MIT22 calculos de eficiencia

8/21/2019 MIT22 calculos de eficiencia

1/24

Sustainable Energy

Toolbox8:

Thermodynamics

and

Efficiency

Calcu

SustainableEnergy10/7/2010


2/24

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 =

&


20/24

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%


21/24

Air conditioning and refrigeration

Type of heat pum

Coefficient ofperformance (C

CQ&

HQ&

&

~35C~25C

ea

pump

H

C

TT

WQCOP

s

=&


22/24

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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MIT22 calculos de eficiencia