's rest energy E by the equation:
E = h F
where h is known as the Planck constant. The Planck constant is actually a composite of other physical constants. The mechanism that determines the precise characteristic frequency F and hence the rest energy E of a stable charged particle is not known.

The measured total rest energy of a free electron is 0.511 MeV and the measured total rest energy of a free proton is 938.2 MeV. Recall that 1 MeV = 10^6 eV. Every free electron at rest in a field free environment has the same rest energy and hence the same rest mass and same natural frequency as every other free electron at rest in a field free environment. Similarly, every free proton at rest in a field free environment has the same rest energy and hence the same rest mass and same natural frequency as every other free proton at rest in a field free environment.

For water the total rest energy per molecule is about:
938.2 MeV X 18 = 16.89 GeV / molecule. Recall that 1 GeV = 10^9 eV.
 

STABLE PARTICLE NET CHARGE:
The measured net electron charge is - 1.60217646 X 10^-19 coulomb. The measured net proton charge is + 1.60217646 X 10^-19 coulomb. As far as is known the net electron charge precisely balances the net proton charge and the magnitude of this net charge is the same for all electrons and all protons. This quantization of stable particle net charge lies at the root of quantum mechanics. The mechanism of this precise charge quantization is not known.
 

SEMI-STABLE PARTICLES:
Semi-stable particles are particles that are stable inside some atomic nuclei but which become unstable when ejected from a nucleus. An example of a semi-stable nuclear particle is a neutron, which within some isotopes has a half life of billions of years but which when ejected from an atomic nucleus spontaneously decays with a half life of about 11 minutes. There are other semi-stable nuclear particles, such as mesons, that have much shorter half lives.
 

NUCLEUS:
An atomic nucleus consists of an aggregation of stable and semi-stable particles. Some atomic nuclei, such as helium-4, are extremely stable. Other atomic nuclei are unstable and may have very short half lives. Some atomic isotopes have simple decay paths that release as much as 25 MeV per decay. A nuclear fission process may release over 200 MeV per fissioning atom. The energy release may be via decay product particle kinetic energy and/or photons. Most nuclear reactions proceed by emission of kinetic or radiant energy at every step. A few nuclear reactions are endothermic and only proceed in a high radiation or high particle kinetic energy environment. An example of such a reaction is:
(Li-7) + n + (kinetic energy) = (Li-6) + 2 n
This endothermic reaction is of great importance in production of tritium and its decay product He-3.
The follow on reaction is:
(Li-6) + n = (He-4) + (H-3)

Nuclei tend to build up in multiples of deuterium. (proton-neutron pairs which in essence are assemblies of 2 protons plus 1 electron).
 

ATOMS:
Free electrons and an atomic nucleus become bound into a mutual potential energy well known as an atom by emission of photons. The electron charges are uniformly distributed along the closed electron motion paths so that in a stable atom there is no emission or absorption of energy. The electrons tend to form pairs with cancelling magnetic fields. Helium has a central electron pair. As the atomic number increases the central electron pair becomes surrounded by four more electron pairs nominally located at the corners of a tetrahedron. That tetrahedron is then surrounded by four more electron pairs nominally located at the corners of a surrounding larger tetrahedron. The electron layers or "shells" continue to build up in this manner and give an atom its chemical properties and its characteristic spectroscopic emission-absorption lines. As the atomic diameter increases the binding energy associated with single electron ionization decreases.
 

IONS:
An ion is an atomic nucleus that does not have the exact number of bound electrons required to balance the positive nuclear charge.
 

CHEMICAL BINDING:
Complete electron shells have a lower energy per electron than incomplete shells. Hence atoms tend to chemically bind together to form complete electron shells. The electron shells are completed either by electron exchange (ionic bonding) or by electron sharing (covalent bonding).
 

PLASMA:
A plasma consists of a mixture of ions and free electrons. Typical laboratory plasmas have free electron kinetic energies in the range 20 eV to 10,000 eV.
 

ELECTRON BINDING ENERGY:
The electron binding energy for a hydrogen atom is about 13.6 eV. This is the energy per electron necessary to cause ionization of hydrogen. Hydrogen atoms tend to bind together in pairs to form H2 gas molecules. For helium the minimum energy per atom necessary to cause single electron ionization is about 24.6 eV.

The electron binding energy in the outer electron shell effectively determines the maximum inter-atomic binding energy for most molecules.
 

MOLECULES: When suitable atoms come together and emit a photon(s) they may become bound together into molecules or crystals. The interatomic binding energy (also known as chemical energy) that forms atoms into molecules is typically about 1.0 eV per molecule. The intermolecular binding energy that forms the heat of vaporization is typically about 0.05 eV per molecule.

Most chemical reactions proceed by emission of kinetic energy or by emission of radiation at every step. However, some chemical reactions can be reversed by supply of energy via application of pressure, heat, electricity and/or by selective physical removal of a particular reaction products as they form. Some chemical reactions can be accelerated by introduction of a catalyst that provides a higher probability energy exchange pathway.
 

GAS:
A gas is a cluster of molecules in which the individual kinetic energy of each molecule exceeds the intermolecular binding energy. Hence the movement of individual molecules of a gas is constrained only by the enclosure walls.
 

CONDENSATION:
Random thermal kinetic (heat) energy can be spontaneously emitted from a cluster of gas molecules via thermal electromagnetic radiation (photons). If there is not a corrsponding amount of radiation absorption this radiation emission process eventually reduces the average random kinetic energy per molecule remaining in the gas to a level below the intermolecular binding energy. The remaining molecules then become bound together by the intermolecular potential energy well to form a liquid or a solid. This process occurs during the condensation of water vapor in the Earth's atmosphere.
 

LIQUID:
A liquid is a bound cluster of molecules in which the individual molecules have sufficient random kinetic energy that they can rotate in place and can easily slide past one another. Hence a liquid in a gravitational field adopts the shape of the lower part of its container.

For water the intermolecular binding energy that defines the transition from the liquid phase to the vapor (gas) phase is given by:
(heat of vaporization) / (Avogadro's number)]
= [(40.65 X 10^3 J / mole) / [(1.602 X 10^-19 J / eV) X (6.023 X 10^23 molecules / mole)]
= .4213 eV / molecule
= 421.3 X 10^-3 eV / molecule
 

CRYSTALIZATION:
Random thermal kinetic (heat) energy can be spontaneously emitted from a liquid surface via either evaporation or via thermal electromagnetic radiation (photons). These cooling processes reduce the average random kinetic energy per molecule remaining in the liquid to a level below that necessary for individual molecules to rotate in place. The remaining molecules are then bound together by the potential energy well to form a solid. A crystal is a solid consisting of a highly ordered assembly of molecules. The heat that must be removed to make the transition from a liquid to a solid is known as the heat of fusion.

The highly ordered nature of crystals makes them structurally weak in certain directions with respect to the crystal axes. For this reason materials such as steel contain small amounts of key impurities and are forged to reduce the material to an aggregation of small randomly oriented crystals that is more capable of reliably bearing structural and impact loads than is an aggregation of larger crystals.
 

SOLID:
A solid is similar to a liquid except that the molecules can not rotate in place and can not slide past each other. An unstressed solid will maintain its shape without a container. The intermolecular binding energy that prevents molecular rotation can be obtained from the heat of fusion of the material. For water this binding energy per molecule is:
(heat of fusion) / [(Avogadro's number) X (unit change)]
= [333.55 X J / g X 18 g / mole] / [6.023 X 10^23 molecules / mole X 1.602 X 10^-19 J / eV]
= 622.2 X 10^-4 eV / molecule
= 62.22 X 10^-3 eV / molecule
 

THERMAL KINETIC ENERGY:
At room temperature the molecular thermal kinetic energy is about 0.025 eV / molecule
= 25 X 10^-3 eV / molecule
 

MECHANICAL EQUIPMENT:
In mechanical equipment a typical maximum CM motion velocity is 50 m / s. The corresponding CM molecular kinetic energy for water is:
(18 X 10^-3 kg / mole) X (50 m / s)^2 / [2 X 6.023 X 10^23 molecules / mole x 1.602 X 10^-19 J / eV]
= 2331.9 X 10^-7 eV / molecule
= .2331 X 10^-3 eV / molecule
 

HUMAN MOTION:
For humans a typical maximum CM motion velocity is 10 m / s. The corresponding CM molecular kinetic energy for water is:
(18 X 10^-3 kg / mole) X (10 m / s)^2 / [2 X 6.023 X 10^23 molecules / mole x 1.602 X 10^-19 J / eV]
= .9327 X 10^-5 eV / molecule
= .009327 X 10^-3 eV / molecule
 

SUMMARY:
The above representative calculations show that the CM molecular kinetic energy available for doing work is many orders of magnitude smaller than the potential (rest) energy and is also usually several orders of magnitude smaller than the thermal kinetic energy components on which it is superimposed. Generally:
(particle rest energy) >> (nuclear particle binding energy) >> (electron binding energy) >> (molecular random kinetic energy) >> (molecular CM kinetic energy)

A well designed single stage combustion turbine operated at its maximum safe material stress produces work output that is still an order of magnitude less than its thermal kinetic energy input. Higher energy conversion efficiencies are realized through the use of heat recovery boilers and additional turbine stages.

Human activity has negligible effect on the Earth's potential energy distribution and produces only a small change in the Earth's thermal kinetic energy distribution. However, life forms can only exist and flourish within a relatively small absolute temperature range. From the perspective of life forms a less than 1% change in the Earth's thermal kinetic energy distribution produces major climate change.
 

This web page last updated March 16, 2017.

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