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Exergy Transfer and Balance

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 and Balance

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  1. Exergy TransferandBalance

  2. 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…

  3. Heat transfer through a finite temperature difference.

  4. 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.

  5. Exergy transfer by mass. Xmass = mψ

  6. 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

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. Example 7-10 This problem was solved for Sgen in chapter 6. You only need to multiply Sgen by T0 to get Xdestroyed.

  12. Example 7-13 This example gives a good equation for the exergy of an incompressible substance.

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