Exergy

1. Exergy A Measure of Work Potential

2. Exergy • Property • Availability or available work • Work = f(initial state, process path, final state)

3. Exergy • Dead State • When system is in thermodynamic equilibrium with the environment • Same temperature and pressure as surroundings, no kinetic or potential energy, chemically inert, no unbalanced electrical, magnetic, etc effects…

4. Exergy • Exergy • Useful work • Upper limit on the amount of work a device can deliver without violating any thermodynamic law. • (always a difference between exergy and actual work delivered by a device)

5. Exergy associated with Kinetic and Potential Energy • Kinetic energy • Form of mechanical energy • Can be converted to work entirely • xke = ke = vel2 /2 (kJ/kg)

6. Exergy associated with Kinetic and Potential Energy • Potential Energy • Form of mechanical energy • Can be converted entirely into work • xpe = pe = gz (kJ/kg) All ke and pe available for work

7. Reversible Work and Irreversibility • Exergy • Work potential for deferent systems • System operating between high temp and dead state • Isentropic efficiencies • Exit conditions differ

8. Reversible Work and Irreversibility • Reversible Work • Irreversibility (exergy destruction) • Surroundings Work • Work done against the surroundings • For moveable boundary • Wsurr = P0(V2 – V1) • Wuseful = W – Wsurr = W - P0(V2 – V1)

9. Reversible Work and Irreversibility • Reversible Work, Wrev • Max amount of useful work produced • Min amount of work that needs to be supplied between initial and final states of a process Occurs when process is totally reversible If final state is dead state = exergy

10. Reversible Work and Irreversibility • Difference between reversible work and useful work is called irreversibility • Wrev – Wuseful = I • Irreversibility is equal to the exergy destroyed • Totally reversible process, I = 0 • I, a positive quantity for actual, irreversible processes

11. 2nd Law Efficiency • Second Law Efficiency, ηII • Ratio of thermal efficiency and reversible (maximum) thermal efficiency • ηII = ηth/ηth, rev • Or ηII = Wu/Wrev • Can not exceed 100%

12. 2nd Law Efficiency • For work consuming devices • For ηII = Wrev/Wu • In terms of COP • ηII = COP/COPrev • General definition • η = exergy recovered/exergy supplied • = 1 – exergy destroyed/exergy supplied

13. Exergy change of a system • Property • Work potential in specific environment • Max amount of useful work when brought into equilibrium with environment • Depends on state of system andstate of the environment

14. Exergy change of a system • Look at thermo-mechanical exergy • Leave out chemical & mixing • Not address ke and pe

15. Exergy of fixed mass • Non-flow, closed system • Internal energy, u • Sensible, latent, nuclear, chemical • Look at only sensible & latent energy • Can be transferred across boundary only when temperature difference exists

16. Exergy of fixed mass • 2nd law: not all heat can be turned into work • Work potential of internal energy is less than the value of internal energy • Wuseful= (U-U0)+P0(V – V0)–T0(S – S0) • X = (U-U0)+P0(V – V0)–T0(S – S0) +½mVel2+mgz

17. Exergy of fixed mass • Φ = (u-u0)+P0(v-v0)-T0(s-s0)+½Vel2+gz • or Φ = (e-e0)+P0(v-v0)-T0(s-s0) • Note that Φ = 0 at dead state • For closes system • ΔX = m(Φ2-Φ1) = (E2-E1)+P0(V2-V1)-T0(S2-S1)+½m(Vel22-Vel12)+mg(z2-z1) • ΔΦ = (Φ2-Φ1) = (e2-e1)+P0(v2-v1)-T0(s2-s1) for a stationary system the ke & pe terms drop out.

18. Exergy of fixed mass • When properties are not uniform, exergy can be determined by integration:

19. Exergy of fixed mass • If the state of system or the state of the environment do not change, the exergy does not change • Exergy change of steady flow devices, nozzles, compressors, turbines, pumps, heat exchangers; is zero during steady operation. • Exergy of a closed system is either positive or zero

20. Exergy of a flow stream • Flow Exergy • Energy needed to maintain flow in pipe • wflow = Pv where v is specific volume • Exergy of flow work = exergy of boundary work in excess of work done against atom pressure (P0) to displace it by a volume v, so • x = Pv-P0v = (P-P0)v

21. Exergy of a flow stream • Giving the flow exergy the symbol ψ • Flow exergy Ψ=(h-h0)-T0(s-s0)+½Vel2+gz • Change in flow exergy from state 1 to state 2 is Δψ = (h2-h1)-T0(s2-s1)+ ½(Vel22 – Vel12)+g(z2-z1) • Fig 7-23

22. Exergy transfer by heat, work, and mass • Like energy, can be transferred in three forms • Heat • Work • Mass Recognized at system boundary With closed system, only heat & work

23. Exergy transfer by heat, work, and mass • By heat transfer: • Fig 7-26 • Xheat =(1-T0/T)Q • When T not constant, then Xheat =∫(1-T0/T)δQ • Fig 7-27 • Heat transfer Q at a location at temperature T is always accompanied by an entropy transfer in the amount of Q/T, and exergy transfer in the amount of (1-T0/T)Q

24. Exergy transfer by heat, work, and mass • Exergy transfer by work • Xwork = W – Wsurr (for boundary work) • Xwork = W (for all other forms of work) • Where Wwork = P0(V2-V1)

25. Exergy transfer by heat, work, and mass • Exergy transfer by mass • Mass contains exergy as well as energy and entropy • X=m Ψ=m[(h-h0)-T0(s-s0)+½Vel2+gz] • When properties change during a process then

26. Exergy transfer by heat, work, and mass • For adiabatic systems, Xheat = 0 • For closed systems, Xmass = 0 • For isolated systems, no heat, work, or mass transfer, ΔXtotal = 0

27. Decrease of Exergy Principle • Conservation of Energy principle: energy can neither be created nor destroyed (1st law) • Increase of Entropy principle: entropy can be created but not destroyed (2nd law)

28. Decrease of Exergy Principle • Another statement of the 2nd Law of Thermodynamics is the Decrease of Exergy Principle • Fig 7-30 • For an isolated system • Energy balance Ein –Eout = ∆Esystem 0 = E2 –E1 • Entropy balance Sin –Sout +Sgen =∆Ssystem Sgen =S2 –S1

29. Decrease of Exergy Principle • Working with 0 = E2 –E1 and Sgen= S2 –S1 • Multiply second and subtract from first • -T0Sgen = E2 –E1 -T0(S2 –S1) • Use • X2–X1 =(E2-E1)+P0(V2-V1)-T0(S2-S1) • since V1 = V2 the P term =0

30. Decrease of Exergy Principle • Combining we get • -T0Sgen= (X2–X1) ≤ 0 • Since T is the absolute temperature of the environment T>0, Sgen≥0, so T0Sgen≥0 so • ∆Xisolated = (X2–X1)isolated ≤ 0

31. Decrease of Exergy Principle • The decrease in Exergy principle is for an isolated system during a process exergy will at best remain constant (ideal, reversible case) or decrease. It will never increase. • For an isolated system, the decrease in exergy equals the energy destroyed