XYLENE POWER LTD.

ENERGY COMPOSITION OF MATTER

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

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

SINGULARITY:
A singularity is a point in space near which simple far field approximations for electric, magnetic and gravitational fields are invalid.

PARTICLES:
A particle is a concentration of energy at or near a mobile singularity. A particle is a local energy solution to the equations that determine the evolution of the universe. In mathematics such a solution is known as an Eigenvalue. There are only a few different stable particle types.

Matter consists of a cluster of particles.

ENERGY COMPONENTS:
Total particle energy consists of potential (rest) energy plus kinetic energy.

The potential (rest) energy of each stable particle consists of a combination of core energy, magnetic field energy, electric field energy and gravitational field energy.

BINDING ENERGY:
As particles approach each other overlap of their fields can cause a reduction in total potential energy and a corresponding increase in total kinetic energy. The initial kinetic energy of free particles is sufficient to allow the particles to escape from the potential energy well that results from overlap of the particle's fields. However, the surplus kinetic energy tends to convert to photons which may radiate away into space. When photons are emitted and there is no off setting photon absorption the remaining particles become trapped together in their mutual potential energy well. The kinetic energy required to allow a particle to exit from this potential well is known as the binding energy.

RANDOM KINETIC ENERGY AND CM KINETIC ENERGY:
The kinetic energy consists of random thermal kinetic energy plus Center of Momentum (CM) kinetic energy that can potentially do work. 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 potential (rest) energy. Hence, in most practical situations the CM kinetic energy is only a microscopic ripple in the total energy.

UNSTABLE PARTICLES:
Many particles are unstable energy states that eventually 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. These particles have half lives in excess of billions of years. Antimatter particles are believed to be 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.

The measured total rest energy of an electron is 0.511 MeV and the measured total rest energy of a proton is 938.2 MeV. Recall that 1 MeV = 10^6 eV. The measured net electron charge is negative 1.602 X 10^-19 coulomb. The measured net proton charge is positive 1.602 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.

As far as is known every electron at rest in a zero magnetic field environment has the same total energy (mass) as every other electron at rest in a zero magnetic field environment. Similarly, as far as is known every proton at rest in a zero magnetic field environment has the same total energy (mass) as every other proton at rest in a zero magnetic field environment.

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

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 in 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 15 minutes. There are other semi-stable nuclear particles such as mesons, that have shorter half lives.

NUCLEUS:
An atomic nucleus consists of an aggregation of stable and semi-stable sub-atomic 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 decay paths that release as much as 25 MeV per decay. The energy release may be via kinetic energy and/or photons.

ATOMS:
Free electrons and an atomic nucleus become bound into an atom by emission of photons. The remaining electrons and the atomic nucleus are trapped in an electric / magnetic potential energy well.

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

PLASMA:
A plasma consists of a mixture of ions and free electrons. Typical laboratory plasmas have free electron kinetic energies in the range 10^2 eV to 10^4 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. For helium the minimum energy per electron necessary to start single electron ionization is 25 eV. For helium the minimum energy per electron required to cause double ionization is over 50 eV. An atom with a large atomic number may require hundreds or thousands of eV per electron to achieve full ionization.

MOLECULE: When suitable atoms come together and emit a photon(s) they may become electrically and magnetically bound together into a molecule. The interatomic binding energy (also known as chemical energy) that forms molecules is typically a few eV per molecule. The intermolecular binding energy that forms a solid is typically a fraction of one eV per molecule.

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.

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 reduces the average random kinetic energy per molecule remaining in the gas to a level below that necessary for individual molecules to escape from their mutual potential energy well. The remaining molecules then become bound together by the potential energy well to form a liquid. This process explains the condensation of water vapor.

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 hence 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 maintains the liquid phase is given by:
(heat of vaporization) / [(Avogadro's number) X (unit change)]
= (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

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.

SOLID:
A solid is similar to a liquid except that the molecules can not rotate in place and hence 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

CRYSTAL:
A crystal is a solid consisting of a highly ordered assembly of molecules.

MECHANICAL EQUIPMENT:
In mechanical equipment a typical maximum CM motion velocity is 50 m / s. The corresponding 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 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 kinetic energy available for doing work is many orders of magnitude smaller than the potential (rest) energy and is several orders of magnitude smaller than the thermal kinetic energy components on which it is superimposed.

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 very little effect on the Earth's potential energy distribution and produces only a small change in the Earth's thermal kinetic energy distribution. However, a less than 1% change in the Earth's thermal kinetic energy distribution produces substantial climate change.

This web page last updated April 13, 2012.