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Publicly Available Published by De Gruyter July 19, 2017

Modern energetics: current problems in energy conversion and utilization of produced energy

  • Michail V. Alfimov and Vladimir F. Razumov EMAIL logo


In this study, we discussed the state-of-art in global energy industry in a historical retrospective and the forecast of its development for the next 25 years. At least in the nearest quarter of a century, the main source of primary energy will remain the chemical energy of different hydrocarbon fuels, including natural gas, coal, oil, and biofuels. In this context, of current importance becomes the problem of more rational utilization of produced energy. We analyzed the basic physical constraints that define a maximum efficiency of energy conversion and utiliztion of primary energy sources.


Energetics is one of most important spheres of human activity that defines civilization progress of human commonwealth. Energetics also dictates current directions of modern R & D, it is also used as a measure of economic level and environment safety, and defines politics and social relations in the society.

By saying energetics we mean the production, utilization, storage, and transportation of different kinds of energy. Power production (PP) is directly related to the size of gross domestic product (GDP): the higher PP, the larger GDP. A level of community development is characterized by the amount of produced and consumed energy per one person. Still another parameter defining a technological level and economic competitiveness is the power intensity of GDP.

To date, the production of a conventional GDP unit of 1000 US dollars requires the consumption of 0.2 tons of oil equivalent (TOE) all over the world – 0.1 TOE for developed European countries and the USA, and 0.3 TOE for Russia and CIS countries. The energy consumption by most developed nations (so-called golden billion) attains a value of 10 MW h per person at a GDP unit of above 10 000 dollars per person; for African and Asian countries the above indices are smaller by a factor of 10–100 [1].

Modern energetics is based largely on non-renewable sources of chemical energy – coal, gas, and oil – whose resources are limited. Great expectations are set on the use of renewable (alternative) sources of energy, which primarily include hydropower and biofuel and in the longer term, wind energy, solar energy, tidal energy, and geothermal energy. With regard to hydro – and bio-energy, they have found their niche in the energy sector, further expansion of limited number of objective reasons. In fact, they are reduced to the limitations of their involvement in real energy without disrupting the natural balance of their resources.

As for wind, solar, tidal energy, and geothermal energy despite their huge potential, the extent of their practical implementation still remains rather low, largely because of their low energy density and a need in large investments. Thus, expectations of a significant increase in the role of renewable energy in the near future is premature.

At least in the nearest quarter of a century, the main source of primary energy will remain the chemical energy of different hydrocarbon fuels, including natural gas, coal, oil, and biofuels. In this context, of current importance becomes the problem of more rational utilization of produced energy.

In this paper we are going to outline the state-of-art in global energy industry in a historical retrospective, the forecast of its development for the next 25 years, and the basic physical constraints that define a maximum efficiency of energy conversion and utilization of primary energy sources.

Main stages of energetics development and forecast up to 2040

In the process of evolution, the mankind went through several stages of primary energy utilization for its vital needs. At the earlier stages, people used to make their living only by hunting and gathering. Primitive man consumed (via meals) about 2000–3000 kcal a day and used only its own muscular energy developing a power of about 100–150 W.

Then the man began to cultivate land, grow grain, breed cattle, and use firewood to warm dwelling. Gradually, the man coped with coal mining and used the power of wind- and watermills to mechanize the grain processing and weaving manufacture. Nevertheless, the technical level of energy consumption remained close to that of primitive man for thousands of years.

The rapid growth in the production/consumption of energy got started with the invention of steam engine at the edge of 18th and 19th centuries. It was the first technological revolution when the mankind realized that coal can not only generate heat but also produce mechanical work by using the evolved heat. The steam engine replaced manual labor and afforded to create a new kind of transportation (locomotive and steamship). The need in machines gave impetus to rapid development of metallurgy and metal processing. For over the past 150 years, the overall production/consumption of energy has grown by a factor of 35 times, while the population of the Earth increased about 7 times (Fig. 1). Thus, the per capita consumption of energy is growing at a faster rate than the growth in total energy production. The main stages and periods in the development of energetics are presented in Fig. 1.

Fig. 1: 
          Energy development and population growth over the last 150 years and forecast up to 2040.
Fig. 1:

Energy development and population growth over the last 150 years and forecast up to 2040.

First stage (1860–1900) is characterized by rapid development of technology for conversion of thermal energy coal combustion into mechanical work of steam engine. At this stage, technological progress based on a new knowledge about heat nature that gave birth to a new branch of physics termed thermodynamics. In those times, the energy production by developed countries was on a level of 1 TOE/person a year.

Second stage (1900–1950) can be characterized by a wide use of internal combustion machine (ICM) and technologies for generation and conversion of electric power. Due to replacement of coal by liquid fuel (oil and products of its processing), ICM combined, two in one, a heat source and an actuating medium, which markedly increased the efficiency factor for conversion of heat into mechanical work. Creation of electric generator and electric motor resulted in transition to a new energy carrier – electric current. Large-scale production of electric power by thermal stations and hydropower plants, long-range energy transportation, and electrification of all spheres of vital activity made a new energetic basis of industrial society. The centralized power supply system came into being and united the output from all kinds of primary energy sources used to produce electricity. At this stage, the specific energy consumption had grown by a factor of 2–3, and the cost of energy got defined by the cost of oil rather than that of coal.

Third stage (since the 70s) can be associated with a sharp (10-fold) growth in oil price, rapid growth in nuclear energetics, and increasing role of renewable sources of energy.

Nowadays we are witnessing a transition to the Fourth stage which will be accompanied by further growth in oil prices. Consumption capacity of primary energy recourses (millions TOE) and forecast up to 2040 [2] are characterized in Table 1.

Table 1:

The consumption of primary energy in the world, million TOE.

2015 2020 2025 2030 2035 2040
Oil 4233 4445 4638 4772 4858 4931
Coal 4032 4314 4557 4726 4860 4952
Gas 3018 3303 3572 3850 4157 4418
Bioenergy 1406 1499 1592 1683 1778 1873
Nuclear power 705 822 917 1031 1111 1210
Hydropower 361 396 433 469 506 542
Others RES 215 350 485 619 755 890
Total 13 971 15 130 16 194 17 150 18 024 18 815

The energy outlook for the next 25 years suggests that the structure of global energy demand will become more balanced. By 2040, it is projected that shares of the major fossil fuels (oil, natural gas and coal) will account for one quarter of total consumption, and one quarter will have on all other fuels, including nuclear, hydro, bioenergy and other RES).

Nuclear energy will continue to increase in absolute terms mainly only at the expense of developing countries, but because of concerns with security issues, its share will not increase significantly.

Another important parameter is the production capacity of electric power worldwide (Table 2) [2]. The main sources of primary energy for generating electricity today are coal (41%), gas (23%) and hydropower (16%), which together provide 80% of the electricity produced. The next most important primary source for producing electricity is nuclear power (11%) and the remaining 9% comes from biofuels, oil, and renewables (wind, solar, tidal, and geothermal energy). In the next 25 years the situation will not change cardinally.

Table 2:

The world electricity generation from various kinds of primary energy, TWh.

2015 2020 2025 2030 2035 2040
Oil 908 880 851 820 786 751
Coal 9923 11 314 12 587 13 710 14 721 15 373
Gas 5576 6592 7757 8941 10 236 11 516
Bioenergy 412 508 643 841 1146 1639
Nuclear power 2732 3196 3578 4030 4352 4742
Hydropower 3857 4287 4722 5154 5586 6010
Others RES 924 1579 2309 3131 4065 5137
Total 24 332 28 354 32 446 36 627 40 892 45 168

It can be expected that in the nearest future the highest growth rates will be exhibited by renewable energy sources (RES) in view of ever decreasing production cost and increasing governmental support. To 2040, the fraction of RES (except for hydropower and biofuel) will attain a level of nuclear power production.

Structure of energy production and consumption

Schematic diagram for production/consumption of energy is depicted in Fig. 2. Non-renewable fossil fuels (oil, coal, natural gas, uranium ore) put together 86% of primary energy, the rest 14% belonging to renewable ones: 10% biofuel, 3% hydropower, and 1% all other alternative energy sources. Extracted primary energy is seen to comprise 91% chemical energy.

Fig. 2: 
          Structure of energy production and consumption.
Fig. 2:

Structure of energy production and consumption.

Produced energy is consumed in the form of heat, illumination, mechanical work, and electric power. Total power of all electric power plants is around 2.8 TW, these produce about 25 000 ТW h of electric power a year. Since total consumption of primary energy is 14 billion TOE, it can be calculated that only 15% of primary energy is converted into electric power. Nearly 70% of electric power is produced from primarily chemical energy in the order: chemical energy→thermal energy→mechanical work→electric power. Since largest losses happen at the stage thermal energy→mechanical work→electric power, the overall the efficiency factor for conversion has a value of 40% maximum. To date, direct conversion of chemical energy into electric power has not found its industrial-scale implementation.

Other types of non-chemical energy (nuclear, hydro, and other renewables) are being used to produce electric power, a higher efficiency being attained in hydropower production. Nuclear energy is converted in electricity via the thermal energy, so that the efficiency factor of atomic power plants never exceeds 33%.

It should be noted that, at the first stage, all primary chemical energy is converted into thermal energy and only a portion of this heat energy is used to produce electricity, in different proportions for different types of primary resources. For example, one third of the coal mined is used to produce electricity, while two thirds are used directly in industrial production, including metallurgy and production of materials. A large portion of produced natural gas (24%) is converted into electricity, but a much larger part of it is used for production of raw material for chemical industry. As for oil, only 3% of its production goes to electricity production, and the rest is used in various fields of consumption, including industrial production and around 80% for transportation needs, i.e. for production of fuel for internal combustion engines. Thus, a significant portion of the thermal energy, which is not converted to electricity, is used in transportation, industrial production, and domestic services.

It can be stated that the existing methods for conversion, accumulation, transportation, and utilization of produced energy result in a loss of 60% of primary energy. The consequences of this consist of not only ever accelerating depletion of non-renewable energy resources but also a significant violation of the ecological balance.

In view of the fact that chemical energy will long remain of key importance it seems reasonable to analyze some chemical aspects of chemical energetics. In this context, a main task objective of modern energetics becomes the quest of new technologies for conversion, accumulation, and transportation of produced energy. It is very important to have a clear notion about physical limitations for the maximum achievable values of the efficiency of converting one form of energy into another.

Physical limitations for energy conversion

There are several physical causes for unavoidable losses when you convert energy from one form to another. One is trivial and relates to the losses for work against friction and resistance. Among others, there are two basic restrictions for the efficiency factor of energy conversion which is defined as a ratio of the amount of energy consumption ΔEu to the corresponding amount of source energy ΔEr.

Restriction 1 is imposed by the second law of thermodynamics that is associated with the concept of energy ‘quality’ defined by entropy S. The smaller S, the higher quality of energy and the lower the efficiency factor for conversion of primary low-entropy energy into high-entropy one.

Restriction 2 is related to the finite rate and time of energy conversion and transportation in real processes. In this context, total entropy change ΔS can be written in the form:

Δ S = Δ e S + Δ i S

where ΔeS refers to the amount of entropy related to imported energy ΔE, and ΔiS is inner generation of entropy that is defined by the rate of energy transport ΔĖ. The dot above symbol E denotes time derivative, i.e. the rate of change in energy:

Δ E ˙ = d ( Δ E ) d t

Inner generation of entropy ΔiS leads to additional dissipation of energy and hence to a decrease in the efficiency factor for energy conversion.

Figure 3 presents the schematic diagram of a conventional energy-generating machine. Some amount of energy ΔEr from energy resource 1 is imported to working substance 2 and converted to respective amount of energy ΔEu to be used by consumer 3. Given that all processes taking place in the energy machine can be regarded as equilibrium ones, the transmission of energy ΔEr to working substance 2 must proceed at temperature Tr while that of energy ΔEu, at temperature Tu. The state of working substance may change periodically. Along with energy, working substance accepts and imparts respective amounts of entropy:

Fig. 3: 
          Conventional energy-generating machine.
Fig. 3:

Conventional energy-generating machine.

Δ S r = Δ E r T r ,     Δ S u = Δ E u T u

This relationship between energy, temperature, and entropy holds true for any kind of energy, and it follows from basic thermodynamic equations written in the form of differential for entropy under constant external parameters of the system.

In principle, the energy machine can work both in a steady and cyclic mode and during the process the energy and entropy of working substance must be kept on some certain level. These are the consequences of the first and second laws of thermodynamics. For this to attain, we need the presence of heat reservoir 4 at temperature T0 that would ensure the balance of energy and entropy between resource 1 and customer 3. In practice, the role of heat reservoir is played by our Earth with a huge heat capacity.

It should be noted that there is a significant difference between cyclic and stationary mode. In a cyclic mode, the working substance may perform the exchange by energy in a quasi-equilibrium mode and every time it returns to its original state. The entropy of the whole system, including the working substance, the primary energy source, the consumer and the thermal reservoir will remain constant. In the stationary mode only the entropy of the working substance will remain constant, and the entropy of the entire system increases due to irreversible energy exchange.

So, the balance equations for energy and entropy can be represented as follows:

Δ E 0 = Δ E r Δ E u ,     Δ S 0 = Δ S r Δ S u + Δ i S

where ΔiS is a total inner generation of entropy in the working substance, ΔE0 and ΔS0 refer to the amount of energy and entropy which the working substance gives up to the heat reservoir or receives from those at temperature T0.

Efficiency factor η of energy machine can be represented as

(1) η = Δ E u Δ E r = Δ E r Δ E 0 Δ E r = 1 T 0 T r ( 1 Δ S u Δ S r + Δ i S Δ S r )

For the particular case of the equilibrium conversion of thermal energy into mechanical one, we have:

Δ i S = 0 ,     Δ S u = 0 ,     Δ S r = Δ S 0 ,

so that Eq. (1) acquires the form of Carnot formula:

η C = 1 T 0 T r

It follows that when Sr>Su, η<1; in other words, the production of high-quality energy always is accompanied by energy losses. And this is a profound meaning of the second law of thermodynamics. But when SrSu, η may become greater than unity at the expense of energy taken from heat reservoir 4, not violating the second law of thermodynamics.

This circumstance opens up a way to more reasonable utilization of produced energy. Another important point is that the high-quality energy (with low S) is much more convenient for transportation and its utilization at destination can be supported by practically unlimited resources of our heat reservoir.

Some important examples

Thermal pump

To get some amount of heat Q1 for heating premises, instead of Joule heating it seems reasonable to use electric power for realization of reverse thermodynamic cycle (e.g. Carnot cycle); that is, to spend mechanical power W for extracting additional heat Q2 from the ground which is always at a temperature of 5–10°C on a depth of 2–3 m. Such a facility is termed thermal pump and its the efficiency factor may attain a value of 1000%:

η tp = Q 1 W = U + Q 2 W = 1 + Q 2 W = 1 + T 2 Δ S ( T 1 T 2 ) Δ S = 1 + T 2 ( T 1 T 2 ) 1000 %

Thermal pump looks promising for its use in housing and communal services, especially during night hours.

Conversion of heat into light

The previous example has demonstrated how we can extract a significant amount of heat from the heat reservoir by doing work. Now let us consider how we can convert thermal energy into light emission, for example, by doing work over a working substance. As is known, the efficiency factor of electrical energy conversion in incandescent lamps never exceeds several percent, because in this case electrical energy is converted into heat, heating up the tungsten filament, which generates radiative heat flux. However, only a small part of this flux corresponds to the visible light. All remaining energy is converted into heat.

But in direct conversion of electric power to optical radiation it is possible to transform some portion of low-grade thermal energy into light emission. In view of [3], let us consider the thermodynamic limitations for the conversion of heat into light. For resultant light flux Φ we have:

Φ = n ω ω 3 d ω ,

and its entropy can be defined by the expression:

S U = [ ( 1 + n ω ) ln ( 1 + n ω ) n ω ln n ω ] ω 2 d ω

where nω is the number of photons with frequency ω and ћ is the Planck constant [4].

The effective temperature of light flux is given by

T u = Φ S u

External electric power W is supplied by current I passing through the heterocontact of n- and p-type semiconductors. Photons are generated upon electron–hole recombination. Steady operation mode of light-emitting diode produces entropy Si. Equations of energy and entropy balance are written in the form:

d E d t = d W d t + d Q d t d Φ d t = 0 d S d t = d S i d t + 1 T d Q d t d S U d t = 0 Q = Φ W

where T is the temperature of actuating medium. In this case, the expression for the efficiency factor of energy conversion η takes on the form (the dot above the symbols denotes time derivative):

η = Φ ˙ W ˙ = 1 T S ˙ i W ˙ 1 T T u = T u T u T ( 1 T S ˙ i W ˙ )

A maximum value of η is attained at Si=0, therefore

η 1 + T T u T

Physical meaning of this formula is clear. In case of narrow spectral distribution, the entropy is low and the second term is insignificant. In case of wide emission spectrum, low-grade thermal energy can be effectively converted into optical emission at the expense of the work produced by electric current.

Photoelectric energy transformation

In this case, the part of primary energy source is played by light flux Φ. Illumination leads to formation of electron–hole pairs or excitons in the working substance. Charge separation at the boundary of pn-transition induces electromotive force and the electric current that produces work W. The equations of energy and entropy balance have the form [5]:

d E d t = d Φ d t d W d t d Q d t = 0 ,     d S U d t d S 0 d t + d S i d t = 0

Accordingly, for η we obtain:

η = W ˙ Φ ˙ = Φ ˙ Q ˙ Φ ˙ = 1 Q ˙ Φ ˙ 1 T S ˙ u Φ ˙ n

In case of black body,

Φ = σ T u 4 ,     S u = 4 3 σ T 3

where σ is the Stefan–Boltzmann constant.

Finally, for ηmax it may obtain [5]:

(2) η max = 1 4 3 T T u

More details the maximum values of efficiency of conversion of light into work was reviewed in [6]. Considering the equilibrium between a working substance and its thermal emission they come to the expression:

η max = 1 4 3 T T u + 1 3 ( T T u ) 4

However, the amendment to Eq. 2 derived in [6], is of the order of 10−6, while ηmax=0.9 according to Eq. 2.

Similar maximal efficiency factor can be expected for photosynthesis, i.e. for conversion of solar energy to chemical one.

It should be noted that the above maximum efficiency is only a thermodynamic estimation of the limiting values and does not take into account the spectral characteristics of specific light absorption of the photovoltaic material and therefore, in reality, have much smaller values.

Electrochemical transformation of energy

The basis of modern energetics, chemical energy, is stored in the chemical bonds of hydrocarbon fuels. Direct conversion of chemical energy is successfully realized in fuel cells. The efficiency factor for conversion of such transformation, ηfc, is given by the expression:

η fc = Δ G Δ H = 1 T Δ S Δ H

where ΔG and ΔH stand for change in Gibbs energy and enthalpy for a given chemical reaction.

For most advanced hydrogen fuel element based on the reaction H2+O2→H2O (ΔG=−237 kJ/mol, ΔH=−286 kJ/mol), ηmax=83%. Depending on a sign of ΔS and ΔH, the ηfc value may turn to be above or below unity. For the exothermic 2C+O2→2CO reaction (ΔH=−221, 4 kJ/mol<0 and ΔS=179, 7 kJ/mol*K>0) the theoretical ηfc magnitude is 124%.

Of course all estimates of the efficiency factors are made using the standard values of entropy and enthalpy in normal conditions and may differ from the actual achievable values.

In the reverse process – electrolysis of water yielding H2 and O2, the efficiency factor for conversion of electric power to chemical energy can be expected to be above unity, since the entropy change entrained from actuating medium will be compensated by supply from heat reservoir and additional conversion of that thermal energy into chemical one.

Irreversible processes of energy conversion

The above estimates for limiting values of efficiency factor for energy conversion refer to equilibrium processes and are far from achievable ones. This is due to Restriction 2, that is, to the finite rate and time of energy conversion and transportation in real processes. This leads to inner generation of rate-dependent entropy change ΔiS(ΔE˙) and to a decrease in η caused by additional dissipation of energy.

As an example, let us consider the conversion of thermal energy into mechanical one in a Carnot cycle. In this case, the isothermal energy exchange between a heater and working substance is caused by temperature change ΔT1 while that between a working substance and heat reservoir, by temperature difference ΔT0. Figure 4 shows the ТS and PV diagrams for ideal (dashed) and non-equilibrium (solid) Carnot cycles.

Fig. 4: 
          The diagrams of equilibrium (dotted line) and non-equilibrium (solid) Carnot cycles.
Fig. 4:

The diagrams of equilibrium (dotted line) and non-equilibrium (solid) Carnot cycles.

Working substance produces mechanical work against external force by enlarging its volume by ΔV in the presence of pressure difference ΔP corresponding to the rate of heat supply. For a given ΔP, the work of non-equilibrium process is smaller than that of ideal one (Weq) by a value of so-called lost work

W lost = W eq W = Δ P Δ V

In Fig. 4, the effective work (shown in gray) of non-equilibrium cycle is seen to be smaller than that of ideal Carnot cycle.

In the non-equilibrium cycle, entropy change grows by a value of

Δ i S = Δ S 0 res Δ S 1 heater = Q 0 T 0 Q 1 T 1 0

At this, the entropy change of working substance remains intact:

Δ S act med = Δ S 1 act med Δ S 0 act med = 0


Q 0 T 0 + Δ T 0 = Q 1 T 1 Δ T 1

and for η we obtain:

η = Q 1 Q 0 Q 1 = 1 Q 0 Q 1 = 1 T 0 + Δ T 0 T 1 Δ T 1 η C

where ηC stands for the EF of a Carnot cycle.

Maximum power output of energy conversion

In real energetics, of key importance is not only high efficiency factor but also maximal power output of energy conversion. For this to achieve, the exchange by energy between external energy sources, working substance, and consumer would proceed rapidly, which is possible in conditions of high temperature/pressure difference and other governing parameters.

The problem of a relationship between the power output of energy conversion and its efficiency was solved by Curzon and Ahlborn [7]. Power W˙ as a function of ΔT1 and ΔT0 is defined as the difference between the heat fluxes between external energy sources, working substance, and heat reservoir:

W ˙ ( Δ T 1 , Δ T 0 ) = Q ˙ 1 Q ˙ 0

W ˙ max is found from the set of equations

d W ˙ d ( Δ T 1 ) = 0     d W ˙ d ( Δ T 0 ) = 0

As a result, for the efficiency and capacity of energy conversion in a Carnot cycle we obtain:

η CA = 1 T 0 T 1 ;     W ˙ max ( T 1 T 0 ) 2

The simplicity of the above formulas suggests these may have a fundamental meaning for irreversible processes of energy conversion similar to that of the Carnot theorem for equilibrium processes. It is interesting to note the Curzon–Ahlborn formula was first suggested by Novikov back in 1957 [8].

The paper by Curzon and Ahlborn (cited about 2000 times) gave impetus to a new field of knowledge termed endoreversible thermodynamics [9]. Validity of the Curzon–Ahlborn formula was checked by Van den Broeck [10] in terms of general Onsager theory for non-equilibrium processes. The line of reasoning was as follows.

Let us consider an energy machine as the sequence of large number of consistently joined elementary converters (Fig. 5) between a source (у=0) and drain (у=1), where y is a dimensionless spatial coordinate. We assume that each of these basic converters does work for some finite period of time and develops power dW˙(y) due to temperature difference ΔT=T(y)T(y+dy).

Fig. 5: 
          Conversion of heat flow Jq~Q˙${J_q}\~\dot Q$ into work flow Jv~W˙~V˙${J_v}\~\dot W\~\dot V$ by the set of elementary converters.
Fig. 5:

Conversion of heat flow Jq~Q˙ into work flow Jv~W˙~V˙ by the set of elementary converters.

Given that Jq is incoming energy flux (in case of thermal energy Jq~Q˙) and Jv the outcoming one, such as volume change Jν~V˙ of actuating medium producing mechanical work.

According to Onsager,

J q = L q q X q + L q v X v J v = L v q X q + L v v X v

For conversion of thermal energy into mechanical one, XqT, Xν~F, where F is the external force against which work W is performed, and Lij are the Onsager kinetic coefficients satisfying the following conditions:

L q q 0 ;     L v v 0 ;     L v q = L q v ; L q q L v v L q v 2 0 ;     q 2 = L q v 2 L q q L v v 1

Power output of energy conversion is written in the form:

d W d t = W ˙ = J v X v T = ( L v v X v 2 + L v q X v X q ) T

from whence

W ˙ max = L v q 2 X q 2 4 L v v T ;     X v max = L v q X q 2 L v v

For ηmax corresponding to W˙max we obtain:

η max = W ˙ max J q = 1 2 Δ T T q 2 2 q 2

The power gathered from element dy of actuating medium is

d W ˙ ( y ) = J q ( y + d y ) J q ( y )

After integrating over y we obtain

J q ( y ) = J q ( 0 ) 0 y d W ˙ ( y )

and then come to the following expression for the efficiency factor:

η ( W ˙ max ) = 1 ( T 0 T 1 ) q 2 2 ( 2 q 2 ) ,     q = L 12 L 11 L 22

At q=1 we come to the Curzon–Ahlborn formula.

Therefore, the generalized thermodynamic theory of non-equilibrium processes also imposes some restrictions on the attainable η values at maximal power of energy. This approach can be expanded to analyzing conversion efficiency from all kinds of energy.

Energy density and umov equation

Another important characteristic of energy-converting machine is the energy flux density that can be achieved with a given working substance in a given process. The process occurs within some certain volume of working substance through the surface of which enters the incoming energy and goes out the converted energy. In 1874, Umov suggested the equation that describes the process of energy motion in a material medium. Actually this is the continuity equation for energy motion based on the law of energy conservation:

ε t + div ( j ) = 0

where ε stands for energy density and is the directional energy flux density (Umov vector). In stationary processes, div(j) defines the rate of energy conversion and hence power output per unit volume of actuating medium. A maximum j value depends on physical parameters of matter, so that

j max ρ ε u

where ρε and u are maximal energy density of a given medium and energy transfer rate, respectively. Knowing these values for a specific working fluid, we can estimate the potential of different energy conversion technologies and perspectives for their scaling.

For example, according to Kapitsa [11], the ratio of output powers for conversion of mechanical energy to electricity in electrostatic and electromagnetic generators attains a value of above 105. This implies that a 100-MW electrostatic generator would have a rotor with a working surface of 1 km2. For this reason, such generators did not find their application in industrial-scale electric power industry, despite their seeming attractiveness.

Instructive seems another example concerning electrochemical transformation of energy in fuel cells [11]. In view of low velocity of diffusion-controlled processes in electrolytes, the Umov equation predicts that a 1-m2 electrode can be expected to produce no more than 200 W of electric power; that is, the production of 100 MW will require a working surface of about 1 km2. Meanwhile, the latest achievements in nano structuring of electrode surface set a record of 20 kW/m2.


Analysis of the current state and main trends in development of world energetics shows that chemical energy will long remain to be the main source of primary energy. Among the main forms of energy used in modern energics, the quality of chemical energy occupies some intermediate position between the high-grade thermal energy and solar (or nuclear) energy (Fig. 6).

Fig. 6: 
          Transformation of primary energy sources into heat, mechanical work, and electrical energy.
Fig. 6:

Transformation of primary energy sources into heat, mechanical work, and electrical energy.

However, the effectiveness of chemical energy still leaves much to desire. This is due to the fact that the existing technologies primarily convert chemical energy into high-grade thermal energy and only then into other usable forms of energy (mechanical, electrical, and luminous).

Most convenient for use electrical energy is produced mainly from chemical energy but through the stages of conversion into thermal and then mechanical energy. This is accompanied by significant decrease in the quality of energy followed by its subsequent transformation into high-quality thermal energy. Main energy losses happen just at these stages.

Currently, direct conversion of chemical energy into electrical one is not used on an industrial scale although there are all prerequisites for this to happen in the nearest future. Similar situation is also typical of nuclear power industry which produces high-quality (low-entropy) energy, but via the conversion of thermal energy.

Fundamental physical laws still keep open some ways to improving the utilization efficiency for chemical energy and some other kinds of energy. For solar energy, theoretically predicted efficiency factors for direct conversion of solar energy into electrical and chemical energy are extremely high.

Another important problem is attaining a maximum power output of energy conversion. In this aspect, clear understanding was reached on fundamental correlations between the efficiency factor and power output in different processes of energy conversion.

Article note

A collection of invited papers based on presentations at the XX Mendeleev Congress on General and Applied Chemistry (Mendeleev XX), held in Ekaterinburg, Russia, September 25–30 2016.


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Published Online: 2017-07-19
Published in Print: 2017-09-26

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