Hi Karolis,

I think you already got a number of very informative answers, but I hope I can add something more.

Second-law analysis is often, rightfully, used in contrast / complement to first-law analysis. First-law analysis is the typical analysis based on energy balance and energy efficiency. The energy efficiency of a Diesel engine is around 40%, that of a boiler 90%, etc (numbers are just for the sake of giving examples, please do not reply "well but boilers can have higher efficiencies").

The point is that as long as I compare similar systems (e.g. two Diesel engines) energy efficiency is just fine: there is not much doubt about which of the two is more efficient if one has energy efficiency 40% and the other 45%. But what about the example I mentioned in the first paragraph? The boiler looks more efficient than the engine, but is it actually so?

The limit of first-law analysis is that it does not account for energy QUALITY. Electric, mechanical, chemical, thermal energy, are all valued the same. However, we know that this is not true. Converting from mechanical to thermal energy is rather easy, and is done even when we do not wish so. The opposite is quite a complex process, as you can see in most of thermodynamic cycles.

So how to deal with this? The second law of thermodynamics comes into help introducing entropy. If you take a more "applied" statement of the second law, you will also get that, for example, it is not possible to have a cycle whose only result is to convert thermal energy to work. The limit of the efficiency of this process is set by the Carnot efficiency.

Where am I going with this? Well, when you use energy efficiency applied to an engine, you are not measure how much it approaches ideal condition, since even with a perfect machine you could not ever have unitary efficiency. But what about comparing engine efficiency with the correspondent Carnot efficiency, i.e. the maximum theoretically achievable? This makes much more sense!

Another example of where exergy analysis (exergy is the thermodynamic property that is supposed to combine energy quantity and quality) is its application to heat exchangers. If you assume (as it is often done) that there is no thermal loss in the exchanger, it will have unitary efficiency. Does this tell you anything about the quality of its design and of its positioning in a more complex network? No.

But what about calculating how much energy QUALITY is deteriorated in the exchange? This can turn out to be much more useful in many applications. And this can tell you for example what is the influence of the exchanger on the system. In general economic analysis favours high-temperature differences exchangers (becaus they are smaller in size and therefore cheaper), but second-law analysis can tell you how much this deteriorates energy quality, and therefore how much possibility of using this energy for other purposes is lost.

I hope I made my point clear. I use second-law analysis every day in my research and it is often for me a fight to make people to understand why exergy is not a typo but a useful property. In my thesis there is a small sub-chapter about this, let me know if you are interested to read it.

Karolis,

I think the simplest answer is that not all of the energy available in a system goes towards doing work. Entropy production decreases the amount of energy that can be used (usually due to heat losses). Exergy is a measure of the "available energy".

For example, a piston is filled with pressurized gas. It can exert a force on its surroundings (e.g. a crankshaft). But, if the piston experiences friction, some of its potential energy will be converted into heat (directly related to entropy through temperature), so it has less energy available to do work on the surroundings. The greater the friction, the greater the entropy production, the lower the exergy.

Entropy production due to heat is the classical example, but it applies to any irreversible process - that is any process where entropy is produced. Whenever entropy production is minimized, exergy (useful energy) is maximized - leading to statements such as "real performance" and "Shows quality of heat transfer process"

Dill and Bromberg wrote an incredible book called Molecular Driving Force (http://goo.gl/cPLqFy) that explains these phenomena. It's one of my all time favourite scientific texts.

Thank you for answer Amir - I am familar with work of Bejan and know entropy generation number usage to find minimum entropy production.

Thank you Tobias for interesting book - content of it will be usefull.

Dear Karolls you are right about the theorical concepts about second law analysis.

But there many works with real applications of second law, showing the real necessity and real applications of these concepts. If you are interested about second law aplications i have a work about first and second law analysis applied on corn drying. If you are interested i can send to you and others friends in this thopic.

Just send me a message.

Regards

Exergy is very important for detailed analysis involving several equipment and processes particularly for complex system. Using this concept you will know equipment/devices that need replacement due to high entropy generation.

I believe that the most important topic in exergy analysis is the second law efficiency. In this century and due to the continuous increase in the energy price, engineers would like to use in machines or plants thermal systems or components that have maximum second law efficiencies. In this manner, they can be confident that they are best utilizing the source energy thus, minimizing the expenditures. Before, when energy cost is very low, the goal of engineers was to invent thermal systems with minimum manufacturing cost. In the future, when countries are not able to sustain their societies development because of increased energy cost the only solution for these countries will be systems with high second law efficiency.

Hi Karolis,

I think you already got a number of very informative answers, but I hope I can add something more.

Second-law analysis is often, rightfully, used in contrast / complement to first-law analysis. First-law analysis is the typical analysis based on energy balance and energy efficiency. The energy efficiency of a Diesel engine is around 40%, that of a boiler 90%, etc (numbers are just for the sake of giving examples, please do not reply "well but boilers can have higher efficiencies").

The point is that as long as I compare similar systems (e.g. two Diesel engines) energy efficiency is just fine: there is not much doubt about which of the two is more efficient if one has energy efficiency 40% and the other 45%. But what about the example I mentioned in the first paragraph? The boiler looks more efficient than the engine, but is it actually so?

The limit of first-law analysis is that it does not account for energy QUALITY. Electric, mechanical, chemical, thermal energy, are all valued the same. However, we know that this is not true. Converting from mechanical to thermal energy is rather easy, and is done even when we do not wish so. The opposite is quite a complex process, as you can see in most of thermodynamic cycles.

So how to deal with this? The second law of thermodynamics comes into help introducing entropy. If you take a more "applied" statement of the second law, you will also get that, for example, it is not possible to have a cycle whose only result is to convert thermal energy to work. The limit of the efficiency of this process is set by the Carnot efficiency.

Where am I going with this? Well, when you use energy efficiency applied to an engine, you are not measure how much it approaches ideal condition, since even with a perfect machine you could not ever have unitary efficiency. But what about comparing engine efficiency with the correspondent Carnot efficiency, i.e. the maximum theoretically achievable? This makes much more sense!

Another example of where exergy analysis (exergy is the thermodynamic property that is supposed to combine energy quantity and quality) is its application to heat exchangers. If you assume (as it is often done) that there is no thermal loss in the exchanger, it will have unitary efficiency. Does this tell you anything about the quality of its design and of its positioning in a more complex network? No.

But what about calculating how much energy QUALITY is deteriorated in the exchange? This can turn out to be much more useful in many applications. And this can tell you for example what is the influence of the exchanger on the system. In general economic analysis favours high-temperature differences exchangers (becaus they are smaller in size and therefore cheaper), but second-law analysis can tell you how much this deteriorates energy quality, and therefore how much possibility of using this energy for other purposes is lost.

I hope I made my point clear. I use second-law analysis every day in my research and it is often for me a fight to make people to understand why exergy is not a typo but a useful property. In my thesis there is a small sub-chapter about this, let me know if you are interested to read it.

Exergy is based on both first and second laws of thermodynamics, and differentiates between two kinds of energy, heat and work. We do more effort and spend more money to have work than to have heat. Exergy is interpreted as the potential of doing useful work to mankind. Obviously work is more useful to mankind than heat; it can be converted totally to heat. If one have a heat source at 1000 K and losses 1000 kJ of heat to surroundings at 300 K, then theoretically we loss 700 kJ potential of doing useful work. However, if the heat source for example at 500 K, then 1000 kJ of energy loss is interpreted as 400 kJ potential loss. Exergy shows us the real value of energy. In a system contains adiabatic throttling process, the first law analysis shows the quantity of energy is conserved, however, the exergy analysis tells us that there is a degradation (loss of doing useful work) of quality of energy equal to the multiplication of the environmental temperature and the change in entropy.

Karolis,

in my opinion:

- the second law (the lost work) is useful to evaluate the thermodynamic irreversibilities accompanying the flows of energy and its conversion

- the exergy analysis allows the evaluation of the maximum available work

both approaches are useful for a critical assessment/indication of the thermodynamic performance of any system of energy conversion. Obviously, within the limits of the simplifications of the mathematical models one uses.

Remarkably, there is at least one classical treatment of entropy -I refer to Landau and Lifschits' "Statistical Physics"- which is based on the concept of 'minimum mechanical work' required by a transformation. This 'minimum mechanical work' is referred to again and again across all textbooks of Landau and Lifschits', where it is applied to different topics like e.g. dielectrics and surface tension. It is strictly linked to the 'exergy' concept.

For understanding the practical meaning of the exergy (and/or entropy) applications I would recommend the following handbook: "Fundamentals of engineering thermodynamics" by Michael J. Moran & Howard N. Shapiro, 6th ed., SI Version. John Wiley & Sons, cop. 2010. Many examples of solved problems are given in that book.

Karolis,

This is a question that I ask myself very often. I think you've already got a lot of helpful answers. I will try to add some of my thoughts.

Exergy is a useful quantity that stems from the second law of thermodynamics. It can be used to clearly indicate the inefficiencies of a process by locating the degradation of energy. In its essence, exergy is the energy that is available to be used, i.e., the portion of energy that can be converted into useful work. In contrast to energy, it is never conserved for real processes, because of irreversibility.

Since exergy analysis is a universally applicable method to assess process efficiency, it is well suited to investigate the sustainability of heterogeneous systems. Indeed, there are a number of studies that apply exergy-based lifecycle analysis (E-LCA) to assess the sustainability of complex systems and technologies. Maybe the following publication can help a bit in explaining the application of the E-LCA to ICT systems:

https://www.researchgate.net/publication/258930531_Energy_Entropy_and_Exergy_in_Communication_Networks

I hope, it can be of some help to you.

Article Energy, Entropy and Exergy in Communication Networks

Dear colleague,

may be our following paper can convince you that a second law analysis really tells you a lot about the physics of a problem:

H. Herwig, B. Schmandt: Drag with External and Pressure Drop with Internal Flows: A New and Unifying Look at Losses in the Flow Field Based on the Second Law of Thermodynamics, Fluid Dynamics Research, 2013

In case you do not have access to the paper: please contact me.

sincerely

H.Herwig

Let me be a bit of an advocatus diaboli:

I would like to distinguish between second law analysis, and exergy accounting.

The main point in second law analysis is to compute the entropy generation (rate) Sgen of a process, and relate it to a loss in work. There must be a factor of unit temperature between the two, so that Wloss = T0 Sgen. Typically T0 is the standard environmental temperature, but, depending on the problem, it might be another one.

If Wloss is compared to the actual work produced in, or required to run, the system, one gets a pretty good idea about the importance of the loss. If the loss is comparatively large, one should think about alternatives for the system that might have smaller loss.

The point is this: To determine the work loss--that is the entropy generation--there is no need at all to talk about exergy. The entropy generation is in the second law, it just needs to be applied. Prof. Herwig's paper is a good example: it's all about determining the loss, exergy is not used.

So why exergy analysis? A typical question that exergy analysis asks is: "how much work could I obtain from with a flow at elevated temperature and pressure, by reversibly equilibrating it with the environment?" The answer is: work = flow exergy. The answer to that question might be useful indeed: You find out how much work you could obtain, and then you decide what to do about that flow.

You can deal with the problem also by means of second law analysis--without using exergy--by asking how much entropy you generate in dumping that flow into the environment. The entropy generated is related to workloss as above.

Since exergy is a combined quantity of energy and entropy, and its balance equation is a combination of first and second law, one can replace the second law with the exergy balance, and go about all thermodynamic analysis with exergy, instead of entropy. What I called work loss above is then exergy destruction. Maybe just a matter of taste. My impression is, however, that this is often done without good reason, and the status of the results is sometimes unclear. Rather, one is forced into the corset of systems interacting with the environment by heat exchange, which means one looses flexibility, and generality.

Here is an example: Consider an irreversible adiabatic turbine (which obviously does not exchange heat with the environment). In the typical textbooks (Moran, Cengel, etc) you find two efficiencies for the turbine: (a) the isentropic efficiency, which compares the actual turbine with an ideal--reversible--turbine which has the same inlet state, same exit pressure, but different exit temperature. (b) the second law efficiency, which compares the actual turbine with a reversible one that has the same inlet and exit states as the actual turbine. Typically, the second law efficiency is higher than the isentropic efficiency. Here my provocation: use exergy only if you can explain why one should use the second law efficiency, and why it is (typically) larger than the isentropic efficieny. I have not found the answer in the textbooks (and I only know the answer to the second question...)

I prefer to deal with the second law directly. All interesting discussion of losses in thermodynamic system requires the entropy generation rate, and then work loss (= exergy destruction) follows from that, the exergy balance is not needed. I am still waiting to see an example where exergy accounting is giving more insight than 2nd law accounting, but I admit, I did not search much ;-)

Probably in simple words, exergy analysis guide us how much more improvement available to be explored in any device, cycle or system esp those relates to thermal energy. It provides theoretical limits of useful energy conversion.

As I see it, a central failure of education, at least in the United States, is the near total omission of the second law in primary, secondary, and university curricula beyond the technical confines of specialized fields (physics, chemistry, engineering...). Recent polls tell us that far more Americans don't believe human activity is a major factor in climate change than do. The absence of even a rudimentary qualitative grasp of the second law I believe plays a major role in the sheer gap between what the overwhelming majority of climate scientists claim and what the general public perceives. Incorporating the concept of exergy, as useful, transformable, available energy offers a qualitative means for grasping the role the second law plays in all aspects of our individual and collective lives, including our crucial impacts on the biosphere. How so? Peter W. Atkins, in his classic non-technical book, "The Second Law," included the powerful metaphor.of a pair of pulleys with two weights, one heavier, one lighter, linked by a rope around the pulleys. The falling heavier weight, representing increasing entropy in the environment, pulls up the lighter weight, representing decreasing entropy in a system, say a living organism, or a smartphone. The falling weight as increasing entropy is somewhat confusing, one rising up the other falling down. If instead of entropy, exergy were deployed in the metaphor, it would make much easier to grasp sense. The environment suffers exergy loss - the falling weight - while the system gains exergy as it rises up against the "natural" tendency to fall. Human activity, thanks to the accelerating power (exergy) of technical multipliers, is the weight rising up against the second law tendency of exergy to fall (entropy to rise). Global warming / climate change is the compensating falling exergy, the falling weight. This easy to grasp second law metaphor, with rising and falling exergy as conceptual handles, might give far more of our species a significantly better grip on creating a sustainable future. For a more in-depth discussion, please see my paper "If Technology is a Dissipative Structure, Bring It On Deserves a Closer Look". (P.S. It's interesting that the spell checker underlines "exergy" in red.)

As far as I understand, it is safe to say that Exergy analysis is useless and meaningless in most practical design applications!!

It is just a physical concept that can be interpreted wrongly. For instance I just read somewhere that "the boiler is very inefficient because its second law efficiency is very low". This is absurd!

Thanks

Morteza Eslamian

To help spread the concept of Exergy - extremely few in the United States in my experience ever heard of the word - it's on my license plate.

Thank you for reply Mr. Eslamian

there are lot of cases when exergy analysis are used as method to demonstrate other point of view. I agree that statement that "boiler is inefficient due to low exergetic eficiency" is partially truth if we compare it with heat pump applications, but it might appear efficient if we compare to direct electric heating. Without context it might sound as absurd and interpreted wrongly...

But what are right cases to use second law approuch ? When more sustainable energy transformation process must by highlighted ? or different energy forms must be compared by turning them to exergy?

I have done a Master's thesis on Exergy analysis, read Bejan's book and wrote a paper and published in the International Journal of Exergy, but I admit that I did not understand the real use of Exergy analysis in design of thermodynamic devices. What a pity!

That is why I think in the design process the main goal should be defined as increasing the first law efficiency keeping in mind the concept of available work, entropy generation and second law.

Exergy analysis and efficiency may make sense but I am not convinced or did not understand it.

Maybe experts in the field could provide a SIMPLE and CONVINCING explanation, rather than a long discussion.

Entropy poses many complex questions which are often not even discussed openly. i and a colleague have been investigating this topic for some time. as yet we have reached no detailed conclusions but below is a list of publications containing our thoughts up to the present. These may be of use/interest to some.

“Entropy, reversibility, irreversibility and thermodynamic cycles”

AIP Conference Proceedings Volume 1316, 2011, pp125-140

(with D. Sands)

“Advances in the Thermodynamics of Ideal Gases by Means of Computer Simulations”

AIP Conference Proceedings Volume 1316, 2011, pp 141-164

(with D. Sands)

“Confusion in Thermodynamics” arXiv:1103.4360 [pdf]

(with D. Sands) Hadronic Journal 34,no.3,(2011) 259-270

. “Reinterpreting Boltzmann’s H-Theorem in the light of Information Theory”

http://arxiv.org/abs/1301.1364

(with D. Sands)

“Clausius’ concepts of ‘Aequivalenzwerth’ and entropy; a critical appraisal”

(with D. Sands)

in ‘The Physics of Reality’, eds. R.L.Amoroso, L.H.Kauffman & P.Rowlands;

World Scientific, 2013.

“Information entropy and the statistics of the classical ideal gas”

(with D. Sands)

in ‘The Physics of Reality’, eds. R.L.Amoroso, L.H.Kauffman & P.Rowlands;

World Scientific, 2013.

“Thoughts on Landauer’s Principle and its experimental verification”

(with D. Sands)

in ‘The Physics of Reality’, eds. R.L.Amoroso, L.H.Kauffman & P.Rowlands;

World Scientific, 2013.

Exergy is a measure of the maximum "available" energy (energy available to do work) by any process which brings a system (with a well defined boundary) into thermodynamic equilibrium with its "environment". It therefore depends on both the thermodynamic characteristics of the system and that of its environment. Note that "thermodynamic equilibrium" means not only thermal equilibrium, but also mechanical and chemical equilibrium. We can therefore speak about thermal exergy, chemical exergy, or mechanical exergy.

However, as mentioned in numerous answers given above, exergy is not a fundamental thermodynamic variable and can always be written in terms of the standard thermodynamic potentials, such as the Helmholtz free energy, or the Gibbs free energy, etc., which, in turn, are written in terms of the real fundamental thermodynamic variables such as entropy, energy, temperature, volume, chemical potential, etc..

Gouy-Stodola theorem allows fast computation of exergy loss (http://www.eoht.info/page/Exergy): the entropy production is the exergy loss divided by the temperature of the surroundings; thus minimizing loss of exergy is equivalent to minimizing entropy production. As for practical applications of exergy, see e.g. Anita Zvolinschi, "On exergy analysis and entropy production minimisation in industrial

ecology", PhD thesis, Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, Department of Chemistry, Trondheim, Norway, (2006).

From my experiance exergy is a very wll suited concept when it comes to convince people from industry also to account for the second law of thermodynamics. They will never accept entropy as a quantity they might deal with - but when you tell them that exergy is that part of the energy that (at least in principle) can be sold for good money  they at least listen ... Hamburg (July 2014)

to summarize what is said. Energy has a quality; exergy. considering quality a better criteria may be found. For example Rail can't be compared with Dollar by simple numbers. But when you consider the quality they can be compared. Energy is so. 1kJ air at 1000 centigrade differs from1kJ at 50 centigrade considering exergy.

I agree with both Herwig and Bahrampoury. From the point of view of the audience at a PowerPoint-assisted talk in a non-academic environment, the main advantage of exergy is that it has the same dimension (Joule) of energy. As such, it can correctly be displayed in red letters in a slide displaying an energy breakdown of a plant, a process etc. Speaking seriously: most engineers feel embarassed when speaking about entropy, because entropy to them is just a recollection of Carnot cycle (which obviously cannot be easily connected to the actual topic of the talk in a simple way). In comparison, they may easily grasp the fact that (approximately at least): "exergy loss = waste". Of course, the fact that the temperature T0 of the surroundings is assumed to be constant in most talks related to energy production turns out to be useful, as Gouy-Stodola theorem enforces the above relationship in this case. And even if T0 changes (e.g. when discussing performances of the same gas-turbine plant in summer and in winter), the lower T0, the lower the exergy loss given the amout  of entropy produced by the cycle. In other words, gas-turbine plants perform better in winter than in summer, a well-known fact in the energy community.

To make R. Bahrampoury's answer more clear, maybe it is necessary to explain in which way "1 kJ air at 1000 C differs from 1 kJ at 50 C considering exergy". And the explanation is that once an environment temperature is defined, say 40 C, then we evaluate for the former case, of air at 1000 C, a temperature difference of 960 C and for the latter a difference of just 10 C. 

In thermodynamics we know what we can do with air with a large 960 C imbalance regarding ambient conditions: for one, we can expand it in a gas turbine to produce electricity. Electricity is a rather noble form of energy, if not the mos noble of all, for we can convert it to almost any other form of energy: mechanical, chemical, pressure, heat. However, for air with a thermal imbalance with the ambient of just 10 C, what can we do? Certainly, we cannot produce electricity, at least by means common in engineering practice. This stream of air may be used though as an ancillary in greenhouses, or to keep warm some room, not much more. Its use is thus rather limited (and, notice that we could do the same with the air at 1000 C in addition to electricity production). Hence, air at a temperature 960 C higher than the environment would offer more possibilities and hence has a higher quality (i.e., exergy), than air just 10 C higher than ambient temperature.

Notice how the selection of the value of the environment temperature becomes part of the exergy definition being used to analyse a given system. If the environment temperature was not 40 C, as chosen for the above discussion, but, say, 990 C, see how the whole discussion would be entirely different. Air at 1000 C would have an imbalance of just 10 C with the environment, and so would have low exergy, while air at 50 C would have a much higher exergy, due to having a thermal imbalance of -940 C. It could be used as the cold reservoir for a thermal engine operating with the environment as the hot reservoir. Such engine would produce work at a level compatible with the generation of the electricity: a valuable form of energy indeed.

Regarding Daniel Vaz clarification, when it comes to exergy, it's differences that make the difference.

J. Robbins: that's a nice sentence to quote!

Actually it's a variation on Gregory Bateson's definition of "information"  in Steps to an Ecology of Mind. Bateson put it this way: "what we mean by

information—the elementary unit of information—is a difference

which makes a difference." See p. 460 at http://www.edtechpost.ca/readings/Gregory%20Bateson%20-%20Ecology%20of%20Mind.pdf. In my paper, "If Technology is a Dissipative Structure, Bring It On Deserves a Closer Look", I defined a "gradient" as "any difference that makes a difference." 

With respect to the applications of exergy on natural resource utilization, the process of quantifying a system requires the assignment of value (both utilized and potential) to resources that are not always easily dissected into typical cost-benefit terms. However, to fully realize the potential of a system to do work, it is becoming increasingly imperative to understand exergetic potential of natural resources, and how human interference alters this potential.

The production of the hot water in a building for washing, bathing and other activities usually requires it to be heated to about 55 Celsius. A “boiler” running at a much higher temperature than that is producing energy with far too high an exergy just to heat water. The exergy need only be 15% or so. In contrast, the efficient operation of electrical appliances and lighting requires the highest possible exergy of close to 100%. That said, incandescent lighting represents an incredible waste in that much of the energy is converted to heat rather than light and in motorised appliances heat is generated through friction and so wasted.

In the environments, there is tremendous amount of energy with negligible quality. we can't use energy at environmental condition for any useful work.. so exergy value of energy is zero at environment condition. so, as we move away from environmental condition exergy value increases.

Dear Agrawal, this is precisely why I don't trust 'renewable energy' technologies too much. Carnot efficiency in any 'renewable' scheme is usually low, to say the least."

To "move away from environmental condition" means precisely "down with renewable energies".

For example, the Carnot efficiency of a photovoltaic cell is about equal to the ratio between photon energy and the sum of Fermi energy and photon energy. In fact, the cell can be considered as a thermal machine working between two reservoirs at assigned temperature. The colder and the hotter are at Fermi energy of electrons in the cell and at (Fermi energy + photon energy) respectively. An external source of energy (the Sun) keeps the former reservoir hotter than the colder. Fermi energy is about 7.5 eV, photon negy (for yellow light) is slightly less than 1 eV. Carnot efficiency is therefore less than 15%. Real efficiency are seldom larger than 1/2 the Carnot efficientyc, so we may conservatively assume a photovoltaic cell has a 8% efficiency. (Of course, this is just a rude approximation; but order of magnitude shuold be correct)

Now, 1 kW solar radiation impinges on 1 square meter of Earth. Out of this, 1/2 is to be cut away due to the circadian cycle. Out of this, 1/2 is to be cut away due to bad weather (iona average per year). Out of this, 1/2 is to be cut away due to latitude effect (radiation impinging at latitude theta is (cos(theta))^2 the maximum value, and the average of (cos(theta))^2 on Earth is 1/2). Out of this, 0.1 is to be cut away due to Earth albedo.

Then, the actual amount of power we can expect from a solar photovoltaic cell is about 1 KW * 1/2 * 1/2 * 1/2 * (1-0.1)* 0.08 = 9 Watt per square meter of photovoltaic cells. (Recently, 25 W/m^2 have been claimed, but with lab scale require nanotechnology only)

Assuming the whole amount of electric energy consumed in the European Unino per year is about 20000 TWh,  in order to supply this whole amount of energy via photovoltaic cells we would need a square with side larger than 300 Km.

Too large a power plant for all practical applications.

Very illuminating answer, Andrea (pun unintended). It puts somewhat of a damper on solar technology, in this case, photovoltaic cells saving us from our collective energy devouring ways. As long as human population continues on its still exponentially growing trajectory, joining forces with escalating energy demanding consumption (I=PAT / Impact = Population X Affluence X Technology), I hope I'm wrong but a sustainable future is looking increasingly dim. Since the 2nd Law is pulling the strings backstage, with exergy in all its forms sliding down the dissipative slopes, one would think that exergy analysis would, at least qualitatively, be a significant component of higher education and not just in engineering or physical science. Unfortunately, my experience with Exergy on my license plate, tells me that it isn't.

Dear Jeff, as an Italian I can speak about Italy only. Here electric power fees are very high (about 20% higher than the average European Union). We pay our refusal to develop our own nuclear power. All the same, the 2014  ACEEE report (ACEEE = American Council for an Energy-Efficient Economy) gives my country the 2nd rank in a world list of countries, as for the efforts in energy saving (not surprisingly, Germany is 1st). I guess the high fees are the cause. Both our families and our small enterprises spare a lot: it runs in the family :-)

I am used to explain the energy conundrum this way, which sounds familiar to an Italian. If you want a glass of red wine, you take a bottle, you pour the wine into the glass, then you pick up the glass and finally you drink. You may want to pour the wine directly on the tablecloth, then take the wet tablecloth and squeeze it until the last drop of wine falls into your open mouth. It is far from surprising that all bistrots give you wine the first way.

The quantity of wine is the same in both cases, but exergy loss is quite different. Energy is the wine, the glass is the 'conventional', high-temperature power plant (coal, gas, oil-fueled or nuclear), you are the user, and the tablecloth is the environment. Sun shines everywhere, not just when we need it. Exergy loss is proportional to the mechanical work of squeezing the tablecloth: in fact, the large the amount of wine, the more you sweat.

For any system design, we need to design component of the system efficiently. so that system gives its best result.

Exergy analysis is the tool for measuring  the performance of the component. 

if component performance is poor than we can redesign it and finally we will  get better result. Usually, we go by thermal efficiency which does does not give component performance, so exergy efficiency is a better way to predict the overall and component performance.

Dear Karolis.

Thanks for your interesting question, which has started this discussion thread. I guess I would agree with Tobias' and Francesco's answers in the usefulness of the approach. I taught a course on Advanced Thermodynamics a few times, focusing on the exergy analysis for closed and open systems (control mass/control volume formulation), and also using its differential formulation as a complement/post process to any CFD analysis of thermal/fluid systems.

My experience with students is that, although they appreciate the approach, they have a hard time justifying its use, both for themselves and for their colleagues and supervisors. It seems to them that the use of exergy is not "pragmatic" or "applied" enough.

I find that it is a good complement to any thermodynamic analysis. As engineers, we routinely use the 1st and 2nd Law to do calculations for design, analysis or control of thermal/fluid systems, and that will not change. Exergy is a nice addition to this mix, as an additional tool to evaluate system performance. While exergy analysis is not used to calculate the thermodynamic states of the system, for example in the way to thermodynamic property relations, 1st and 2nd Lay are used, exergy is used and useful as a post-processing step, to aid in our interpretation of what is going on, and to formulate strategies to improve the thermodynamic performance of the system being analyzed.

Hi there. I just want to ass this:

Although exergy analysis has some roots in studies conducted in early 1900’s, the theory and applications on exergy analysis have evolved after the oil crisis in 1973 when the governmental agencies and industries have started to focus on energy savings. Since this date, it has been better understood that increasing the efficiency of the energy production systems requires a thorough understanding of the location and magnitude of irreversible losses occurred within the system. For this purpose, the usage of exergy analysis has been dramatically increased within the last decade.

Exergy is defined as the maximum work that may be achieved by bringing a system into equilibrium with its environment. Every substance not in equilibrium with its environment has some quantity of exergy, while an object or system that is in equilibrium with its environment has, by definition, zero exergy since it has no ability to do work with respect to its environment. Unlike energy, exergy is not generally conserved but destroyed by irreversibilities within a system. These irreversibilities may be classified as internal and external irreversibilities. Main souces of internal irreversibilities are friction, expansion, mixing and chemical reaction. External irreversibilities arise due to heat transfer through a finite temperature difference. Exergy is lost, in general, when the energy associated with a material or energy stream is rejected to the environment.

Exergy analysis is a method that uses the conservation of mass and conservation of energy principles together with the second law of thermodynamics for the analysis, design and improvement of energy systems. The exergy method is a useful tool for furthering the goal of more efficient energy-resource use, for it enables the locations, types, and true magnitudes of wastes and losses to be determined. Many engineers and scientists suggest that the thermodynamic performance of a process is best evaluated by performing an exergy analysis in addition to or in place of conventional energy analysis because exergy analysis appears to provide more insights and to be more useful in efficiency improvement efforts than energy analysis.

You can also read this article attached. 

Hi everybody,

My final project is related with the exergy analysis of combined ejector-double effect LiBr/H2O absorption system. When I was carrying out research about the components of exergy, I had to involve the chemical exergy at my analysis. When I finish my investigation about total exergy in the absorption systems, I determined the exergetic efficiency of each system.

Why I said this, because exergy analysis gives us a vision about how and how much the Quality of Energy is used, and for synthesising my point of view, I have to say that the exergetic efficiency lets me to conclude what, only a little part of quality of energy is used by absorption systems for producing cooling. For instance, I compared the coefficient of performance (COP) of combined absorption system with single and double effect conventional absorption systems, with the purpose of validating the functioning of the ejectors at the absorption systems.  But, coefficient of performance only gives me the ideal of how much I can improve the performance of the absorption systems and, as a consequence COP only means that the functioning of the absorption systems is good or not. But, what about the energy (or quality of energy), How can I enhance the functioning of the absorption systems with respect of quality of energy? I think that the only thermodynamic tool that supply me this information is the exergy. In my case of study, exergetic efficiency since, when I was validating my outcomes, I found that this efficiency for my combined absorption system is only 24%.

For summarising, I think that in many cases our knowledge only it has been focused on the performance of the systems or thermodynamic systems and not it has been focused on the performance of using the quality of energy which, truly it can be compare with many areas of engineering.

My apologise for my English, I tried to give my best for explain my final project and my point of view about exergy.

There has been a good discussion so far, some provided some explanation on the use of Exergy concept in engineering. I do not agree that exergy analysis is a useless one in the design of thermodynamic systems. There have been several publications, books and journals and very famous researchers have dedicated a lot of time on that.  The best way to say that is look at a steam power plant. The Q rejected from condenser could have the same value with a output work from first law of thermodynamic however when you take exergy into the consideration, you will see the difference. Exergy analysis is a potential tool as it provides you with a vision within the system. There are other clear examples of exergy efficiency, when you use high temperature to produce electricity the exergy efficiency is lower than energy efficiency for example in CCPP where the GTIT is around 1300 C to generate electricity a true measurement is exergy concept.  

See these papers: 

My papers talking about:

*It could be used as a measure of system sustainability level

http://www.sciencedirect.com/science/article/pii/S0360544213007937

https://link.springer.com/article/10.1007/s12206-011-0219-0

https://link.springer.com/article/10.1007/s12206-011-0219-0

http://www.sciencedirect.com/science/article/pii/S0360544213007937

This paper may helpful for you.

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity

Dear Zhang

Why your ans for this question is "Entropy: A concept that is not a physical quantity"???

Your answer is not relevant to this question.

Calculus is not "take for granted", ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

It is well known that calculus has a definition.

Any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

An exergy analysis of a developing technology makes sense if power generation processes are involved. Exergy analysis doesn't deny energy (first law analysis). Saying this, redesigning a technological scheme based on exergy analysis can allow to have the same heat (Q=mCp(Tin-Tout)) but at a greater average temperature (Tin+Tout)/2. In its turn, this allows to generate more electricity from the same Q (Carnot cycle law). I would recommend a short paragraph 6 in Wikipedia (Combined cycle)

https://en.wikipedia.org/wiki/Combined_cycle#Natural_gas_integrated_power_and_syngas_(hydrogen)_generation_cycle

and my article where first and second laws were applied together.

M.Granovskii, M.Safonov (2003). "New Integrated Scheme of the Closed Gas-Turbine Cycle with Synthesis Gas Production". Chemical Engineering Science, 58(2003)3913-3921

Exergy computation is useful in ranking different energy systems from the point of view of how appropriate an energy source is used to fulfill a certain task (e.g. cooling, heating, work production). However, some people consider its computation more difficult and for this reason, they avoid its assessment. For those people, and not only, I proved that exergy efficiency equals the relative to Carnot efficiency in case of working, cooling, heating cycles. The proof is valid for many other energy processes. (see my work:

Staicovici MD., 2018a, About A More Intuitive Exergy Efficiency Calculus Applied To Heat Pumping And Working Cycles And Other Basic Aspects Issued Thereof. Proc. 13-th Gustav Lorenzen International Conference, 18-20 June 2018, Valencia, Spain.)

See my work attached.

Exergy is a combination property of a system and its environment because unlike energy it depends on the state of both the system and environment.

[ Ref Wikipedia ].

It is worth making the distinction between the exergy flow (power) at a temperature Th (K) for a continuous process and the exergy associated with a quantity of heat in a body at a temperature Th (K) above ambient. In the latter case (which is not relevant to a continuous process) the exergy of the body is the maximum work (Joules) that can be obtained when bringing the body from Th to equilibrium with the environment at To. It is apparent that as the body is cooled and delivers work, its temperature falls, and the effective mean temperature for delivering work is the so-called thermodynamic mean temperature, which is obtained from the familiar expression: Tm = (Th-To)/ln(Th/To).

Energy analysis will give you the efficiency/COP, but you won't know where loss takes place.

Exergy analysis will tell you where the loss actually is. So, you should do both. Further, to know if the loss in a particular component is because of itself or because of loss in other component, you should do advanced exergy analysis. Exergoeconomic analysis is useful to know if entire thing is worth running economically.

COP is exergy like. Each device has as well a COP and a COP ideal. The loss is calculated by the COP/COP ideal ratio in the same way the E outlet/E inlet is assessed.