What is Exergy?

Summary

Exergy

I will summarize what is exergy in just five lines that a 10th-standard student can understand. Exergy is the available energy to do maximum work. In reality on earth everything is irreversible and so is energy. Once energy is lost that equivalent of work is lost. So there is a destruction of exergy. There is nothing more and nothing complex about exergy. Well, at an advanced level when you want to calculate the exergy of a process you need to know the?basics. So, don't get frightened or anxious by complex words.

For engineers, exergy destruction is maximum when a system reaches equilibrium since entropy is at peak at this point.

?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.

?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

?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 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 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.

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 surrounding have run out of energy. Therefore, because there is maximum entropy, there is 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.

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