Download Exergy

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(S2S1)+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:
X   m   dV
V
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

 Vel dA
X
mass
n
c
Ac

X
mass
 m   X massdt
t
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