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XYLENE POWER LTD.

ENERGY BALANCE

By Charles Rhodes, Xylene Power Ltd.

CONSERVATION OF ENERGY:
A simple expression of the law of conservation of energy is: Everything is formed from energy. Energy cannot be created or destroyed but can be changed in form.
 

WORK:
A guided flow of energy has the capacity to do work which means that it can be efficiently converted into mechanical or electrical energy. Electricity flowing along a power transmission line is an example of a guided flow of energy. Water flowing downhill in a pipe is a guided flow of energy. By contrast solar energy absorbed by Earth almost immediately becomes heat which is not guided energy, it is thermal energy.
 

PRIME ENERGY SOURCES:
The sources of prime energy that mankind can utilize are: past solar energy, present solar energy, Earth's residual kinetic energy, Earth's residual thermal energy and nuclear energy. All other energy forms available to man are derived from these five prime energy sources.
 

STEADY STATE ENERGY BALANCE:
At steady state conditions the Earth's average surface temperature is constant. The total energy flux supplied by prime energy sources equals the total infrared energy flux emitted into outer space.
 

WORK:
At steady state conditions work can be done when the absorbed prime energy flux has a higher per photon energy than the 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, doing work causes an increase in entropy.
 

SOLAR ENERGY:
Most of the solar energy that is incident on the Earth consists of electromagnetic photons with wavelengths in the near ultra-violet (.1 um to .4 um), visible (.4 um to .7 um) and near infrared (.7um to 2.8 um) ranges. About 30% of the incident solar photons are reflected back into space. The remaining solar photons are absorbed. A solar photon can cause a chemical reaction, a change in state, a change in phase or a change in temperature. Eventually the energy carried by the absorbed solar photons is all converted into heat. This heat is radiated back into space via infrared photons. Small long term oscillations in the average rate of absorption of solar energy and average rate of emission of infrared energy cause cause temperature oscillations known as ice ages.

Man has devised various ways of obtaining work from the processes that convert solar photons into infrared photons. Two examples of man's intervention in these processes are as follows:

1) Past Solar Energy: Past solar photons incident on green plants caused photosynthesis whereby carbon dioxide and water combined to form carbohydrates. A small fraction of these carbohydrates accumulated at the bottom of water bodies or underground where over a long period of time anaerobic biochemical reactions converted the carbohydrates into hydrocarbons. Today man mines these natural accumulations of hydrocarbons (coal, natural gas and oil) and burns them, thus releasing as heat past solar energy that was absorbed by the green plants. This heat is radiated into space via infrared photons. Over the long term The the solar energy absorbed equals the infrared energy flux transmitted, but man obtains work via the process of converting higher energy solar radiation photons into a larger number of lower energy infrared radiation photons.

2) Present Solar Energy: Present solar photons absorbed by the ocean cause evaporation of water. The resulting water vapor rises and cools at higher altitudes where it condenses emitting part of its energy as infrared photons. The water falls as rain onto high elevation land. This water becomes part of a river that flows downhill to the ocean. However, along the way man may use a hydro-electric generator to change part of the kinetic energy of the flowing water into electricity. This electricity is transmitted along a power line and is converted into heat or chemical energy at the electrical load. The chemical energy ultimately becomes heat. All of the heat is radiated away from the Earth via infrared photons. Over the long term the solar energy absorbed equals the infrared energy emitted, but man has obtained work via the process of converting higher energy solar radiation photons into a larger number of lower energy infrared radiation photons.
 

EARTH'S RESIDUAL KINETIC ENERGY:
Residual kinetic energy of the Earth-Moon system causes ocean tides. Residual kinetic energy together with solar energy causes wind. Man can convert tide and wind energy into electricity, which is dissipated in the electricity load as heat. This heat is radiated into space via infrared photons. The related energy flux is constant, but man can obtain work from the process of conversion of residual kinetic energy into infrared radiation.
 

EARTH'S RESIDUAL THERMAL ENERGY:
Residual thermal energy in the Earth's core can be accessed via deep drilled wells in active volcanic areas. In this case the heat source is inside the Earth. To obtain work man arranges things so that a flow of water is heated by the hot magma to form steam. After passing through a turbine to generate electricity the steam is condensed to water. As part of the condensation process infrared radiation is emitted into space. At the electrical load further heat is dissipated which becomes infrared radiation. The total infrared radiation carries the same energy flux as is captured by the water from the hot magma.
 

NUCLEAR FISSION ENERGY:
The source of nuclear fission energy is stellar supernova processes that formed the nuclear fuel prior to the formation of planet Earth. A nuclear reaction releases heat. Typically in a nuclear power plant this heat is used to make high presure steam. Part of the heat in this steam is converted into electricity. The remainder of this heat is removed by cooling water and is dissipated as infrared radiation.

The electricity converts to heat in the load. All of the aforementioned heat is ultimately radiated into space via infrared photons. Man obtains work from the process of converting energy carried by high temperature (high frequency) photons from the nuclear reaction into low temperature (low frequency) infrared photons.
 

NUCLEAR FUSION ENERGY:
The source of nuclear fussion energy is fusion of hydrogen atoms into helium atoms, similar to the processes that presently operate in our sun. A nuclear fusion reaction releases high temperature heat. Typically in a nuclear power plant this heat is used to make high pressure steam. Part of the heat in this steam is converted into electricity. The remainder of this heat is removed by cooling water.

The electricity converts to heat in the load. All of the aforementioned heat is ultimately radiated into space via infrared photons. Man obtains work from the process of converting energy carried by high emperature (high frequency) photons from the nuclear reaction into low temperature (low frequency) infrared photons.
 

THERMAL EFFICIENCY:
Energy Ea of a high temperature photon:
Ea = h Fa
where:
Fa = photon frequency
and
h = Planck constant.

Similarly, energy Eb of a low temperature photon:
Eb = h Fb

Energy input via high temperature photons:
Na h Fa
where:
Na = number of input photons

Energy dissipated via low temperature photons:
= Nb h Fb
where Nb = number of dissipated photons.

Conservation of energy requires that:
Na h Fa = Nb h Fb
= Na h Fb + (Nb - Na) h Fb

Hence:
Na h (Fa - Fb) = (Nb - Na) h Fb

The maximum possible work is:
W = Na h (Fa - Fb)
where the maximum possible work that is available from each input photon is:
(Ea - Eb) = h (Fa - Fb)

The input energy is:
Na h Fa

Thus the maximum possible efficiency of conversion of a thermal energy into work is:
Efficiency = W / (Na h Fa)
= Na h (Fa - Fb) / (Na h Fa)
= h (Fa - Fb) / h Fa
= (Ea - Eb) / Ea
= (Ta - Tb) / Ta
which is also known as the Carnot efficiency. It is a fundamental limit on the efficiency with which a flow of heat can be converted into mechanical power.

Work is useful mechanical energy that can be transmitted via electricity. Thus this relationship limits the efficiency of thermal electricity generation. The only way to improve this efficiency is to have higher energy photons in the working fluid (steam) where work is harvested via a two stage turbine. That efficiency is generally limited by the high temperature strength of the materials used. In the steam system of a typical water cooled nuclear power reactor:
Ta = 600 deg K
Tb = 300 deg K
Carnot efficiency = 1 / 2
Actual realized efficiency = 1 / 3
 

SUMMARY:
Thermal energy that provides useful work operates by conversion of an energy flux carried by high energy photons into an equal energy flux carried by a larger number of lower energy photons.

Short term storage of energy is possible but over the long term the absorbed solar energy plus the released nuclear energy plus the decrease in Earth's residual kinetic energy plus the decrease in the Earth's residual thermal energy must equal the total emitted infrared energy.
 

This web page last updated September 25, 2020.

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