## ENTROPY REDUCTION BY VOLUNTARY/INTENDED ACTIONS

Bahaa El-Din M. Mansour

Proceedings of the Seventh (7th) International Conference on Energy and Environment, Vol. 1, Cairo, Egypt, 11-13 March 2000

**ABSTRACT**

According to the principle of the increase of entropy, the human universe is approaching a dead state. It indicates degradation of exergies, decomposition of systems and complete randomness. This paper analyses entropy for the purpose of understanding the sources of producing entropy in the human universe. Consequently, it finds out the possibilities of reducing entropy. Based on useful information, introduction of voluntary actions for ordering/controlling systems and building-up exergies and valuable systems is a typical addition of negative entropy. In this concern, this work emphasizes on the photo-synthesis process development. It is a typical negative entropy addition by plant voluntary action utilizing renewable energy. Also, it emphasizes on the creativity of breeding fissionable new fuels from other fertile elements like breeding Pu239 and U233 from other elements, U238 and Th232 . It is a typical negative entropy addition by human action. Planned human voluntary actions may change or postpone the expected fate of the principle of the increase of entropy. Also, this paper suggests taking the statistical entropy as a quantitative measure of information and labor skills added value.

.**Introduction**

By the middle of the nineteenth century, the entropy was first discovered in the field of mechanical power generation from the heat energy. In that decade, experimental work was introduced by Carnot (1824), [1]. After that, the statements of the 2nd law of thermodynamics was introduced by Plank and Kelvin (1851) , [1]. Complementary works introduced by others led to the discovery of entropy. The entropy function was first explicitly introduced by Cluasius in 1865, [1]. Since that, the entropy is an essential function in the analysis of processes by the 2nd law of thermodynamics.

In 1872, Boltzman, [2] revealed the relation between the concept of entropy and probability. By statistical entropy, the general concept the entropy increase of a system indicates that it is changed from a less probable state to a more probable state.

Also, within the statistical concept of the entropy, Hartly (1928) , [3] introduced the entropy as an essential parameter in the information theory. By this the entropy increase indicates loss of information or increase of uncertainty encountered in a system or in an information carrier.

In relation to the second law of thermodynamics, the principle of increase of entropy or, alternatively, entropy maximum principle, is stated in all thermodynamic texts. It indicates that the total net change of entropy of a system and surroundings (or of an isolated system) due to any process is either zero or entropy increase. This means that the human universe will approach the complete equilibrium, or the dead state.

In the present work, analysis of entropy; its phases and indications is introduced. The analysis is held for the sake of finding out the sources of entropy increase. Consequently, finding out possibility of entropy reduction is investigated.

2. Phases of entropy

The entropy is first introduced as a function in the macro level. The following is the concerned function which describes the entropy change,

ds = Q/T (1)

where,

ds is the entropy change, kJ/K

Q is the quantity of heat (thermal energy) added to the system, kJ

T is the absolute temperature at which dQ is added, K

Thus, in general the entropy measures by one quantitative value the amount of heat added at its indicated absolute temperature. Meanwhile, the 1st law of thermodynamics is concerned only with the balance of heat added or taken without distinction of the temperature at which added or extracted.

In 1872, Boltzmann revealed the relation between entropy and probability by the following general form, [4, 5]

S = k ln w (2)

where,

S is the entropy, kJ/K

k is Boltzmann constant, (=Gas constant (R)/Avogadro’s No. (N)), kJ/K

w is the total number of possible microscopic states available to a system in the concerned conditions

Equation (2) can be modified to a more general form, as follows,

S – So = k ( ln w – ln P ) (3)

where

P is the whole population of all possible micro-states

Then, formula (2) is modified to

S = k ln (4)

where

is the probability of the set ( w ) concerned to the state conditions (= w / P)

Equations (3) and (4) were deduced in the two theories which relate the microscopic behavior of molecules to the macroscopic properties of thermodynamics. The two theories are the kinetic theory and statistical mechanics, [6]. The two equations (3) and (4) hold true provided that the quantum states are equally probable. If the micro-states are not equally probable, the equation is modified to the following expression, [6]

S = – k q ( Pi ln Pi ) (5)

where

Pi is the probability of the quantum ( micro-state) state “i”, between q states

If the constant k is adapted to concerned application, the two equations (1) and (2) lead to the same quantitative result, [6].

A word bit is an abbreviation of “ binary digit”. In order to appoint one option of two, 1 bit of information is required. In order to appoint one option of eight, 3 bits of information is required. In order to appoint one out of N options, I bits of information are required, where,

I = log2 N (6)

This formula was suggested by Hartly in 1928. Similar to formula (5), Shannon, 1948, [2, 3] suggested the following equation to appoint one decision from unequally probable N options, or symbols (like the letters in the English language ),

I = – N (Pi log2 Pi ) (7)

where

Pi is the probability of the i decision, between N options

I is amount of information required, bits

Thus, entropy has two phases applicable in the macro as well as the micro-level (statistical entropy), both of them lead to the same result. Also, the principle of entropy is applicable in thermodynamics, general measurement of order/disorder of populations/systems and as measurement of certainty/uncertainty in the information carrier.

3. Measure of thermodynamic potential

In the simple thermodynamic (P, V, T) system, there are two intensive properties, namely, the pressure (P) and the temperature (T). The potential due to the pressure difference (P) can be directly measured by mechanical work units. It is the integral of the value (P.dV), where P is the gauged pressure. Also, the potential due to the temperature difference (T) can be measured in mechanical wok units by applying Carnot cycle principle between the concerned two absolute temperatures. Name, it equals (Q (T/Th ), where Q is heat added at the hot temperature Th in Carnot cycle. Thus, the general measure of the thermodynamic potential due to differences of pressure and temperature combined together is evaluated in mechanical work units. The general measure can be taken with respect to a (Po, To) plane as exergy. This proves the significance of the available work (exergy) as a measure for the thermodynamic potential, Mansour, Ph. D. thesis submitted to Cairo University, 1998, [7].

Whenever there is a destruction of thermodynamic potential, there is a liberated work (exergy). If the exergy of concern is recovered as mechanical work, the process is able to be reversible. On the other hand, if the mechanical work is not completely recovered, the process is irreversible.

4. Entropy is a state property

By applying the 1st law of thermodynamics on a closed system, where material do not enter or leave its boundaries,

Q = dU + W (8)

where,

dU is change in the internal energy in the closed system, kJ

W is the work produced by the system at its boundaries, kJ

For a reversible process, Q = T.dS, then,

T.dS = dU + W

By substitution for dU = Cv . dT and dW = P. dV , P = RT/V and rearranging, then

dS = Cv . (dT/T) + R . (dV/V) (9)

Equation (9) proves that dS is an exact integral, because integrals of (dT/T) and (dV/V) do not need definition of the route of the process. Thus, the integral is

S2 – S1 = Cv . ln(T2 / T1 ) + R . ln(V2 / V1 ) (10)

Equations (8), (9) and (10) are also applicable on the irreversible processes. This is because if the full amount of the reversible work produced is recovered at the boundaries of the closed system, then it is a reversible process. But, in case of destruction of a part of the reversible work into internal irreversibility, this will produce additional heat absorption into the substance. The process can be considered as superposition of a reversible process accompanied by destruction of a part of the produced work into internal friction. Consequently, the produced heat of friction is absorbed into the system as additional heat. The three items of the equation (8) will adapt themselves to indicate this internal irreversibility /absorbed heat. Thus, the equations are applicable on irreversible as well as reversible processes.

Thus, the entropy change is an exact integral i. e. depends only on the state conditions at the initial and final points of concern. This means that entropy is a state property. Consequently, it indicates that entropy can stand alone as a measure for some significant values.

5. Entropy is the only indicator of loss of potential

As stated before temperature and pressure potentials are together evaluated as exergy. Exergy may be completely recovered as mechanical work (reversible process) or not (irreversible process). The produced mechanical work is either utilized in useful process or not. At all cases the mechanical work/ electricity will be finally dissipated as proper heat or friction transformed into heat at lower temperature. The irreversible part of exergy is transformed from the very beginning to heat absorbed at lower temperature.

Heat transfer at finite temperature differences (Th – TL ), is a type of exergy destruction (= Q (T/Th ). This amount is absorbed at the low temperature TL . Final increase in the entropy is ( = exergy destruction/ TL ). This value of entropy increase is ( = Q . (Th – TL )/ Th . TL ), which is completely equal to S ( = (Q/ TL ) – (Q/ Th ) ).

By invoking the significant fact that entropy is a state property, then detection of state conditions is sufficient for indicating exergy destruction even if there is no heat or work or mass transfer at the system boundaries. Entropy is the only indicator of loss of potential in isolated systems as it is detected in the state conditions.

6. The principle of entropy increase

By the previous analysis, for an isolated system, the process is either reversible or irreversible. For the reversible process, the total entropy produced is equal to zero. For irreversible process, the total entropy produced is a positive value. These two statements combined produce the following equation,

total Sisolated system 0 (11)

This equation indicates that entropy of isolated systems is tending to its maximum possible value. If the universe is considered an isolated system, it is approaching its maximum entropy. It means that the universe is approaching the equilibrium state. These statements or similar are encountered in most of the thermodynamic textbooks. The physical meaning indicates that all thermal potentials are going to be depleted. This would be done either utilized in useful processes or just spontaneously dissipated.

7. Intrinsic relation between spontaneity and the principle of entropy increase

Process changes are implemented by potential (exergy) expenditure. Expended exergy is dissipated as heat into lower temperature sink and detected as increase in the total entropy.

In relation to these facts, changes are driven by the influence of intensive properties which need to be controlled to be utilized. If there is no control, then under any disturbance changes will spontaneously take place driven by the influence of intensive properties while not utilized. Thus, intensive properties need to be ceased/controlled to stop/utilize their intrinsic tendency for driving system change. Utilized changes as well as unutilized changes are driven by expenditure of potentials (exergies). Consequently, entropy increases to realize the equilibrium state.

On the other hand, by considering the concept of statistical entropy (equation (2)), when the entropy increases to its maximum, it means that the total number of possible microscopic states (w) is the realized case. This means that the system is in the most probable state. In the probability theory, systems tend to be spontaneously in the most probable state.

Thus, tendency of isolated systems to the maximum entropy state is intrinsic under the influence of intensive properties and spontaneous tendency of systems to the most probable state. Consequently, the principle of entropy increase worth to be written as follows;

“ Negative entropy cannot be spontaneously added or generated in an isolated system”

8. Intended actions against spontaneity

Processes cannot be driven against there spontaneous direction except be intended action. Intended action means planned action based on right information to achieve the final goal of concern. This can be well understood in chemical reactions, where chemical potential is evaluated by Gibbs function. Also, the same principle can be well explained in case of pumping liquids to higher levels or pumping heat to higher temperatures. But, in all these cases expenditure of exergy (chemical exergy, or mechanical work) is a must. Also, expenditure of exergy in such processes may be reversible(i.e. with complete efficient storage/transformation of potentials/exergies ) or irreversible (i.e. with some exergy losses and entropy increase).

But, in the present work the author intends to explain that there is a possibility of addition of negative entropy to the isolated system either by intended action from outside or from inside as a voluntary action. In the present text, voluntary is used according to the definition: “1. Done, made, brought about, undertaken, etc., of one’s own accord or by free choice, 2. Of, pertaining to, or acting in accord with the will, [8].

9. Some possible phases of negative entropy

According to phases of entropy (item 2), counter actions can be done against spontaneity. The following are some possible actions for negative entropy production and addition for systems.

a. Reduction of uncertainty by information

As stated before phases of entropy encounter uncertainty. Reduction of uncertainty can be done by production of information for the purpose of reduction of uncertainty. Although, information without action utilize it will not add sensible changes to the system. But, generally it can be utilized in the strategic sense. Information stimulates useful changes in the correct efficient sense. Also, whenever it is used, it is a valuable negative entropy. Thus, reduction of uncertainty by information is a negative entropy addition to the concerned system.

b. Reduction of disorder by voluntary actions

Disorder increase means additional entropy of a system. Thus, ordering a system in the sense of increasing its feasibility for achievement of a certain goal is a negative entropy addition to the system.

c. Creation of exergy

According to Einestein’s law, mass and energy can be exchanged from one to

another according to the law, [9],

E = (1/gc) mc2 (12)

where,

E is energy liberated in joules, J

gc is conversion factor to balance units, ( = 1.0 for the present units)

m is mass, kg

c is the velocity of light, ( = 3 x 108 m/sec )

Both chemical and nuclear reactions are either exothermic or endothermic. All exothermic reactions liberate energy by conversion of mass to energy. In chemical reactions, the liberated amount of energy is so small that the mass change cannot be measured. Also, in chemical reactions, the reactants are changed to another chemical compounds without change in the nuclei structure. But, in nuclear reactions the reactant nuclei is changed to another isotopes or to other nuclei. Also, mass changes can be measured in atomic mass units (amu), [9].

Thus, it is required to process a planned voluntary action to convert mass to exergy. Such exergy is a pure negative entropy creation because it comes from non-exergy source. Due to differentiability of nuclei and isotopes, they are not all equally able to react by what is presently known by fission, fusion or being radio active. In fusion, two or more light nuclei fuse to form a heavier nucleus. In fission, a heavy nucleus is split into two or more lighter nuclei. In both fusion and fission, there is a decrease in mass resulting in exothermic energy, [9]. Due to the present available technologies practical limitations, nuclear fuels are limited.

Artificially produced fusion may be accomplished when two light atoms fuse together into a larger one. To cause fusion, it is necessary to accelerate the positively charged nuclei to high kinetic energies. In order to overcome electrical repulsive forces, temperature of reaction must be raised to hundreds of millions of degrees resulting in a plasma. The most important difficulties in controlling artificially made fusion reactor comes from generating and maintaining high temperatures and the instabilities in the medium (plasma). Suitable fuels for fusion present technology are isotopes of hydrogen deuterium (H2) and tritium (H3), [9].

Artificially produced fission, is practically accomplished by striking the positively charged nucleus by neutron at high, moderate or low speeds without being repulsed. Obtaining an artificial fission may be attained, but obtaining a sustainable (or critical ) chain reaction requires taking factors affecting the reaction into consideration. Such factors are:

– The nuclei have radii roughly 1/1000 those of atoms, [9].

– Neutron flux, it is the number of neutrons crossing an area of concern per unit time. It increases with neutron velocity.

— The probability of neutrons colliding or interacting with nuclei is proportional to an effective, rather than actual, cross-sectional area of the nuclei in question. This is called the microscopic cross section, or simply the cross section, of the reaction and is given the symbol (, barn ). It varies with the nucleus, type of reaction, and neutron energy, [9].

– Probability of reaction increases by the specific cross section of the reaction ( ) and the neutron flux (number of shot neutrons together with their velocity), [9 ].

– Relations between the cross section of reaction and fission neutron energy (neutron velocity) per materials of importance are studied, [9]. The study elaborated that there are three important regions. They are (1)the low neutron energy, (2) the resonance region, and (3) the fast neutron region, [9]. The resonance region is the region where maximum neutron absorption occurs. Fuels with good fission characteristics are those which are fissionable at low neutron energies.

– When a neutron is absorbed in a fuel, it produces neutrons. One of these must be reserved for further absorption to keep the reaction going, [9]. Conversion or breeding ratio (C) is the number of produced neutrons per each absorbed neutron minus one reserved for fission substitution. Thus, a reaction with C 1 indicates that it produces additional gained neutrons for reaction. Such reactor is called a breeder, [9]. For sustainable reaction, it is required to release two or three neutrons per each one absorbed, [9].

There are only a few fissionable isotopes. Uranium U235, Pu239 and U233 are fissionable by neutrons of all energies. U238, Th232 and Pu240 are fissionable by high-energy neutrons only, [9]. Natural uranium mostly appears in nature in a composition of 99.282 mass percent U238, 0.712 mass percent U235 and 0.006 mass percent U234. Many isotopes that do not appear in nature are synthesized in the laboratory or in nuclear reactors. For example, uranium is known to have a total of 14 isotopes that range in mass numbers from 227 to 240, [9]. Thus, production of new isotopes or atoms from older or parent atoms can be practically accepted.

In this concern, the author like to emphasize on the present practical possibility on constructing breeder reactors. A breeder reactor is one in which more fissionable fuel is produced than is consumed, or one that has a conversion, or breeding, ratio greater than 1. Such a system would convert the abundant U238 (99.3% of all natural uranium) to fissionable Pu239 and hence extend the human fuel reserves for centuries to come, [9]. In a fast breeder reactor, the objective is to maintain a chain reaction with fast neutrons that have an average energy of about 1 Mev by fission in U235 and Pu239. It also, must provide additional fast neutrons sufficient to convert U238 to Pu239, [9]. This is a breeding reaction that converts fertile U238 into fissionable Pu239, [9]. Fast breeder reactors are already designed and constructed in Britain, USSR and France. France has what must be considered the most ambitious program. A 600-MW(t), 250-MW(e) reactor, the Phenix has been in operation since 1973 and has given excellent service, [9]. Also, the Super-Phenix, 1200-MW fast breeder reactor is expected to be operating at present, [9].

Thus, a breeder reactor is one in which more fissionable fuel is produced than is consumed, or one that has a conversion, or breeding, ratio greater than 1, [9]. It is a typical creative voluntary/intended action work for producing exergy from non-exergy resources.

In addition to the previous example, the maximum possible attainable temperature by solar heating without concentrators, cannot exceed 200 oC. This indicates how poor exergy is obtained by utilizing the solar energy in it’s spontaneous form. By introducing voluntary/intended actions in the field of solar energy i.e. by introducing solar energy technologies, the thermal energy collected can be put at higher temperatures or converted to electricity. Thus, raising exergy obtainable from a renewable energy source rather than amount obtained spontaneously. But, among the possible voluntary/intended actions for increasing obtainable exergy from the solar energy, there is the immense voluntary action executable by live plants. It is the creative voluntary photosynthesis process. It cannot be produced except by live plants. By photosynthesis, storage of hydrocarbons (chemical exergy) is executed. By combustion, this chemical exergy can be released as thermal energy at high adiabatic temperatures. Finally it is production of exergy from renewable energy source by successive voluntary actions. This is noting that Photosynthesis utilizes the ultraviolet while heating utilizes the infra-red of the solar spectrum.

10. Negative entropy calculations

Total negative entropy change from initial state to final state is a declaration of entropy change of the three phases declared in item (2). The initial state conditions can be taken as the maximum entropy state conditions or can be taken any arbitrary state. The author suggests to express the total entropy in the form of a vector contain the three phases of entropy, (information, system internal order, exergy destruction). This is to express the specific characteristics of each component. Information has the property to be strategic negative entropy. The following is the suggested calculation method.

a. Entropy change due to information

The only counted here is only information which removes uncertainty, [2]. From a pragmatic point of view, information will be utilized for obtaining a workable decision (or the right predicate in a proposition). In case of availability of zero information, the decision is taken completely at random. Either formula (6) or (7) is applied. By earning more information, the set of the workable decisions will occupy larger portion from the population of available options. Entropy will decrease. The set of workable decisions can be got to further narrow set by introducing the set of optimum solutions. The optimum may be a unique solution. Then, information entropy goes to zero. Also, the entropy units can be bits as suggested by the information theory, or it can be dimensionless while taking the change in the solution set divided by the population. The dimensionless entropy is more simple and still indicative because this change is the important part for the statistical entropy study.

b. Entropy change due to system internal order

Based on the correct information, the system is put into a narrow state conditions. This can be done by system ordering or by industrial processes. Narrow or fine quality specifications of the acceptable product increases ordering/industrial processes. This is expressed in skillful processes and thorough tolerances. As this must be implemented while putting the system into the solution set conditions, then the final entropy probability set will be the product of the two probabilities, the decision/information and the implementation probabilities multiplied. The entropy formula No. (4) is suggested to take the following form,

Simpl = ln (inf . impl.) (13)

where

Simpl is entropy due to implementation of decision, dimensionless

inf , impl is the probability of the set at the state conditions (= w / P), with subscripts inf and impl for the information and implementation phases respectively

c. Entropy change due to exergy changes

Calculations of this phase are the normal calculations as declared by equations (1), (2),(4) and (5). If formula (1) is used in actual fission process the amount of heat (Q) and the absolute temperature at which heat is recovered will indicate exergy generated. Negative entropy will be calculated considering raising amount of heat (Q) from the ambient temperature (temperature of the heat sink) to the temperature of the reactor.

As an alternative, the three entries can be added together if the information entry is calculated on natural logarithm basis and exergy degradation component is divided by k, Boltzmann constant. Thus, the three components of entropy are considered in the direction of addition of ordering the system into closer sets.

Examples:

In the present text there are two significant examples of negative entropy addition examples, (item 9.c). The first is production of fissionable fuels from fertile fuels. Information was stratified in a strategic storage up to a certain critical amount, it was able to imply to a suitable decision. In this concern, the uranium itself had not been considered as a source of energy/exergy up to the year 1939. Historically, this can be at that year, 1939 with the famous letter sent by Einstein to the United States President to draw his attention to the possibility of atomic bomb. This dramatic event was made possible by Hahn and Strassmann’s discovery, the final necessary link in a chain of scientific discoveries that made the whole thing feasible, [9]. The negative entropy vector of concern was able to be filled only by figures in it’s first entry. After achieving the critical amount of information, a decision for producing exergy (fissionable fuel), and an industrial process was able to be specified. Each step in the industrial process indicates it’s own necessary information. Also, skill required for implementation. Negative entropy encountered in skillful process is expressed in the narrow tolerance. Workable design may be achieved, but industrial capabilities may need additional industrial capabilities. These capabilities are expressed in the second entry of the negative entropy vector. Negative entropy due to fuel breeding is calculated by the equations of fuel exergy calculations or by equation (1) as indicated in section (10. c).

The second significant example is the photosynthesis. From a human point of view, the plant system is fueled by a renewable energy. Also, a very significant process of extracting O2 from CO2 which is a process against the spontaneous direction of chemical reactions. Just driving this process against spontaneity is a creative process which may indicate some figures in the first and second two entries of the negative entropy vector. Also, the same argument can be raised for production of food or useful agricultural products. But, these valuable processes are done by the intrinsic activities of plants. Noting that these processes cannot be done by dead plants, then they are typical voluntary actions. Evaluation of the entries can be done from the human present capabilities. This is just to understand how much valuable processes done by plants for humanity.

11. Conclusions

By the present work, neither the second law of thermodynamics nor the principle of the entropy increase is violated. Spontaneous tendency of isolated systems to the maximum entropy state is intrinsic under the influence of intensive properties forces and spontaneous tendency of systems to the most probable state. Utilized changes as well as unutilized changes are driven by expenditure of potentials (exergies). Thus, driving any change against spontaneity of systems must be done by a voluntary/intended action.

The principle of entropy increase states that the universe, as an isolated system spontaneously tends to complete degradation of potentials, decomposition of systems and complete randomness. This is true on condition that there is no negative entropy added.

The three phases of entropy are the information, order/disorder, and exergy. By voluntary actions, negative entropy can be added to the systems. Evaluation of the negative entropy added is declared by a vector encounters the three entries of information, implementation, and exergy creation. As an alternative, the three entries can be added together if the information entry is calculated on natural logarithm basis and exergy degradation component is divided by k, Boltzmann constant to be dimensionless. Thus, the three components of entropy are considered in the direction of addition of ordering the system into closer sets.

Fast breeding of fissionable fuel from fertile materials is a typical negative entropy production by voluntary/intended actions. Also, the plant creative operations in the photosynthesis activities is another example of voluntary/intended actions for negative entropy production. The photosynthesis processes cannot be implemented by dead plants.

The negative entropy is a genuine physical quantity can be voluntarily produced and added to systems. This quantity measures the amount of creativity in the added value to the system; (information, order, exergy).

Although negative entropy calculations are introduced in the text in the field of exergy production, it is recommended to be applied for value added evaluation in the creative or industrial processes.

References

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