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

This web page reviews physics related to use of a flow of energy to do work. Energy that can do work is tiny ripple on the total energy distribution. However, this little ripple has commercial value and supports our civilization.

Since the dawn of civilization man has needed water for use at elevations above the level of local wells, ponds, lakes and rivers. A consistent measure of work done in a day was the weight or volume of water lifted in a day multiplied by the height that the water was raised. Thus the amount of work done in a day by free men, slaves, draft animals, water power, wind power, heat engines and electricity could readily be compared. This work was measured by the amount of gravitational potential energy developed.

Recall that for a single particle i:
Ei = Eik + Eip
Eik = kinetic energy
Eip = potential energy
Ei = total energy

dEik = change in kinetic energy
dEip = change in potential energy
dEi = change in total energy = work absorbed

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

If otherwise isolated systems interact in a manner that causes a transfer of an element of energy dE and an element of momentum dP to pass from one system to the other system then the system that supplied the transferred energy is said to have done work on the system that received the transferred energy.

On the web page titled: BASIC PHYSICAL CONCEPTS PART A - ENERGY & MOMENTUM it is shown that the kinetic energy transferred between systems is given by:
dE = [d(Pc - Po) / dT]*d[(Xc - Xo)].

Capacity to do work comes from harnessing a 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 thermal expansion/contraction of a gas (as in a heat engine or wind turbine), from evaporation/condensation of a vapor in a gravitational field (as in hydroelectric power), from gravitational shape distortion of the rotating Earth (as in tidal power) or from conversion of mass into kinetic energy and emitted radiation (as in nuclear 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 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 can be converted into potential energy, kinetic energy, radiant energy or heat. In an engine heat is used to expand a gas under pressure. Expansion of the gas in a specific direction develops relative momentum and kinetic energy that can be used to do work.

The rate at which steady state work that produces random molecular kinetic energy (heat) can be done is limited by the rate at which the heat can be dissipated and radiated into outer space.

The total energy E of an isolated system as seen by an inertial observer at Xc, Vc is given by:
E = Sum of all Ei

A fundamental issue in the structure of the universe is that each particle is surrounded by a vector field containing potential (rest) energy which is part of Eip. The potential energy / unit volume at X contained in the external vector field due to the singularity at Xi is proportional to the (local vector field strength)^2. This relationship is a fundamental property of the universe. With different proportionality constants this relationship holds for gravitational, electric and magnetic fields.

The total external radial vector flux from a particle is proportional to the contained energy or contained charge and hence is nearly constant because most of the energy or charge is concentrated close to the nominal position of the particle. The surface area of a sphere of radius |X - Xi| is:
(4 Pi |X - Xi|^2).
Hence, for a single isolated particle the external local vector field strength diminishes approximately in proportion to:
1 / (|X - Xi|^2).
Vector fields from different particles add linearly. Hence, overlap of vector fields from multiple particles changes the local vector field strength and hence the total potential energy.

Force is the result of change in total potential energy with respect to particle position that causes a corresponding change in kinetic energy with respect to particle position.

F = (dE / dX) = (dP / dT)
F = force
E = energy
X = linear position
P = momentum
T = time

The force Fi on singularity i causes a change in kinetic energy dEki during a change in position d(Xi - Xo). Hence:
dEki = Fi * d(Xi - Xo)

The mechanism of interactions between fields that cause force at a distance is discussed at FIELD THEORY

The law of conservation of energy requires that for any isolated system the total system energy measured by an inertial observer is constant. Hence, if overlap of vector fields causes a change in potential energy the law of conservation of energy requires a corresponding change in kinetic energy to keep the total energy constant.

If two objects forming an isolated system interact the individual object energies can remain unchanged or an element of energy dE can be transferred from one object to the other or a new particle can be formed and emitted but the total system energy remains unchanged. Note that a process involving creation and emission of a new particle from an interaction between two previously existing particles is usually not reversible because such reversal requires a three body interaction. Except in neutron stars, the probability of occurrence of three body interactions is extremely small.

From the perspective of an external observer the total energy and the net linear momentum of an isolated system can be considered as being located at the CM of that system.

Thermal kinetic energy and rotational kinetic energy seen by an observer at the CM but that cannot be resolved by an external inertial observer become components of the rest energy seen by the external inertial observer. For the external inertial observer the velocity of the CM in the external observer's frame of reference establishes the kinetic energy due to linear momentum seen by this external observer. The change of thermal kinetic energy and rotational kinetic energy seen by an observer at the CM into potential energy seen by an external inertial observer is a very important concept. This concept explains how heat and rotation increase the CM rest energy as seen by an external observer.

The planet formation sequence is:
1) Widely separated dust particles contain maximum gravitational potential energy;
2) The gravitational potential energy converts to ordered kinetic energy;
3) The ordered kinetic energy converts to heat via inelastic collisions leaving the dust trapped in a gravitational potential well;
4) The heat converts to thermal electromagnetic radiation;
5) The thermal electromagnetic radiation propagates into space. This radiation reduces the remaining random kinetic energy that would otherwise allow some dust particles to escape from the gravitational potential well.

A net flow of energy along an axis (a flow of momentum) has the capacity to do work. For example: electromagnetic energy flowing along a power transmission line can do work; solar radiation flowing from the Sun to the Earth can do work; water flowing downhill can do work; and wind flowing in a specific direction can do work.

All of human civilization is based on harnessing flows of energy to do useful work. Once the work is done the total energy flow becomes a flow of atmospheric temperature heat. This heat is dissipated into outer space by emission of thermal infrared radiation.

Energy measurements usually take one of the following forms:
1) Measurement of mass of a fuel (eg Tonnes of coal);
2) Measurement of volume of a liquid fuel at a particular temperature (eg litres of oil);
3) Measurement of volume of a gaseous fuel at a particular pressure and temperature (eg standard m^3 of natural gas);
4) Measurement of capacity to do work (eg kWh of electricity);
5) Measurement of work done (eg Joules of gravitational potential energy formed);
6) Measurement of heat output (eg Joules of heat);
7) Measurement of mass or volume of liquid vaporized at a particular pressure and temperature (eg Kilograms of steam, litres of steam condensate).

Known material parameters such as the density of water at a particular temperature and the heat of vaporization of water at a particular pressure are used to convert these measurements to energy units.

Most energy conversion processes are characterized by an efficiency of the form:
Efficiency = (useful heat, work or capacity to do work output) / (heat, work or capacity to do work input)
However, energy efficiency does not have a unique definition, so a measurement of energy efficiency is only meaningful if the relevant definition of energy efficiency is also specified.

In some cases, such as commercial boilers, energy efficiency is calculated by measuring rejected waste heat as a fraction of the theoretical heating capacity of the fuel consumed.

At steady state conditions work can be done when photons are formed so that the energy flow remains the same but there is an increase in the number of photons and a decrease in average energy per photon. For example, on Earth work can be done when the flow of absorbed solar radiation has a higher per photon energy than the balancing energy flow of emitted infrared radiation. Another way of viewing this matter is that work can be done when heat flows from a hot source to a cooler sink. In scientific language, work can be done when there is an increase in entropy. When the energy flow remains constant but the average energy per photon decreases there is an increase in entropy.

All processes that can provide on-going useful work operate by conversion of an energy flow carried by high energy particles or photons into an approximately equal energy flow carried by a greater number of lower energy particles or photons.

Consider an energy conversion system that inputs photons each with energy Ea and for each input photon outputs a photon along one path with energy Eb and a photon along a different path with energy (Ea - Eb). In order to maintain a steady state energy flow Eb is fixed by the ambient atmospheric temperature. The theoretical maximum efficiency of this energy conversion process is given by:
(Ea - Eb) / Ea
Students of thermodynamics will recognize this expression as the Carnot efficiency, which is the theoretical maximum possible efficiency of a heat engine.

Once the work is done any steady state kinetic energy output will ultimately be converted into heat. Hence there will be more photons emitted at photon energy Eb, which increases the entropy of the universe.

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 minute fraction of total energy.

This web page last updated December 27, 2013.

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