XYLENE POWER LTD.

ENERGY OVERVIEW

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

INTRODUCTION:
This web page introduces various energy concepts.

ENERGY - A HISTORICAL DEFINITION:
A historical definition of energy is "capacity to do work". This historical definition is adequate for commerial transactions involving exchange of capacity to do work but does not properly describe physical phenomena.

ENERGY - A MORE GENERAL DEFINITION:
Energy is "the basic constituant of the universe". Everything that exists is composed of energy.

CONSERVATION OF ENERGY:
The foundation of modern science is the belief that energy can neither be created nor destroyed but can be changed in form. In an isolated system the total amount of energy remains constant independent of time.

ENERGY QUANTA:
Energy occurs and propagates in finite size packets known as quanta (singular is quantum). In certain circumstances a high energy quantum can convert to multiple lower energy quanta.

PHYSICAL LAWS:
A set of mathematical relationships (physical laws) that govern the behavior of energy and hence the evolution of the universe. These mathematical relationships account for the formation and interaction of energy aggregations known as photons, particles, atoms, molecules, dust, rocks, planets, stars and galaxies.

ENERGY OCCURRENCE:
Energy is contained within particles, in the electric, magnetic and gravitational fields surrounding particles and in propagating photons. Net electric charge occurs only in integral multiples of the electron charge (1.602 X 10^-19 coulombs). Net electric charge causes an electric field. Electric charge motion causes a magnetic field. The presence of energy causes a gravitational field.

MAXWELLS EQUATIONS:
The behavior of electric charge and electric and magnetic fields is described by a group of differential equations collectively known as Maxwells equations. Maxwells equations have both propagating and stationary solutions.

ELECTROMAGNETIC RADIATION:
Photons, also known as quanta of electromagnetic radiation, are solutions to Maxwells equations that linearly propagate at the speed of light. Each photon has a characteristic energy, frequency and momentum, but has no rest mass. Examples of photons are:
gamma rays
x-rays
light
microwaves
radio waves
AC power waves

PARTICLES:
A charged particle at rest is a stationary solution to Maxwells equations. Examples of stable charged particles are the electron and proton. A charged particle has distributed charge that moves along a closed path within the particle. The distributed charge extablishes a spherically symetric radial electric field. The charge motion causes a nearly cylindrically symetric magnetic field. The electric and magnetic fields contain energy that contributes to the particles rest mass. The particle has additional rest mass that is referred to herein as core energy.

UNSTABLE PARTICLES:
Unstable particles are particles that spontaneously break into other particles and/or photons. An example of an unstable particle is a neutron. A free neutron has a half life of about 15 minutes and will spontaneously break into a free electron, a free proton and a neutrino. Neutrinos propagate at the speed of light.

PHOTON EMISSION / ABSORPTION:
In a constant ambient magnetic field a stable charged particle has a stable energy. If there is a change in the ambient magnetic field, which affects the stable energy value, the particle will absorb or emit a photon to reach its new stable energy value.

QUANTUM MECHANICS:
Planck, Einstein, Bohr, Schrodinger and others developed mathematical equations that accurately describe atomic energy transitions. These equations are collectively known as quantum mechanics. In quantum mechanics a quantum of energy can only take certain discrete values.

PLANCK CONSTANT:
A photon is a quantum of electromagnetic radiation. The energy E carried by a photon is given by:
E = h F
where:
h = Plancks constant
= 6.626069 X 10^-34 J-s
and
F = the electromagnetic wave frequency as seen by an inertial observer (observer not subject to acceleration).
The Planck constant h is a function of the net particle charge, speed of light and the permiability of free space.

PHOTON ENERGY:
Due to its higher value of F a gamma wave photon contains many orders of magnitude more energy than a radio wave photon. Absorption of a gamma ray photon will damage a DNA molecule whereas the same molecule can safely absorb a radio wave photon. Hence gamma rays pose a serious biological health hazard whereas radio waves and radiation from low frequency AC power systems are not normally biological health hazards.

REST ENERGY:
Each particle has a rest energy Eo which is the total energy of the particle measured by an inertial observer when the particle is stationary in the frame of reference of the observer.

KINETIC ENERGY:
The kinetic energy Ek of a particle is its energy component due to motion of the particle in the frame of reference of the inertial observer.

TOTAL ENERGY:
Each particle has a total energy E which includes both potential (rest) energy and kinetic (motion) energy in the frame of reference of the inertial observer.

Thus:
E = Ek + Eo
When there is no particle motion in the frame of reference of an inertial observer:
Ek = 0

LINEAR MOMENTUM:
Each particle has a linear momentum P given by:
P = (E V) / C^2
= M V
where:
V = particle linear velocity in the frame of reference of the inertial observer
C = speed of light
M = particle mass

When there is no linear particle motion in the frame of reference of the inertial observer:
P = 0

RELATIVITY:
Einstein developed equations relating rest mass, rest energy, total energy, linear velocity in the reference frame of an inertial observer and gravitation. Usually gravitation is only significant in the proximity of very large energy aggregations.

The linear momentum P is related to total energy E and rest energy Eo via the equation:
E^2 = (P C)^2 + Eo^2
Note that (P C) and Eo are orthogonal to each other.

REST MASS:
The rest mass Mo and the rest energy Eo are related by the equation:
Eo = Mo C^2

KINETIC ENERGY APPROXIMATION:
The above equations give:
E^2 = (P C)^2 + Eo^2
= (E V C / C^2)^2 + Eo^2
= (E^2 V^2 / C^2) + Eo^2

Rearranging this equation gives:
E = Eo / (1 - (V / C)^2)^0.5
Hence:
Ek = E - Eo
= Eo[ (1 /(1 - (V / C)^2)^0.5) - 1]

For the common case of |V| << C this equation for Ek simplifies to:
Ek = (Eo / 2)[(V / C)^2]
= (Mo C^2 / 2) [(V / C)^2]
= (Mo V^2 / 2)
which is the Newtonian approximation for kinetic energy.

SPIN:
A particle rotating on its own axis with no translational motion is usually considered to be at rest. Its energy of rotation is usually considered to be part of the particles rest energy. Within a particle the charge motion that results in a magnetic field is more complex than simple rotation and is referred to as "spin".

REST ENERGY COMPONENTS:
The rest energy of a particle consists of the sum of the core energy plus the field energy. In interactions between particles portions of the field energy can be used to do work. Core energy cannot be used to do work unless a particle interacts with a corresponding anti-particle.

FIELD ENERGY COMPONENTS:
The field energy per unit volume has gravitational, electric, magnetic and momentum components.

FORCE:
A change in total rest energy due to a change in particles field overlap causes changes in particle momenta which are interpreted as a force.

PAIR PRODUCTION:
In certain circumstances a very high energy photon can change into a matter-antimatter charged particle pair (such as an electron plus an anti-electron). The sum of the particle and anti-particle charges is zero. The particle and anti-particle have equal rest energies.

CLUSTERS OF PARTICLES:
To evaluate the effect of field overlap within a cluster of particles the total rest energy of the cluster of particles is compared to the total rest energy of an equal number of identical but individually isolated particles.

In a cluster of particles the kinetic energy can be purely random (as with heat) or can be partially ordered which causes net cluster momentum that can to do work.

In a cluster of particles the total kinetic energy related to random charged particle motion can increase due to absorption of photons from an external source or can decrease due to emission of photons into space. Note that net absorption or emission of photons occurs at the outer surface of the cluster.

WORK:
Work is an energy transfer that causes a cluster of particles to acquire momentum (energy motion) in a particular direction. Work is required for important functions such as pumping fluids, moving goods and generating electricity.

Capacity to do work comes from directional flow of energy (momentum). Capacity to do work may come from capture of a stream of photons from the sun by a solar panel, from local thermal expansion/contraction of a gas (as in a heat engine or wind turbine), from local evaporation/condensation of a vapor in a gravitational field (as in hydroelectric power) or from gravitational shape distortion of the rotating Earth (as in tidal power).

Delivery to a remote location of capacity to do work may be done by closed loop circulation of an energy transport medium such as electrons in a metal conductor or hydraulic fluid in a pipe. Delivery of capacity to do work may also be done by open loop transport of combustible fuel, in which case the atmosphere provides the return path for loop closure.

Work converts to potential energy, kinetic energy, radiant energy or heat. The rate at which steady state work can be done is usually limited by the rate at which the resulting heat can be dissipated and radiated into outer space.

RELATIVE SIZES OF ENERGY COMPONENTS:
Generally for particles with rest energy:
Particle Core Energy >> Particle Field Energy
Particle Field Energy >> Particle Random Kinetic Energy
Particle Random Kinetic Energy > Particle Ordered Kinetic Energy (energy that can do work)

Hence energy that can do work is generally only a tiny fraction of total energy.

STAR FORMATION:
Stars such as the sun are believed to have formed by gravitational aggregation of neutral atoms, mainly hydrogen, from interstellar space. Interstellar hydrogen is believed to be a result of electrostatic aggregation of free electrons and free protons. The free electrons and free protons are thought to be products of the early universe.

SOLAR SYSTEM:
In our solar system particle core energy cannot be converted to photons because there is no available anti-matter. Hence, all energy in our solar system that can do work comes from existing kinetic energy or from overlap of particle fields.

NATURAL FLOWS OF ENERGY:
Nuclear fusion processes within a star such as the sun slowly convert solar hydrogen into heavier elements and liberate heat. In the heavier elements the average energy per constituant particle is less than for free particles. The sun loses energy primarily by emission of photons into space. The solar hydrogen loss via particle emission is relatively small compared to the solar hydrogen loss via fusion.

During their lifetimes stars emit large amounts of electromagnetic radiation. This radiation flux is radial, not random. This radial radiation flux enables capture and re-emission of energy by planets in a manner that allows performance of work on the surface of the planets.

About 30% of the solar photons that are incident upon the Earth are reflected back into space. About 70% of the solar photons that are incident upon the Earth are absorbed by atomic electrons near the Earth's surface, giving these atomic electrons surplus energy.

Atomic electrons occupy discrete energy states. An electron decaying from a high energy state to a lower energy state can transfer its surplus energy to another particle or can emit a photon. A change in electron energy due to photon absorption can cause an electric current which can drive a chemical reaction or which can be used to do work.

Electrons with surplus energy gradually lose energy by interaction with nearby molecules. The resulting local surplus in random molecular kinetic energy can expand a gas such as the atmosphere to create wind or can evaporate a liquid such as sea water to create rain. Wind and rain can be harnessed with suitable turbines to do work.

At steady state conditions all work eventually converts to random kinetic energy of molecules (ambient temperature heat). Randomly vibrating and rotating molecules containing separated electric charges continuously absorb and/or emit infrared photons. At the Earth's surface some of these infrared photons are emitted into outer space.

ENERGY FLOW BALANCE:
The Earth's surface temperature automatically adjusts to keep the average daily energy loss by emission of infrared photons into outer space approximately equal to the average daily energy gain by capture of solar photons. The difference between these two energy flows causes net thermal absorption / emission by the Earth.

ENERGY TRANSPORT:
Typically a natural directional flow of energy such as a water fall is used to supply energy to one end of an energy transport loop such as an electricity transmission line. At the other end of the energy transport loop the excess energy is used to do work and/or produce local heat. Both the work and the local heat ultimately become ambient temperature heat which converts into infrared photons that are emitted into outer space.

NON-DETERMINISTIC NEAR FUTURE:
The combination of energy aggregations and the ongoing radiative energy flows provides an environment that enables life as we know it. At the atomic and molecular scale the quantum mechanical equations for particle energy have multiple distinct real solutions. This multiplicity of real solutions together with suitable energy flows gives life forms a limited degree of choice regarding their own future.

DISTANT FUTURE:
There are only a finite number of free charged particles. The stars are constantly capturing these particles, converting their electromagnetic energy into photons and emitting those photons into outer space. Absent a mechanism for replacing the free charged particles, eventually the supply of electromagnetic energy from free charged particles will be exhausted.

It is possible to speculate that black holes, quasars or other massive astromomical objects might provide a mechanism for regeneration of free charged particles. However, that issue is beyond the scope of this web site.

This web page last updated April 13, 2012.