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

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 xke = ke = vel2 /2 (kJ/kg)

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

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

Wsurr = P0(V2 – V1)

Wuseful = W – Wsurr = W - P0(V2 – V1)

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

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

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%

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

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

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

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.

Exergy of fixed mass

When properties are not uniform, exergy can be determined by integration:

VdVmX

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 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

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

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

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

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)

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 dAVelX c

Acn

mass

dtmt

massmass XX

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

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)

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

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

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

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