Exergy: An overview
Contents
Exergy: Definition
Exergy is not conserved
Significance of exergy
How was the concept of exergy developed
Exergy and thermodynamics
Exergy destruction
- Irreversibilities
- Equilibrium
Heat vs electrical exergy: 2nd class vs 1st class energy
Friction vs entropy
Exergy of kinetic energy vs potential energy
Exergy balance
Exergy efficiency
Exergy transfer equations
- Flow
- Heat
- Work
Destruction of Exergy in Heat Exchangers
References
What is exergy in the simplest language?
The exergy of a system is the maximum useful work possible during a process before the system reaches equilibrium with a heat reservoir, reaching maximum entropy. In real-life processes which are irreversible, there is always some entropy generation and correspondingly loss of work potential of energy. Our concern is exergy loss because it means that ‘first-class energy’ which can do work is converted to ‘second class energy’ (heat at the temperature of the environment) which cannot do work. So, the particular properties of heat and temperature are a measure of the movement of molecules, given limitations in our possibilities to utilize energy to do work. Due to these limitations, we have to distinguish between exergy which can do work, and anergy which cannot do work. All real processes imply inevitably a loss of exergy as anergy.
Everything on the earth requires energy to do work but all energies put into the object do not convert into work. Some energy is lost while the work is performed.
When thermal energy does work it loses some energy while doing the work in the disorder that thermal energy generates. This disorder is known as entropy. The lost energy is called ‘Anergy’. After providing for anergy the amount of energy left in the system is available to perform work. This energy is called ‘Exergy’
Therefore, the exergy is work performed in a system by energy free from entropy before the system reaches thermodynamic equilibrium with its environment.
Exergy is the theoretical limit for the work potential that can be obtained from a source or a system at a given state when interacting with a reference (environment) at a constant condition.
Energy is conserved but not exergy: 1st law of thermodynamics vs 2nd law of thermodynamics
It is seen from this description that exergy is dependent on the state of the total system (= system + reservoir) and not depend entirely on the state of the system. Exergy is therefore not a state variable.
This definition of exergy is used in engineering to express the efficiency of power plants. The energy efficiency of power plants is of course 100%, according to the first law of thermodynamics, while the interesting efficiency is the exergy efficiency: how much of the chemical energy (exergy) in the applied fossil fuel if fossil fuel is the energy source is converted to useful work (exergy)? What is not converted to exergy in form of electricity is lost as heat to the environment at the temperature of the environment – it contains therefore no work potential.
Notice that the exergy of the system is dependent on the intensive state variables of the reservoir. Notice that exergy is not conserved. Only if entropy-free energy is transferred, which implies that the process is reversible, exergy is conserved. All processes, in reality, are, however, irreversible, which means that exergy is lost (and entropy is produced). Loss of exergy and production of entropy are two different descriptions of the same reality, namely, that all processes are irreversible, and we unfortunately always have some loss of energy forms that can do work. So, the formulation of the second law of thermodynamic by use of exergy is ‘all real processes are irreversible which implies that exergy inevitably is lost’. ‘Exergy is not conserved’, while the energy of course is conserved by all processes according to the first law of thermodynamics.
Recap: Entropy
In simple and short language, heat transfer from hot to cold is related to the tendency in nature for systems to become disordered and for less energy to be available for use as work. The entropy of a system is a measure of its disorder and of the unavailability of energy to do work.
Significance of exergy
Exergy analyses are very convenient methods for assessing the performance of energy conversion systems. Exergy analysis helps in finding the type, location, and magnitude of energy losses in a system
How was the concept of exergy developed?
The concept of exergy came from the second law of thermodynamics while attempting to determine and quantify the quality or “work potential” of energy.
The exergy is the part of thermodynamics that intersects with all three domains of thermodynamics the energy, entropy, and exergy fields.
Exergy and thermodynamics
The First Law of Thermodynamics states that in any process energy is conserved for a steady-state flow process,
H0 – H1 = Q + W
The Second Law of Thermodynamics says that energy transformations in which entropy is reduced are not possible. From the definition of entropy
S0-S1 > or = Q/T0
If you combine the above two equations,
T0 [ S0-S1] > or = [H0-H1]-W
The maximum work available from a process is, therefore,
W = [H1-H0]- T0[S1-S0]
W is exergy or the work available post entropy losses.
Let us call it the exergy equation.
Exergy and free energy
There is a razor-thin difference between exergy and free energy.
Look at the exergy equation, W = [H1-H0]- T0[S1-S0], W is exergy. If you see this equation, it is the same as Gibbs free energy equation,
dG = dH - TdS
W, the exergy has replaced free energy change G. But free energy and exergy are not same. Gibbs equation says free energy is energy available in a system at a constant temperature [isothermal] and pressure [isobaric] conditions to do work after providing energy for entropy losses.
The amount of exergy in a system is not dependent on whether or not it’s 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 cannot be said for the Gibbs free energy.
Exergy and free energy are related though - conceptually.
Exergy destruction
The primary contributors to exergy destruction are irreversibilities associated with chemical reactions, heat transfer, mass transfer, mixing, and friction in a process.
Irreversibilities
Any process [ closed system] operating above ambient temperature loses energy as entropy. Suppose a process generates heat Q, at temperature T1. Entropy generation in process S = Q / T1. The process then transfers the entropy to surrounding the entropy at lower temperature T2, the entropy generation in the surrounding, S2 = Q/T2. Since T2< T1, S2> S1, the system losses energy to the environment.
When the system transfers energy to surroundings that energy is permanently lost. While a system can be reversed the surrounding can’t. You lost the work potential of energy to the surroundings that cannot be reversed. This is irreversibility.
Equilibrium
A system is said to be in equilibrium when both system and surroundings have the same entropy. At equilibrium, a system is fully reversible and you get maximum work.
Example
Imagine an ice cube on a glass plate left to melt in the environment at temperature 298 K. Let us take a look at what thermodynamic processes are taking place while the ice melts. Specifically, look at entropy and exergy changes while the ice cube melts.
The melting of ice is an endothermic process. Ice needs heat from the environment to melt. Heat for enthalpy changes that are required to melt ice is the heat or enthalpy of melting ice, ΔH = 6.01 kJ/mol. This heat the ice cube is absorbing to melt from solid to liquid water. Since ice is solid consisting of more ordered molecules than liquid water there is an increase of disorder meaning there is an increase in entropy when ice melts into water. The entropy creation in ice is ΔH/T kJ/mole-k that stands at S1 = + 6.01/273 = + 0.022 kJ / mole-k. There is a positive sign because this entropy was added to the system. There is a gain of entropy. While transferring 6.01 kJ /mole heat to ice the environment at 298 k lost this amount of heat. As a consequence, there was a drop in the entropy at the environment at 298 k by an amount of S2 = - 6.01/298 = - 0.0201 kJ / mol-k. This has a negative sign because there is a loss of entropy. Therefore, the total entropy exchanged between the system and surrounding while the ice is melting is S1 + S2 = + 0.022 + [- 0.0201] = + 0.0019 kJ /mol- K or 1.9J/mol-k increase in the total entropy of ice melting.
Now, look at the exergy equation and see what is happening to exergy?
W = [H1-H0]- T0[S1-S0], S is entropy, H is enthalpy, T is temperature and W is work.
Enthalpy of melting ice = + 6.01 kJ/mol [ endothermic process]
Entropy of melting ice dS = dH/T = 6.01/273 x 1000 = 22 J/mol-k [ at 0 degc].
Exergy, W at 0 degc = 6.01 - [273 x 22 / 1000]
= - 0.004 kJ/mol = 0 KJ/mol.
What does it mean?
The melting of ice is a classic example of a near-equilibrium process with a small entropy generation of 1.9 J/mol-k. When a process has small entropy generation [ System + Surroundings] it means the system and surroundings have the nearly same state of disorder. It further means that both the system and surroundings have nearly run out of energy. This further means that the system and surroundings have near-zero residual energy for any useful work. This further means that a system / surrounding couple in such a situation would reach near-zero exergy. That is what we see in the melting of ice. Exergy is a signal to a process engineer and also a good tool to know where does the energy of his process stand.
Exergy destruction [EXd] is expressed as
EXd = Tx dS [gen]
Exergy destruction EXd is a product of temperature T and entropy generation dS [gen]
There are three cases:
EXd > 0: irreversible process
EXd = 0: reversible process
EXd > impossible process
At equilibrium exergy = 0
Equilibrium and Reversibility are the most confusing concepts of thermodynamics
Are equilibrium and a reversible process the same – the answer is no
More about equilibrium
The total entropy of the system + surrounding is always increasing. When the system and surrounding both reach maximum entropy, there is equilibrium. At equilibrium, both the system and surroundings have run out of energy. Therefore, because there is maximum entropy, there is a maximum disorder at equilibrium. The energy is more spread out at maximum entropy. A system has the least energy at the highest entropy. A system has maximum stability at the highest entropy. The principle of minimum energy which is essentially a restatement of the second law of thermodynamics states that for a closed system, with constant external parameters and entropy, the internal energy will decrease and approach a minimum value at equilibrium.
Reversible process
Entropy is zero in a reversible process. It is just the opposite of equilibrium.
If a system is undergoing a change from a state A to state B, the entropy change is given by
dS = dQ/T
And for a reversible process, the surrounding undergoes an equal and opposite change as the system. Therefore, for a reversible process, +dS of system = - dS of surrounding = 0
Which means that entropy change for a reversible system [dS (sys]-dS (surr)] = 0.
Example: A process has 100% exergy destruction. How would you define the process?
Is it closer to equilibrium or away from equilibrium?
Explanation
The answer is the more you go near-equilibrium there is more entropy generation. At equilibrium, both the system and surrounding would reach their maximum entropy. When the total entropy has reached the maximum value there is no energy available to do any more work. Both the systems and the surroundings have run out of energy. Since as per the 2nd law of thermodynamics total entropy can only increase and it cannot decrease when both system and surrounding have the highest amount of entropy the process stays there and we call it equilibrium.
100% destruction of exergy means the system has only entropy. Exergy = 0. The system has no useful energy to do work. The system is dead.
Let us go back to the fundamental equation of exergy that we have discussed above.
W = [H1-H0]- T0[S1-S0]
W is exergy or the work available post entropy losses. At zero exergy, W =0
Therefore, [H1-H0] = T0[S1-S0]
What does it mean?
It means the system's all energy creation between state 1 and 0 has got locked up in entropy creation between state 1 and 0. It means the system has no energy to do any work. Therefore, there is 100% destruction of exergy or the exergy of the system is zero.
Entropy will always increase in an irreversible process. The problem lies with reactions that generate heat. The extra entropy due to exothermic reactions will push the reaction towards equilibrium and slow down the reaction if you do not remove the heat. As you approach equilibrium and a higher state of entropy there is more disorder and hence more disorder of energy as well and spread out of energy and the system is moving towards a low energy stable state. You do not want that. You want the reaction to move forward and do not reach equilibrium. You cannot go back from low to high energy because of the 2nd law of thermodynamics does not allow it. Low energy can only be further lower. The only thing you have under your control delay the process of the reaction reaching equilibrium until you have achieved your conversion.
Just to reiterate, exergy is the theoretical limit for the work potential that can be obtained from a source or a system at a given state when interacting with a reference (environment) at a constant condition. A system is said to be in the dead state when it is in thermodynamic equilibrium with its environment. Unless otherwise stated, assume the dead state to be: P0 = 1 atm and T0 = 25°C A system delivers the maximum possible work as it undergoes a reversible process from the specified initial state to the state of its environment (dead state). This represents the useful work potential, we call exergy. Exergy is a property of the system-environment combination (not the system alone).
Heat vs Electrical exergy
Heat energy
Heat energy is considered to be second-class energy. Every time heat converts to work there are entropy losses. This explains why heat energy is not fully convertible to work energy and heat energy has low exergy.
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Electrical energy
Electrical energy is defined as the overall work done in an electrical circuit. Energy is the amount of work done to move an object. In an electrical circuit, electric charges are moving. The work done on the electric charges to cause movement is known as electrical energy.
How electrical energy generates heat
The charge particles basically hold energy, termed as potential energy and when force is applied to them then motion gets built up and the stored energy is released in the form of heat. It is the conversion of potential energy into kinetic energy. In the case of electric charge, the force is considered to be either attractive or repulsive. The movement of charge in an electric circuit leads to the generation of electric current. Thus, we can say that the energy required to generate an electric current is called electrical energy.
Suppose V is the potential difference existing across a circuit, I is the current flowing through it and Q is the quantity of charge flowing in time t.
Work by electrical energy
Then work done will be, W = VQ, V is the potential difference between two points. Q is the charge, Q = It [ Ohm’s law] W = VIt joules, Therefore, to conclude, in the case of electrical energy the conversion to work depends only on the potential difference V which is in volts and current which is in ampere. There is no entropy or heat reservoir concept like in heat energy. Therefore, electrical energy has more useful energy than heat energy [Exergy]. Electrical energy is called 1st class energy with little exergy losses
Friction vs entropy
Entropy increases due to friction
Reason
∆S=∆q/T
Due to friction, some mechanical energy is converted into heat (I.e., heat is added up into the system which increases the entropy of the system.
Exergy of kinetic energy vs potential energy
Explanation
Kinetic energy + potential energy together is mechanical energy.
Kinetic energy
W [ KE] = V^2/2 kJ/mol [ W is exergy]
where V is the velocity of the system relative to the environment.
Temperature is proportional to the kinetic energy of molecules and atoms. Increasing temperature increases the overall kinetic energy, the random motion of molecules, and so increases entropy. If you add heat Q to hot water in a closed system you will generate Q/T1 entropy in the system. Since a closed system is permeable to heat, the same Q will generate far more entropy in the surroundings, Q/ T2 since T2< T1. There will be an increase in the total system + surrounding entropy.
Correspondingly the work potential of the system would reduce. There would be a decrease in exergy.
Potential energy
W [PE] = gh [kJ / kg] [ h is elevation]
This is a tricky part of the explanation.
First, recall what does high KE or high entropy mean? It means more disorder of energy. It means more spread out of energy. It means the system is near equilibrium.
Now think what does high potential energy mean? It means more concentration of energy. It means more stored energy. It means less disorder of molecules. It means less entropy. It means more work potential of energy. It means potential energy has more exergy.
Some Definitions:
Surroundings work:
It is the work done by or against the surroundings during a process. This work cannot be recovered and utilized. For a cylinder-piston assembly, one can write: W surr = P0 [V2 /V1]. The difference between the actual work W and the surroundings work W surr is called the useful Wu:
Wu = W – W surr = W - P0 (V2 – V1)
Reversible Work:
W rev is the max amount of useful work that can be produced (or the min work needs to be supplied) as the system undergoes a process between the initial and final states. When the final state is the dead state, the reversible work equals exergy.
The net reversible work is determined by
Irreversibility: I is equal to the exergy destroyed.
I = W rev,out – W actual out
Exergy balance
All transfers of energy imply that exergy is lost because energy is transformed to heat at the temperature of the environment. It has therefore been of interest to set up for all environmental systems an exergy balance in addition to an energy balance.
The exergy balance introduces the term exergy destroyed, which represents the maximum work potential that cannot be recovered for useful purpose due to irreversibilities. For a reversible system, there is no exergy destruction, since all work generated by the system can be made useful. The exergy destruction and entropy generation are related by the following expression: EXd = T0 dS , where T0 is the reference temperature. If, EXd > T0 dS then the process is irreversible, if EXd < T0 dS , then the process is reversible; if EXd < T0 dS, the process is impossible.
The total exergy entering a thermodynamic system must be balanced by the total exergy leaving the system, plus the change of exergy content of the system plus, the exergy destruction. The above figure is an explanatory sketch. Exergy can be transferred to or from a system by three means: work, heat, and mass.
Based on the sample sketch shown below the exergy balance equation can be expressed generally in rate form as
Exergy efficiency
The exergy efficiency is the ratio of useful energy (work) to total energy which always is less than 100% for real processes, which always are irreversible. This efficiency expresses that a part of the energy cannot be utilized as work and that all processes are irreversible because exergy is lost by all energy transfer processes as heat to the environment.
Exergy efficiency, defined as work performed divided by the total exergy available, is also of interest, particularly in technology. It expresses how much of the work capacity we are able to utilize.
Exergy transfer concepts
Exergy of a Flow Stream
A flowing fluid has flow energy; that is the energy needed to maintain flow in a pipe or line;
W flow = PV
The flow work is the boundary work done by a fluid on the fluid downstream. The exergy associated with flow energy can be written as
x flow = PV – P0V = (P – P0) V
The exergy of a flow stream can be found from:
X flowing fluid = x nonflowing fluid + x flow
X flowing fluid = (u – u0) + P0(V – V0) – T0(s – s0) + V2
/2 +gz + (P - P0) V
where V is the velocity of the system and V is the volume.
X flowing fluid = (u + PV) – (u0 – P0 V0) – T0(s – s0) + V2
/2 +gh
X flowing fluid = ψ = (h – h0) – T0(s – s0) + V2
/2 +gz
The flow exergy is represented by symbol ψ.
Exergy transfer by Heat
Heat is a form of disorganized energy, thus only a portion of it can be converted to work. Heat transfer Q at a location at thermodynamic temperature T is accompanied by exergy transfer:
X heat = [ 1 – T0/T] Q (KJ) [ X is exergy]
Exergy transfer by work
X work = [W – W surr] Boundary work
where W surr = P0 (V2 – V1). Therefore, the exergy transfer with work such as shaft work and electrical work is equal to the work W. Note that the work done or against atmosphere is not available for any useful purpose, and should be excluded from available work.
Exergy destruction in heat exchangers
In a heat exchanger, the following are the two key events
-The hot fluid transfers heat to the cold fluid
- There is some amount of pressure drop as the fluid flows through the tubes.
The exergy destruction of a heat exchanger is expressed by the equation
W = −˙BQ+T0˙σ ∆T+T0˙σ ∆P
Where [˙I∆T] =T0˙σ ∆T and [˙I∆P] =T0˙σ ∆P. σ denotes entropy generation.
[˙I∆T] and [˙I∆P] are exergy destruction by temperature drop and pressure drop respectively.
Some amount of heat is also transferred by the heat exchanger to surrounding because of temperature difference The heat transfer to the environment does not actually mean that exergy is destroyed, but rather that it abandons the heat exchanger, as denoted by ˙BQ.
The obvious question is what happens? Where does the exergy go?
Obviously, it is irreversibility and entropy generation that causes exergy destruction.
Both the above-mentioned activities of a heat exchanger generate entropy.
-When hot liquid transfers heat to the surrounding it generates entropy in the surrounding at a lower temperature
- Pressure drop means velocity and velocity means more disorder therefore, the pressure drop increases entropy. This also increases frictional losses.
Both above two factors are the reasons for exergy reduction in a heat exchanger. But some losses are inevitable. ∆T is the driving force for heat exchange. ∆P gives velocity and the velocity gives the turbulence to enhance heat transfer rate. Without ∆T and ∆P there is no heat transfer. Only if you are aware of the sensitivities of ∆T and ∆P in exergy destruction you will be more careful before changing the process parameters.
References
Principle of minimum energy
Equilibria and Reversible Processes
Exergy
Exergy balance equation
Exergy
Calculation of Internal Exergy Loss in a Heat Exchanger
Exergy loss formulas
Exergy balance
Exergy destruction in heat exchanger