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Exergy Transfer and Balance. Exergy transfer by heat transfer, Q. The Carnot efficiency η c = 1-T 0 /T is the fraction of Q from T that can be converted to work, so…. Heat transfer through a finite temperature difference. Exergy transfer by work, W.

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Exergy transfer by heat transfer, Q.

The Carnot efficiency ηc = 1-T0/T is the fraction of Q from T that

can be converted to work, so…


Heat transfer through a finite

temperature difference.


Exergy transfer by work, W.

Xwork = W – Wsurr for boundary work where Wsurr = P0(V2 – V1)

Xwork = W for other types of work

Work done by or against the

atmosphere is not available for

any useful purpose, and thus

should be excluded from

available work.


The Decrease of Exergy Principle In an isolated system:

(or increase in entropy principle)

ΔEsystem = E2 – E1 = 0

ΔSsystem = S2 – S1 = Sgen

ΔXsystem = X2 – X1 ≤ 0

Or, the exergy of an isolated

system during a process always

decreases or in a reversible

process, remains constant.

Or exergy is always destroyed

in a real process.

Any system and its surroundings

constitutes an isolated system


Anything that generates entropy always destroys exergy.

Xdestroyed = T0Sgen≥ 0

Xdest is also called lost

work or irreversibility.

So, exergy of the universe

is always decreasing.


Exergy Balance of Closed Systems

The general exergy balance is Xin – Xout – Xdestroyed = ΔXsystem

For a closed system, reduces to Xheat – Xwork – Xdest = ΔXsystem

Or: Σ(1-T0/Tk)Qk – [W – P0(V2 – V1)] – T0Sgen = X2 – X1

Can be used to find Wrev by setting Xdest = T0Sgen = 0

three balances
Three Balances
  • We have three balances we can use now: energy, entropy, and exergy.
  • However, the exergy balance was obtained by adding the energy balance and the entropy balance together.
  • Therefore, you can only use either the entropy balance or the exergy balance, but not both to be the second law expression.

The exergy destroyed in the exergy balance is the exergy

destroyed only in the system. If Xdest = 0 then the system is

internally reversible.

Exergy destroyed outside

system boundaries can be

accounted for by writing an

exergy balance on the

extended system that

includes the system and its

immediate surroundings.


Example 7-10 This problem was solved for Sgen in chapter 6.

You only need to multiply

Sgen by T0 to get



Example 7-13 This example gives a good equation for the

exergy of an incompressible substance.