Saturday, January 24, 2009

A Riddle of Energy Part 1



Girish Abhyankar

Phone: +91 9860547471

Concept of energy

Universe is made up of particles – molecules, atoms, ions, photons. Particles cause various forces resulting into their own motion. “Motion of particle” we call energy.

Human societies use motion of particles - kinetic energy - in following different forms.

All the molecules forming a body constrained to move in one velocity vector: we call mechanical energy. Velocity measured in meters per second.

Random movement (in fluids) and random vibrations of molecules /diffusion of electrons (in solids): we call thermal energy or heat. Temperature indicates velocity of the motion.

Motion of electric charges constrained to move through conductor from one pole to the other: we call electrical energy. Electric current (in Ampere) indicates velocity of motion.

Free or constrained motion of photons: we call radiant energy.

All forms of energies are simultaneously present in any matter. We name mechanical, electrical (both constrained forms), radiant and thermal (normally random and free forms but can be constrained partially) energy depending on which motion we put to use. (Piston of an engine moves, and is also hot, radiating and electrically charged. We use only the constrained movement of all the molecules that make the piston and call it a source of mechanical energy).

Quantity of kinetic energy is a function of mass/number of particles and their velocity.

If particles, due to their specific positions, are capacitated to release kinetic energy (by a trigger), we call it potential energy or stored energy.

Human societies use the following different forms of potential energy.

Gravitational energy is the positional (height) energy of a body with reference to a datum, used as mechanical energy when released.

Chemical energy is the energy stored in configured arrangement of atoms/ions, used as thermal/electrical energy when released.

Accumulation of electric charges in capacitors is the stored electrical energy, used again as electrical energy when released.

Energy possible to be released by fission or fusion of atomic nuclei is nuclear energy, used as thermal and radiant energy when released.

Energy to activate a trigger for release of stored or potential energy into kinetic energy is called activation energy.

Laws of energy, traditionally called laws of thermodynamics:-

First law or the law of conservation: The energy of the universe is constant.

Second law or the law of entropy: The entropy of the universe always increases [2].

Both the laws are fundamental and applicable universally.

Entropy: At any moment of time every particle occupies a unique position in the universe. (Since one particle is occupying a position there can not be any other particle in the same position at that moment of time.) Forces depend on positions. Since position of every particle is unique, every particle experiences unique forces acting on it and therefore, motion of every particle is also unique. It is highly improbable that motions of particles are identical in respect of their velocity vector. Completely irregular motions of particles, as per the Law of Statistical Behaviour [1], result in their dispersal.

Entropy is a measure of dispersal of particles.

In all physical processes molecules and energies associated with their motions and positions disperse [3] in the direction of increasing probability [1]. Entropy is a function of the number of different ways or microstates in which the energy of the molecules in a system can be arranged by positions and velocities. The number of accessible microstates for dispersal of energy depends on the constraints imposed by internal and external forces on the molecular motions. If the number of microstates accessible for dispersal of energy is small, due to constraints, entropy is low. If the number of microstates accessible for dispersal of energy is large, with no constraints, entropy is high [3].

Entropy is at the highest when the rate of dispersal of energy is infinitesimal i.e. the dispersal virtually stops - a state of equilibrium corresponding to maximum of probability [1] for local and temporal frame of reference.

Entropy is independent of the path of the process (technology) and medium (materials) and depends only on the endpoint condition i.e. volume and temperature [2].

The Law of Entropy: Any spontaneous changes in a physical system occur in the direction of increasing entropy [1]. Energy of any type will change from being localized to becoming dispersed or spread out -- in space, in quantum states ("energy levels") of microstates and thereby yield systems with greater numbers of microstates [3].

Thus in processes of energy transformation, storage or transportation energy output is always less than the energy input because energy disperses continuously - entropy increases - and the energy available for the intended final usage reduces 1) in such processes 2) with the time.

Decrease of entropy is reversal of dispersal - collection.

Principle of decreasing entropy: Entropy in one part of the system can be decreased if there is a compensating increase of entropy in its other part. The Law of Entropy requires only that the total entropy of the system increase and this can be arranged by making the second factor larger than the first.

Example: Some weight is placed on a shelf above the floor. According to the Law of Conservation of Energy, it is impossible that this weight will spontaneously and without any external help rise toward the ceiling. On the other hand it is possible to drop one (larger) part of this weight to the floor and use the energy thus released to raise another (smaller) part upward [1]. This trick is possible only if the weight is initially at a good height – possesses sufficient gravitational potential energy. If the weight is already near the floor, nothing can be raised upward.

Entropy can also be decreased by applying energy from outside the system under observation - weight lifted by a crane powered by an engine that runs by increasing entropy of coal or crude oil. But the energy stored as gravitational potential energy in the lifted weight is always less than the coal/crude oil energy spent in running the engine.

Decrease of entropy is a fall-out effect of increase of entropy somewhere in the universe. Energy for collection (decrease of entropy) is always more than the collected energy.

Observations in Nature

Since entropy of the universe is increasing, we observe, universe is expanding. Stars throw out matter and energy in space. New, smaller stars are formed out of the matter and energy released from breaking-up of larger bodies. Matter and energies tend towards uniform distribution in space, on earth: denudation of mountains, soil erosion, etc.

Solar radiation is due to entropy increasing on the sun. Solar radiation, as received on surface of the earth, is composed mainly of three frequency ranges. About half lies in infrared (IR) range, the other half is in visible range and some also lies in ultraviolet (UV) range. Intensity of solar radiation received on earth’s surface varies greatly throughout the day and the year. Since solar radiation reaching earth has no constraint, it is high entropy energy.

Frequency band of IR radiation generally matches natural frequency of many molecules over the surface of the earth and their random resonating vibration is the heating effect. Most of IR radiation is converted into heat.

The life on earth has to convert the only energy source on earth - solar radiant energy - into a suitable form required for survival and reproduction. Surface heating - random motion with no constraint, high entropy energy - creates conducive temperature and other conditions, winds, rains etc, but can not be converted into low entropy forms of energy such as mechanical or chemical energy, because decreasing entropy is impossible.

Plant kingdom is able to store the other half - visible light and UV – of radiant energy falling on it as chemical energy: complex bio-mass molecules by synthesising carbon dioxide, water and salts. Synthesis is decreasing entropy, possible by using huge amount of high entropy solar energy. Since energy necessary for collection of the same energy is more than the energy collected, plant kingdom remains stationery and collects whatever solar energy falls at their location. Plant kingdom grows very slowly because input solar energy is of low power. Plants spread themselves over larger surface area to receive maximum of solar radiation. They also use wind, rain and animal kingdom for their expanse to remote places, and grow wherever all inputs required by them are present.

For millions of years, photosynthesis has been the only method of decreasing entropy using solar radiant energy, not superseded by more efficient method by life on earth.

Animal kingdom on earth enjoys energy collected by plant kingdom in the form of biomass - food and raw material (low entropy energy). Animal kingdom maintains itself at a temperature higher than the ambient temperature by burning food and can, therefore, convert heat to mechanical energy for movement and to electrochemical form for data processing and communication, memory, etc as movement related functions. Input energy requirement of animal kingdom is large due to losses in energy conversions, heat radiation and friction met by consuming high energy density food readily available from the plant kingdom.

Animal kingdom survives by adopting itself such that it lives and reproduces on food generated energy, free natural services and not requiring any other external energy.

External Energy (other than food generated energy)

Human societies use external energy, besides food generated energy, for additional security - shelters and storages - , for comfortable living - tools and machines - and for enjoyment - toys and communication gadgetry.

Resource energy can seldom be used by human societies directly in the form it is available in nature. Energy transformation, storage and transportation are necessary so that the energy is made available at the desired place, at the desired time and in the desired energy form with the desired specifications - temperature/voltage. This involves decreasing entropy. This is possible only if the resource energy is low entropy energy and entropy of some part of this energy can be decreased during sudden increase of entropy.

Thus, only low entropy resource is of any physical benefit to human societies; high entropy resource, however large in quantity and available perennially, is not. Example: A tanker ship full of crude oil is a low entropy source because crude oil molecules are constrained inside the tank with fewer accessible microstates for dispersal. This resource is useful. But, if the crude oil spreads over the sea due to shipwreck, the crude oil molecules free, not constrained, with far more accessible microstates for dispersal, the entropy goes high, total energy remaining the same. Crude oil of increased entropy is useless for any benefit to the human society.

Decreasing the entropy has been possible by all kinds of heat engines (equipments) working on the above mentioned principle because the resource energy - coal and crude oil - is constrained in small volume and therefore, entropy is low. Ores found spread out in nature; at the lowest energy levels - the highest entropy - are collected, refined and then heat engines (equipments) are built using crude oil and coal energy. Building equipments is, thus, a process of decreasing entropy. Part of crude oil and coal energy used is deemed embodied in the energy conversion and support equipments to access, extract/collect, process, transport, install, store, activate, control, dispose the waste generated and also maintain both, the equipments and the environment affected. Embodied energy is the stored energy in positional/structural arrangement of molecules, manifested by saving in the process energy or facilitating energy transformation. However, embodied energy itself does not participate in the energy flow.

Examples of saving in the process energy: energy put-in to make a knife is deemed stored in the knife as embodied energy. Knife saves energy in the process of cutting. Vehicles, tools, machinery and explosives save process energy. Shelters save energy for protection. Processed food, medicines save internal body energy. Telecommunication equipments save data transportation energy.

Examples of facilitating energy transformation: Energy converters such as boiler, turbine, engine, cell, alternator, transformer, motor, pump, radiator, compressor, etc.

Storages such as battery and dam – facilitating energy/material storage;

Transmission lines, pipelines – facilitating energy/material transport.

According to the Law of Entropy, energy essentially disperses during conversions, storages and transportations. Embodied energy also disperses marked by continuous degradation of original properties of the equipments due to weakening of structural bonds - rusting, wear and tear, deformation, chemical changes, aging and eventual break-down, faster with the usage. Dispersed energy is lost, not preventable by any technology.

Using technology human societies accelerate entropy increase of a low entropy energy resource: coal/crude oil (entropy increase of coal/crude oil will otherwise continue at a very slow rate) by way of friction, radiation, scattering and scrap and achieve their purpose in the process.


Considerable technological effort is devoted to development of all imaginable energy sources besides coal and crude oil because coal and crude oil reserves are exhaustible and also, their inefficient usage is damaging the environment. Solar radiation, wind, nuclear, hydro (rain and tidal) and natural/biogas are harnessed for electricity generation. Farm produce is converted to high density fuels as alternative to petrol and diesel. Energy from solar, wind, nuclear, rain water, tidal, hydrogen, geothermal, bio-fuels, etc is claimed to be renewable/sustainable/inexhaustible and friendly to the environment. It is necessary to check the correctness of these claims in larger interest of the human society. Attempts to evaluate these claims by energy accounting methods do not lead to conclusion.

Evaluation of the claims

The claimed renew able/sustainable/inexhaustible resources are evaluated below for conversion to any low entropy or constrained energy, particularly electricity, a desired energy form because it can be converted to mechanical, thermal, chemical or radiant energy conveniently. Electrical energy is movement of electrical charges, constrained to move through conductors from one pole to the other with very limited accessible microstates for dispersal and hence electrical energy is very low entropy energy.

Wind energy: Air molecules and their kinetic energy (A) are free, unconstrained and therefore, wind energy is high entropy energy, not possible to convert to low entropy, mechanical or electrical energy.

It is not possible to build a windmill of embodied energy (B) using energy in the wind because, due to high entropy, usable energy in wind (A) is less than the energy necessary to make the windmill or (A) < (B). Coal and crude oil energy (F) is, therefore, used for making windmills.

Energy embodied in windmill is less than the energy used making the windmill (B) < (F). In a windmill system, output energy is less than the input energy,

(C) + (B) < (A) + (F) where total energy delivered by the windmill in its life time is (C).

Rearranging the above expression, (C) + (B) ─ (A) < (F).

(A) < (B) and, therefore, (B) ─ (A) is always positive.

Thus, (C) < (F) or total energy delivered by the windmill in its life time is always less than the coal and crude oil energy input making the windmill.

Rearranging again, (C) < (A) + (F) ─ (B).

Since (F) ─ (B) is always positive, (C) < (A).

But as (A) < (B), (C) < (B) or the total energy delivered by the windmill in its life time cannot provide energy to make another windmill of the same capacity.

Solar energy: Radiant energy (A) from the sun is unconstrained and, therefore, the entropy is high, not possible to convert to low entropy thermal or electrical energy. Solar radiation concentrator or photovoltaic cell is made using crude oil and coal energy (F). The total energy delivered by the concentrator or the photovoltaic cell in its life time 1) is always less than the coal and crude oil energy input making them 2) cannot provide energy to make another concentrator or photovoltaic cell of the same capacity.

Hydro energy: Kinetic energy of rain or tidal water molecules (A) is unconstrained and hence entropy is high, not possible to convert to low entropy electrical energy. Hydro power plant is made and operated using crude oil and coal energy (F). The total energy delivered by the hydro power plant in its life time 1) is always less than the coal and crude oil energy input making it 2) cannot provide energy to make another hydro power plant of the same capacity.

Nuclear energy: Isotope of uranium, U-235, is the only fissionable substance on earth, always found strongly diluted by the heavier unfissionable isotope U-238 (0.7% of U-235 and 99.3% of U-238), hindering the development of the progressive chain reaction in natural uranium. It is, in fact, only because of this dilution by the inactive isotope that the highly fissionable atoms of U-235 still exist in nature, since otherwise they would have been all destroyed long ago by a fast chain reaction among them [1]. Since energy dispersal from the nuclear energy raw material has virtually stopped; the resource is at equilibrium. The entropy is the highest and therefore, it is not an energy resource of any energy. Nuclear power plants are built and operated using coal and crude oil energy. The total energy delivered by the nuclear power plant in its life time 1) is always less than the coal and crude oil energy input making it 2) cannot provide energy to make another nuclear power plant of the same capacity.

Natural/Bio gas: Gaseous form energy resource is a high entropy resource because gas molecules bubble out are free, unconstrained with very large number of accessible microstates to disperse. (Molecules of crude oil in liquid form are constrained by strong bonding forced with few accessible microstates for dispersal and, therefore, entropy is low. Energy density of natural gas as available on surface of the earth (STP) is 39.6 kJ per liter as compared to crude oil 37300 kJ per liter.) It is impossible to harness natural gas energy without external help. Gas power plants are built and operated using coal and crude oil energy where natural gas is compressed to 250 bar pressure to 11160 kJ per liter or liquefied to 25780 kJ per liter (decreasing entropy) for use in automobiles as fuel equivalent to petrol - 34920 kJ/liter or diesel - 38520 kJ/liter.. The total energy delivered by the gas power plant in its life time 1) is always less than the coal and crude oil energy input making it 2) cannot provide energy to make another gas power plant of the same capacity.

Farm produce: Natural biomass, 7.5 tons/hector, crop standing 1 m tall, in 100 days is 11000 kJ per square meter or 110 J/liter/day is a highly spread-out energy resource equivalent to less than a drop of crude oil/day - high entropy. Making and operating equipments, providing other inputs required cultivating, collecting the farm produce from very large area and processing them to high density fuel is done using crude oil and coal energy. Energy cultivating, collecting and processing is more than the net energy available from the farm produce generated high density bio-fuels.

Human/animal generated mechanical energy from farm produced food as original source is also high entropy energy and, therefore, its conversion to low entropy electrical energy is not possible.

Hydrogen, geothermal, natural biomass, etc are also high entropy sources and provide no net energy benefits to the human societies. None of the energy sources is renew able or sustainable for current high energy density technology and life style.

As (F) is always greater than (C); harnessing high entropy resources uses crude oil and coal in larger quantity; depleting their reserves faster and damaging the environment even more than if crude oil and coal were used directly for the same purpose.

Evaluation methods

Evaluation of energy sources for their renew ability or sustainability by energy accounting method requires input energy data independent of exhaustible energy source. But, equipments for harnessing energy are necessarily made using exhaustible crude oil and coal energy as original source and therefore, energy accounting method is not applicable. Observing entropy of the resource energy is the only method of evaluation.

Our energy measuring system has to be and is unidirectional - in the direction of increasing entropy. We convert all energies in question to heat and compare. We convert solar radiant energy to heat and measure. We burn biomass and measure the heat released. We compare these two measurements and conclude that 100 kJ of solar radiant energy must have been necessary to make 1 kJ of biomass energy.

We can not measure in the direction of decreasing entropy. We can not experimentally measure how much solar radiant energy is converted to say 1 kJ of electrical energy. A photovoltaic cell is necessary for this conversion which is made using coal and crude oil energy as original source. We can not experimentally measure input solar radiant energy, energy for compression and thermal energy that go in making coal and crude oil used in making a photovoltaic cell. Thus overall efficiency of photovoltaic cell can not be estimated. Input/output method of evaluation is not applicable to non-biomass – solar, wind, nuclear, hydro, etc - energy sources.

Coal and crude oil is available for free in nature. We pay only for the human services involved in providing us derivatives of coal, crude oil or biomass energy. Original source energy is free. If the input energy is largely free evaluation of an energy source for sustainability, independent of coal and crude oil, by input/output method is misleading.


Solar, wind, rain water, tidal, hydrogen, geothermal and bio-fuels are not renewable/sustainable/inexhaustible energy sources and they with nuclear and natural gas are not friendlier to the environment than coal and crude oil. Machines and gadgetry converting these energy resources into any low entropy energy are perpetual machines of the second type and do not deliver any energy on the net basis.

Energy resources that are of low entropy on or very near the surface of the earth - coal and crude oil - are only useful for current high energy density technology and life style.

Corollary: Superconducting energy for net energy saving is impossible.


[1] George Gamow, One Two three...Infinity (Bantam Books, 1979) p. 200, 226-8, 186-7

[2] Feynman Leighton Sands, The Feynman Lectures on Physics Volume 1 (Narosa publishing House 1997) p. 566, 568

[3] Frank L. Lambert, Professor Emeritus Occidental College, Los Angeles, CA.



November 15, 2010