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Sustainable Energy
Toolbox8:
Thermodynamics
and
Efficiency
Calcu
SustainableEnergy10/7/2010
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First law: conservation of heat plus wor
Heat (Q) and work (W) are forms ofenergy.
Energy can neither be created ordestroyed.
=
Applies to energy (J, BTU, kW-hr,) or power (W, J/s, hp)
Work comes in several forms: PdV, electrical, mgh, kinetic,
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Energy,massbalances.
Control
Volume
Conservationofenergy:in
in
out
out
E=Q+ W+Ek
nk
Ek
nk
k k
Chemicalspeciesconservation:
n = nin
nout
+ r dV dt
Image removed due to copyright restrictions. Please see Fig. 4.6
and M. Modell. Thermodynamics and its Applications. 3rd ed. E
Hall, 1996.
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Convertingheatandwork
Intheoryvariousformsofworkcanbeinterconvertedwithhighefficiency(i.e.witmakingalotofheat):
Kinetic,mgh,electricity Inpracticeitisdifficulttoefficientlyconvertso
typesofwork:chemical/nuclear/lighttendtom .
Workcaneasilybeconvertedtoheatwithefficiency:Electricalresistanceheaters,friction,exotherm
reactions(e.g.combustion,nuclearreactions Impossible toconvertHeattoWorkwith
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probable state
Entropy(S)andthesecondlawofthermodynamics
Q
Entropy:ameasureof d S
disorderT
rev
Entropyoftheuniverseisalways increasing universeS 0 Movestomorestatistically
pro a es a e Entropyisastatefunction
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Heat-to-work
conversions
Image removed due to copyright restrictions. Please see Fig. 14.7 in Tester, Jefferson W., and M. M
Thermodynamics and its Applications. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.
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Heat-to-work
conversions
Qin
Win Wou
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A
simple
heat
engine
Energybalance:
Q& Accumulation=InOut+GenerationC
0(firstla0(steadystate)
H
0
=
Q&H W& W&W& Entropybalance:
Accumulation=InOut+GenerationC
gen0(steadystate)
Q& Q
0=
H &+S
gen S
&
=
T
gen
H
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A
possible
heat
engine
Energybalance:
Q& Accumulation=InOut+GenerationC
0(firstla0(steadystate)
H
0
=
Q&H Q&C W& W& =W& Entropybalance:
Accumulation=InOut+GenerationC
gen
0(steadystate)
Q&C & &QH
QC & Q&
0= +
S
gen S
&gen
=
C
TH
TC
TC
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Maximum efficiency of heat engine
HQ&
W&0HC ==
QQS
&&&
H
workheatQ
W
&
&
To maximize efficiency:
Q& =HC TT
CQ& Algebra:
H
CHH
CH T
T
QQQQW =
=
&&
&&&
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Carnot
efficiency
W& T
max C=
1Carnot
Q&
H TH Setsupperlimitonworkproducedfromaproces
hasahotandcoldreservoir
powerplant,internalcombustionengine,geothepowerplant,solarthermalpowerplant
Note:AlltemperaturesmustbeexpressedinKeRankine)!
TcusuallycannotbebelowenvironmentalT. THlimited by materials (melting, softening, oxidizing
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m n
FreeEnergyandExergy:Measures
How
Much
Chemical
Energy
ispotentially
available
to
do
work
Usualmeasureofabilitytodowork:Freeenergy
G = H TS = U + PV - TS Wehavesomeminimumtemperatureinoursys
Tcooling,~300K),andaminpressure(e.g.Pmin=
V
CallG-TcoolingSPminV theexergy:howmuchenergygoingintoadeviceisavailabletodowo
Shouldalsoconsiderthelowest-chemical-energ(e.g.H
2
OandCO2
),notordinarystandardstate(H2,O2,graphite).
A ton of room temperature air has quite a lot of t
cooling min
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Rankine
cycle
Image removed due to copyright restrictions. Please see Fig. 14.7 in Tester, Jefferson W., and M. M
Thermodynamics and its Applications. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.
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Which of these Six Cases are not Feasib
Q
Q
QFeasible
Not Feasible. Violates Seco
Not Feasible. Violates Seco
HotCold
WQ
WQ
Feasible. Example: electric h
Feasible. Heat Engine
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Combustion Turbine CT as lants
Common
heat-to-work
engines
in
practi
Rankine cycle:(shownbefore)
Brayton cycle:combustiongasesaredirexpandedacrossaturbineandexhausteCombustionTurbineCTgasplants
Combined cycle (CC):BraytoncyclefollbyaRankinecycleontheturbineexhaus
IGCC:CCappliedtosyngasproducedfromc
Internal combustion engine:combustiogases powering a piston
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In
most
Heat
Engines,
Work
extracted
a Boilingaliquidunderpressure:bigvolumechan
lotsofW=PdV
Turbines,pistonsextractmechanicalworkfrompressurizedgasbyanearlyadiabaticexpansion
T V
1=T V
1 P V
=
P V
hi hi lo lo hi hi lo lo
nRT
V
W
=
hi
highP
=
C
/
C 1
1
VlowP
p V
WouldliketoarrangesothatPlo~1atm,Tlo~lo
feasibletemperature Low T good for Carnot efficiency
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Exhaust tends to be too hot T >> ambient
Impractical
to
arrange
ideal
Phi,
Thi
Materiallimitsonpressure,temperature
SteamcyclesconfinedtorelativelylowThi
InternalCombustionEngines,Turbines
Exhausttendstobetoohot T >>ambient
Alotofenergycarriedawayaswasteheatinexhaust(LHV,exergyanalysis).SodespitehtheseareusuallymuchlessefficientthanCa
NeedtocombineToppingandBottomicycles.
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electricity from high T and use
ne
Combined
heat
and
power
(CHP)
Heatandpowerareoftenproducedtogethertomaximize
theuseofotherwisewastedheat.
Topping cyclesproduce
electricityfromhighT,andusethewasteheatforotherprocessneeds(e.g.,MITcogenfacility)
Bottoming cyclesare
processeswhichusemediumheatTheattogenerateelectricity
Topping
Q&H
elW&
&QC
Low-
temp.
heatneed
Bott
Q
Hitemhene
Q
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Heat pumps
Move heat from cold
Coefficient of perfo(COP)
Q& T&
Practically, COPs ar
3x as much heat c
supplied as electri Limited by power g
efficiency
Heatpump
&
W&
10C
~25CH
w TW =
&
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Select the More Efficient Home Heating
Burn NG with 90% efficiency furnace
OR
Use electricity to drive heat pump
NG Power Plant Combined Cycle with 50% e
Transmission and distribution losses are 10%
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Air conditioning and refrigeration
Type of heat pum
Coefficient ofperformance (C
CQ&
HQ&
&
~35C~25C
ea
pump
H
C
TT
WQCOP
s
=&
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Canconvertheattochemicalenergyb
run
into
Carnot
limit
CH4 + 2 H2O + Q = CO2 + 4 H2
H >0andS >0rxn rxn NeedtosupplyheatathighT(toshift
RemovehotH2 fromcatalysttofreezetequilibrium.
WhenwecoolhotH2 toroomT,emithealowerT(makesadditionalentropy).
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.
Conclusions
1. Heatplusworkisconserved(fromtheFirstLaw
2. Heatcantbeconvertedtoworkwith100%effic(fromtheSecondLaw).
3. Realprocessessufferfromnon-idealitieswhichgenerallykeepthemfromoperatingclosetothethermodynamiclimits(fromreallife,plustheSe
.
4. Chemical,nuclearenergyinprincipleareworkmostpracticaldevicesconvertthemintoheat,theatenginestoextractPdVwork:Carnotlimit
5. Carefulaccountingforenergy/exergyandtheliwhatispossibleisnecessaryforassessingnew
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Fall 2010
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