Exergy A Measure of Work Potential

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

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…

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)

Exergy associated with Kinetic and Potential Energy Kinetic energy  Form of mechanical energy  Can be converted to work entirely  x ke = ke = vel 2 /2(kJ/kg)

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

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

Reversible Work and Irreversibility Reversible Work Irreversibility (exergy destruction) Surroundings Work  Work done against the surroundings  For moveable boundary W surr = P 0 (V 2 – V 1 ) W useful = W – W surr = W - P 0 (V 2 – V 1 )

Reversible Work and Irreversibility Reversible Work, W rev  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

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

2 nd Law Efficiency Second Law Efficiency, η II Ratio of thermal efficiency and reversible (maximum) thermal efficiency η II = η th /η th, rev Or η II = W u /W rev  Can not exceed 100%

2 nd Law Efficiency For work consuming devices For η II = W rev /W u In terms of COP  η II = COP/COP rev General definition  η = exergy recovered/exergy supplied  = 1 – exergy destroyed/exergy supplied

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 and state of the environment

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

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

Exergy of fixed mass 2 nd law: not all heat can be turned into work Work potential of internal energy is less than the value of internal energy W useful = (U-U 0 )+P 0 (V – V 0 )–T 0 (S – S 0 ) X = (U-U 0 )+P 0 (V – V 0 )–T 0 (S – S 0 ) +½mVel 2 +mgz

Exergy of fixed mass Φ = (u-u 0 )+P 0 (v-v 0 )-T 0 (s-s 0 )+½Vel 2 +gz or Φ = (e-e 0 )+P 0 (v-v 0 )-T 0 (s-s 0 ) Note that Φ = 0 at dead state For closes system  ΔX = m(Φ 2 -Φ 1 ) = (E 2 -E 1 )+P 0 (V 2 -V 1 )-T 0 (S 2 - S 1 )+½m(Vel 2 2 -Vel 1 2 )+mg(z 2 -z 1 )  ΔΦ = (Φ 2 -Φ 1 ) = (e 2 -e 1 )+P 0 (v 2 -v 1 )-T 0 (s 2 -s 1 ) for a stationary system the ke & pe terms drop out.

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

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

Exergy of a flow stream Flow Exergy  Energy needed to maintain flow in pipe  w flow = Pvwhere v is specific volume  Exergy of flow work = exergy of boundary work in excess of work done against atom pressure (P 0 ) to displace it by a volume v, so  x = Pv-P 0 v = (P-P 0 )v

Exergy of a flow stream Giving the flow exergy the symbol ψ Flow exergy Ψ=(h-h 0 )-T 0 (s-s 0 )+½Vel 2 +gz Change in flow exergy from state 1 to state 2 is Δψ = (h 2 -h 1 )-T 0 (s 2 -s 1 )+ ½(Vel 2 2 – Vel 1 2 ) +g(z 2 -z 1 ) Fig 7-23

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

Exergy transfer by heat, work, and mass By heat transfer: Fig 7-26 X heat =(1-T 0 /T)Q When T not constant, then X heat =∫(1-T 0 /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-T 0 /T)Q

Exergy transfer by heat, work, and mass Exergy transfer by work  X work = W – W surr (for boundary work)  X work = W(for all other forms of work)  Where W work = P 0 (V 2 -V 1 )

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-h 0 )-T 0 (s-s 0 )+½Vel 2 +gz] When properties change during a process then

Exergy transfer by heat, work, and mass For adiabatic systems, X heat = 0 For closed systems, X mass = 0 For isolated systems, no heat, work, or mass transfer, ΔX total = 0

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

Decrease of Exergy Principle Another statement of the 2 nd Law of Thermodynamics is the Decrease of Exergy Principle Fig 7-30 For an isolated system  Energy balance E in –E out = ∆E system 0 = E 2 –E 1  Entropy balance S in –S out +S gen =∆S system S gen =S 2 –S 1

Decrease of Exergy Principle Working with 0 = E 2 –E 1 and S gen = S 2 –S 1 Multiply second and subtract from first  -T 0 S gen = E 2 –E 1 -T 0 (S 2 –S 1 ) Use  X 2 –X 1 =(E 2 -E 1 )+P 0 (V 2 -V 1 )-T 0 (S 2 -S 1 )  since V 1 = V 2 the P term =0

Decrease of Exergy Principle Combining we get  -T 0 S gen = (X 2 –X 1 ) ≤ 0 Since T is the absolute temperature of the environment T>0, S gen ≥0, so T 0 S gen ≥0 so  ∆X isolated = (X 2 –X 1 ) isolated ≤ 0

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