The Gibbs free energy is the amount of available work for an isothermal and isobaric process. Exergy is more of a measurement of total available work until a system reaches equilibrium with its surroundings. You can't replace one with the other, but they are similar in concept.

Tte amount of exergy a system has is not dependent on whether or not its an isothermal or isobaric process. It could be any type of process and it will still have the same amount of exergy regardless. The same can not be said for the Gibbs free energy.

Exergy is more of a general term used to describe the useable amount of work that can be extracted from a thermodynamic system whereas Gibbs is for a specific process (i.e. constant temperature and pressure). They are related though - conceptually.

Exergy is dependent of the systems surroundings while the GFE is independent of the systems surroundings. You can have a system that is isothermal and isobaric where GFE = Exergy but your assuming the conditions are such that all available work can be extracted when the system reaches equilibrium. This isn't always the case as for a systems equilibrium may not allow all available energy to be extracted, which can be determined by the GFE, still assuming an isobaric and isothermal process of course.

Ref: http://www.physicsforums.com

The Gibbs free energy is the amount of available work for an isothermal and isobaric process. Exergy is more of a measurement of total available work until a system reaches equilibrium with its surroundings. You can't replace one with the other, but they are similar in concept.

Tte amount of exergy a system has is not dependent on whether or not its an isothermal or isobaric process. It could be any type of process and it will still have the same amount of exergy regardless. The same can not be said for the Gibbs free energy.

Exergy is more of a general term used to describe the useable amount of work that can be extracted from a thermodynamic system whereas Gibbs is for a specific process (i.e. constant temperature and pressure). They are related though - conceptually.

Exergy is dependent of the systems surroundings while the GFE is independent of the systems surroundings. You can have a system that is isothermal and isobaric where GFE = Exergy but your assuming the conditions are such that all available work can be extracted when the system reaches equilibrium. This isn't always the case as for a systems equilibrium may not allow all available energy to be extracted, which can be determined by the GFE, still assuming an isobaric and isothermal process of course.

Ref: http://www.physicsforums.com

In simple words, work (energy) can be seen as comprised of "expansion work" (PΔV) and "non-expansion work" which is manifested in the form of chemical energy, electrical energy or any other form.

Gibb's free energy(G) basically gives an idea of the amount of non expansion work contained by a system. But generally we are more interested in the change in Gibb's free energy(ΔG) which gives us an idea about the spontaneity of the system (system is spontaneous if ΔG is -ve) . And at equilibrium, the system's ΔG=0, suggesting that there is no more driving force in the system, unless any changes are made in the operating parameters of the system.

Hope that helps.

Hi Srujan,

Thanks. you mean the Gibbs concept is only able to help us for chemical processes? what about a process of expansion and chemical reaction simultaneously? 

All the best

Reza

Dear Dr. Mansoori

thanks, could you please just state more details about or refer me to a source? I am doing exergy analysis for a chemical reaction and I am wondering what is the difference between using Exergy and free Gibbs energy in my case.

Regards

Dr. Mansoori

Totally it was helpful. nice interpretation. Thanks indeed

Reza

Exergy is a work, or the potential of doing useful work, however Gibbs free energy function is a property. We may compare both concepts if we talk about exergy function (not exergy) and Gibbs free energy function, here, the exergy function is h-T0s, where T0 is the reference temperature (atmospheric), while Gibbs free energy function is h-Ts, here T is the system temperature, both functions are equal when the system temperature and atmospheric temperature are equal.

Definition of Gibbs free energy is:  G=U-TS+PV.  Isothermal and isobaric changes in the Gibbs free energy for a closed system is:  ΔG=ΔU-TΔS+PΔV.  For a reversible isothermal process under the isobaric conditions ΔG=0,  That means ΔU=TΔS-PΔV,  The change in the energy of the closed system is the difference between the amount of heat received and  the  work done by the system.  Where  Δ  operator denotes infinitesimal reversible process, which means there is throughout the process equilibrium between the system and its surroundings. For a finite change, reversible throughout, Δ  operator implies finite variation.

One of the importance of  Gibbs free energy change appears if there is an isothermal and isobaric change in multi-components system through the chemical reactions and/or exchange of species with the surroundings ( or between the individual phases in the system)  Then one has ΔG= SUM OVERk ( Chemical Potentialk x ΔNk) =0.   (negative for natural processes). 

Hi Reza,

Nice from you to bring this into attention. Gibbs free energy was used to be called available energy. It is defined as

del(G)=del(H)-Tdel(s)

 It is usually used to see whether or not a reaction is spontaneous. If a reaction is  spontaneous, it releases energy which could be said the del(G)

Actually U, H, F, G are all called characteristic functions having their own appropriate independent variables (P, V, S,T) , which can be deduced from each others by Legendre transformations, According to Gibbs; they are connected by the Fundamental Equations or 'Pfaffian Differential equations’. If you know any one of these functions and their derivatives with respect to their arguments, then you can calculate all other Characteristic functions and their arguments (See: Guggenheim).

We can give some meaningful interpretation for delF and delG in irreversible thermodynamics using the concept of Dissipation Function or Dissipation of energy.

One can show that for isothermal changes in closed system Δw EQG del F, If we define ΔW=Δw-del F , then one has: ΔW EQG 0 (This is also known as Planck Inequality, 1887). It is Positive for natural changes, and zero for reversible changes. Where W is called  dissipation function 'energy' by R. Haase. ΔW = T del S (internal entropy), which is  EQG 0. Similarly, for isochoric system where delV=0, and ΔW=-delF, which is EQG 0, Isobaric changes ΔW=-del G , which is EQG 0.

That means Infinitesimal change in Gibbs function (energy) is negative definite for natural isothermal isobaric process, where it  is equal to the  dissipation of energy with a sign inversion.. In the case of isochoric isothermal changes Helmholtz function (energy) becomes negative definite. I have used and developed these concepts starting with the positive definite character of internal entropy production  in the formulation of  the irreversible thermodynamics of surfaces and interfaces.

THEREFORE IN GENERAL IT IS MEANINGLESS TO CALL   F AND  G    as ENERGY, which brings confusion as stated by Guggenheim as well as By  IUPAP  (1955).!!!!

Note: Planck claimed to deal with 'any infinitesimal change' of 'any system in nature'  including 'any homogeneous or heterogeneous system of bodies at a common temperature'. Unfortunately ,  C. Truesdell (Proceedings of Chicago Symposıum, May 1965) did overlook  Planck Inequality  by stating that ' it stands makes no sense at all'. We have also used this inequality in our variational formulation of surfaces and interfaces as a supplementary for  the micro-discrete elements approach to the problem:

Gibbs free energy of formation of a mineral from elements is calculated from enthalpy of formation and entropy of formation form elements.  free energy and enthalpy of formation of elements are by definition equal to for all temperature and pressure.

Entropy of elements are equal to  zero at Zero °K absolute T but are not equal to zero at reference temperature. Entropy  are measured from third law entropy. 

Throughout from the first law of thermodynamic energy is not suitable for sustainability accountancy as it not able to categorize resources according to their quality. Even entropy is sensitive to quality and is a measure of disorder and therefore is an abstract and not very pacifical property.

exergy combines both laws and is able of simultaneously expressing the quanta and quality of any resource. It is additive and as opposed to entropy, is expressed in more understandable units (kJ/mole) It has the ability to objectify all the physical characteristics of resources, independently of their market value.

Exergy content is not suitable as an indicator for resource accounting, as it would consider all resource generation processes to be reversible. If resources were assessed with energy, the values obtained would be very low.  This is because all real processes are irreversible. So even if energy is the starting point for the assessment, itv is the energy cost that provides information which is closer to Man's perception of value. The concept of energy cost is defined as the amount o-f the resources measured in terms of energy required to built a product.  It involves all irreversibility's that appear in the process . 

Exergy cost is the key concept of thermoeconomics

'Energy' is the broad concept encompassing the work done on or by a system in all processes:  physical, chemical, biological, mechanical or whatever.  On the other hand, the Helmholtz free energy (F) is useful for describing the energy of a system in contact with a heat bath or reservoir (i.e., at constant temperature).  It emerges quite naturally in the canonical-ensemble formulation of statistixal mechanics.  In passing, it highlights the 'complementarity' between absolute temperature and entropy.  Likewise, the Gibbs free energy (G) is convenient for describing the energy of a system in both thermal and mechanical contact with a bath (i.e., at constant temperature and pressure).  It emerges quite naturally in the grand (or Gibbs)-canonical-ensemble formulation of statistical mechanics.  It  highlights the complementarity not only between temperature and entropy, but also between pressure and volume.  F and G are, therefore, special cases of 'energy'; they can be viewed as thermodynamic potentials reeflecting specific constraints imposed on the system (constant temperature in the case of F, and constant temperature as well as constant pressure in the case of G).  Incidentally, I humbly believe that the word 'free' is misleading here; 'Helmholtz energ'y and 'Gibbs energy' should suffice!

Dear Professor Ghassib; The names and  symbols for characteristic functions were discusses by E. A. Guggenheim (1959).  According to Guggenheim, F  was called by Gibbs (1875) as 'The force function for constant temperature' and by Helmholtz (1882)  as the 'free energy'. European school uses the alternative names free energy and Helmholtz function. Similarly,  G  was also advocated by Gibbs (1875), and it was called as  'free energy' that thus causing confusion between F  and  G.   In USA _where I had been educated_  to reduce confusion  G has been called as 'Gibbs Free Energy'.   In Europe  -without exception-  it  was preferred to call as    ' Gibbs Functions'  by Guggenheim,  Denbigh, Haase,  de Groot, etc.

But you are definitely right to kick out the free, which was really misleading.

During the development of irreversible thermodynamics of surfaces and interfaces I have realized   that for isothermal changes  the global Helmholtz and Gibbs free energies variations are nothing but the energy dissipations (with a  proper negative sign) associated with the isochoric and isobaric systems, respectively, where not only the bulk but the external boundaries are considered.  Best Regards. 

Dear Professor Ogurtani:  Many thanks.  A good scientist almost invariably digs into the history and philosophy of his field.  This is exactly what you do.  All the very best.

Thank you all,

Actually, in this discussion I learnt a lot and I would like to express my deep thank to you as experts in area of thermodynamics. 

All the best

Reza

Hi all,

I found the discussion quite enjoyable :-)

However, I am still stuck at a very basic question.

When calculating the chemical exergy of a substance(lets say A), it can be done as follows,

for a ch. reaction

A + 2B = 3C + 4D

where A is not present in the exergy RE and B, C and D are present in the RE(ref. environ).

Ex of A = del(G)  + RT ln [concentration of (C^3) and (D^4)/conc of (B^2)]

or another form, commonly used for a reaction dealing with fuels is written as

Ex = -del(G) + RT ln[conc of (B^2) / concentration of (C^3) and (D^4)] 

I understand the del(G) is the maximum work obtainable at STP, where if G>0, energy is required, G

Dear Sanober, if one doesn't  grasp  the fundamental concepts of  chemical thermodynamics then he/she just jungles the equations around without going any where. First try to get  a good text book on chemical thermodynamics and start to learn by your self going through every concepts, assumptions, and hypothesis very critically. I try to catch their weaknesses and pin holes if any while you doing that don't believe that the author of the text  book is smarter then you!!  Solve as many as problems you could reached from your book selves .  That is my advice. BEST REGARDS

Note:  When people talk about the chemical energy in any given chemical reactions they mean ENTHAPY balance  or the difference between the enthalpies of products and reactants for one mole advancement in the reaction. All you have know the stochiometric equations. 

A + 2B = 3C + 4D

DELA H =  [ 3 HC   + 4  HD ] - [ HA  +  2  HB ]         for one mole A

IF  DEL  > 0   Endothermic    IF  DEL  < 0   Exothermic  Reaction.  

I think the main difference between exergy and free enthalpy is as follows:

Free enthalpy is a state variable, exergy is not (because the environment is included)

Thakns Gyan,

But what is the difference between Gibbs and Exergy?

Thanks Muschik

Both are characteristic state functions having different arguments -independent variables, which can be connected  from one to another through the Legendre transformation.(SEE; Thermodynamics by H.B. Callen -The best thermodynamics for physicist-TO). Thermodynamics Energy is function of Entropy, Volume -or Strain Tensor-, and composition;  Gibbs Free energy Function of  Temperature, Pressure-orStress Tensor- and Composition.  Connection is through double Legendre transformation by   -TS   and  + PV  or  for deformable bodies   -Sigma : Epsilon., Namely:

G= E +PV -TS  which yields  dG=-SdT + VdP +  SUMk  Mhuk  dNk  Open System,

G =E - Sigma : Epsilon -TS,   dG = -SdT - Epsion : d Sigma  +SUMk Mhuk dNk Deformable Elastic Bodies 

Where  Mhuk  is the chemical potential associated with  the k'th chemical species.

One selects  the most proper characteristic function depending  upon the constrains on the thermodynamics system. Any given thermodynamic functions and states variables can be represented by any given characteristic function (SEE: Thermodynamics by Guggenheim). BEST REGARDS

In order to be master of classical thermodynamics  one should be able to handle the following mathematical realities at  least:

Euler Theorem of Homogeneous Fct, Legendre Transformation,  Jacobian Trans formations,  Maxwell Connections, Quadratics ,  Multi-Variable Taylor Expansions  and Calculus of Variations and ALGEBRA.

Regarding the thermodynamic functions of state Gibbs free energy (G) and Exergy (Ex) to compare them, the first for application does not depend on the thermodynamic parameters around the thermodynamic system under study while the second (Ex ) if you need to know the thermodynamic state of the substance of the thermodynamic same pressure and temperature around the system work. In short when calculating the value of both functions are not the same results are obtained and in no case have the same thermodynamic meaning.

G = H - TS

Ex = H-H0 - T0(S-S0）

See the book  Thanatia , the destinity of the earth.

see alson the Alicia Valero's thesis (in Saragosse , Spain) . You 'll havve all examples of computation of exergy  for elements , minrals and different compounds

Thanks a lot Dr. Philippe

Actually, that thesis helped me alot to find exergy definition of aqueous ions.

Regards

Reza

Arguments of Dr. Krishna and some others colleagues  in regards to Gibbs characteristic function are  misleading and  disagree with the definition of founding father '' GIBBS'. (SEE: The Scientific papers of J. Willard Gibbs, V-I  Thermodynamics p.87-89).

Guggenheim also criticizes that G  has been  called some times as free energy thus causing confusion between F  and  G.  (SEE: Gibbs in page 89 ), Originally  G , which was introduced by Gibbs, and it  has been called as  total thermodynamic potential  or merely  thermodynamics potential for good reason. Since    G= SUMk  [Chemical Potentialk x  Mole Numberk ] which is true not for the equilibrium processes  but also for the irreversible processes . (SEE: De Groot.). Gibbs calls   F  as a force function at constant temperature,  and  E  is the work function at constant entropy. Actually one has the following equality  at constant temperature;     -dF= dW,   where dW  is the infinitesimal reversible work done on the system at constant temperature. Similarly        -dE= d W, is the infinitesimal reversible work done on the system at constant entropy. d  denotes inexact differential operator.

Thanks indeed professor Oğurtani for detailed explanation, I am learning alot here

The following inequalities are very important for the isothermal changes in closed systems:                (i.e., where we redefined     w   as is the work done on the system):

dT= 0,       w  >   dF  Natural (İrreversible) isothermal,

dT=  0,        w =   dF  Reversible    isothermal,

dT=0,         w <    dF   Unnatural isothermal 

For the system enclosed by fixed rigid walls,

dT= 0,   dV=0,     0 >   dF  Natural (İrreversible) isothermal,

dT=  0,   dV=0,    0 =   dF  Reversible    isothermal,

dT=0,      dV=0,    0 <    dF   Unnatural isothermal 

For each phase  that alpha kept its pressure constant:

 w= SUMk  Pk  dVk = SUMk d(Pk Vk )=d[SUMk  Pk  Vk  ]     Then one may see from the definitions  of  F and G  that    w= dF- dG  which results the following useful inequalities:

dT= 0,   dPk=0,     0 >   dG  Natural (İrreversible) isothermal,

dT=  0,   dPk=0,    0 =   dG  Reversible    isothermal,

dT=0,      dPk=0,    0 <    dG   Unnatural isothermal 

REMARK:   Actually I was elaborated and used above expressions in the Variational  formulation of  irreversible thermodynamics of deformable bodies ( Hookian elastic and/Hyper elastic solids) with external and internal surfaces , with and without applications in our recent papers,  which are appearing in RG.

I am interested in thermodynamic applications to solid state micro structures as tools for predicting thermodynamic state functions. Especially in steels and nonferrous alloys.

Dear Roberto;   We do that for dynamical systems such as grain boundary grooving and concurrent surface morphological evolution under the constant uniaxial tension by computer simulations using the irreversible thermodynamics theory with applications developed by Ogurtani and his coworkers at METU, last fifteen years. 

First paper deals with GB dynamics where the system is isobaric the G for bulk and Surface calculated as function of time.

The  paper deals with dynamic of Stranski-Krastanow Islanding (Q-Dots) in strain thin films, where the system is isochoric then deals with Helmholtz free energies or bulk and surface concurrently.

These simulations have proved that the transient stage  control by Maximum Entropy Production Hypothesis as advocated by  Jaynes and the  Non-equilibrium stationary state regime on the other hand is controlled by Minimum Entropy Production hypothesis proposed by Prigogine.  

Energy as we know it is still m0c2. Have a look at the 7-Base Units at

http://www.bipm.org/en/measurement-units/base-units.html

(Note Avogadro's number as follows is written as NA)

Normal Value is J m mol-1, NA hc = 0.119626566 with Standard Uncertainty 0.000 000 000 084; and Relative Standard Uncertainty, Sci = 1.00E-10; Concise is 0.119 626 565 779(84); and the Reciprocal Standard Uncertainty written as a Fraction is 8 1/3.

The Reference Point for Temperature is the Triple Point of Water, 273.16 on the Kelvin Scale.

Keep in mind - PV = nRT is still a valid scientific equation.

I have also proven that for the  isobaric systems under the constant applied loading the global Gibbs variation associated with the isothermal and spontaneous evolutions of  the external  surfaces and/or  interfaces is directly related to the rate of internal positive entropy production  with following connection:

dSint /dt  = - 1/T dDelGglobal / dt >  0    Natural Isothermal change, where  Del G= DelGSurface + DelGBulk , Where Del operator refers with respect to the unstrained state of the deformable body. 

This shows that    DelGglobal < 0is the dissipation of energy associated with irreversible isothermal changes taking place in isobaric system.  Similarly;   dDelG/dt < 0     is the POWER DISSIPATION.  One has similar relationship for the isochoric isothermal changing where Gibbs free energy is jst replaced by Helmholtz free energy.

Hi Sanober Hassan Khattak

My answer is regarding the sign before RT, as B is on left side of the reaction equation & chemical exergy of  species i=-RT ln yi, so after putting exergies of all species i.e B,C and D, it will come + before RT.

Its easy, see carefully you will get it.

Last few months I am working on the unfolding energetics and kinetics of alpha-peptides  3.6 11 (DNA ) having helical conformation as a secondary structure. This system in the  helical form carries large amount of stored rotational elastic energy and its stability closely related to pH level of the aqua solutions that  constitute  their natural environments. Under the constant atmospheric pressure and isothermal (ısobaric) conditions one has to choice global Gibbs free energy, which also includes interfacial free energy to take care of the pH effect of the environment. If your interest to study the kinetics such as the life time of  DNA  under the realistic conditions what one should choice as a characteristic function at least to get some rough estimation of the life time. As we know n the earth temperature definitely has shown large temperature fluctuations last few hundred million years (it is known that  DNA  macromolecules have made almost no appreciable change in their pitch value last  few hundred years at least) but very little atmospheric pressure variations. Here you can use energy since that is good characteristic function for the adiabatic processes under the constant volume, how about Enthalpy that is good for again for the adiabatic process under the constant pressure. Helmholtz free energy good for isothermal and isochoric processes that means they should be isolated from the surface tractions and body forces (i.e., Gravitational field). It can be used for the energetic or stability consideration for those system having stored elastic energy without worrying its volumetric variations to adjust itself to stable configuration under isothermal conditions.

This problem involves natural  changes therefore at least one should attempt to handle it by irreversible thermodynamics in its naive form!!!

BEST REGARDS

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