1.1 EnergyUnits,Conversions,andDimensionalAnalysis
İlhamiYıldızandYuLiu, DalhousieUniversity,Halifax,NS,Canada
r 2018ElsevierInc.Allrightsreserved.
1.1.1Introduction
1.1.2.3DerivedQuantities3
1.1.2.4MultiplesandSubmultiplesofQuantities3 1.1.2.5TypesofQuantityEquations4
1.1.5.5UseofSymbolsforMathematicalOperations9
Nomenclature
aAtto
a Index;acceleration,ms 2;constant,2897 mmK
AUnitofelectriccurrent,ampere;area,m2
b Index
BtuBritishthermalunit
cCenti
c Index;speedoflight,3 108 ms 1
CUnitofelectriccharge,coulomb;Celsius
C Specificheat,Jkg 1 K 1 orBtulbm 1 1F 1
cdLuminousintensityunit
dDeci
daDeka
EExa
E Energy,JorBtuh 1
fFemto
FFahrenheit
F Force,Norlbf
g Gravitationalacceleration,ms 2
GGiga
hHecto
h Height,m;pumphead,m;enthalpy,Jkg 1 ,
heattransfercoefficient,Wm 2 K 1 orBtuh 1
ft 2 1F 1;Planck’sconstant,6 626 10 34 Js
hpUnitofpowerinI–P,horsepower
I Radiant fluxdensity,Wm 2 orBtuh 1 ft 2
JUnitofenergyandwork,joule
kKilo
k Dimensionlesscoefficient,thermal conductivity,Wm 1 K 1 orBtuh 1 ft 1 1F 1
kgUnitofmass,kg
kWhUnitofenergy,kilowatt-hour( ¼ 3.6MJ)
KUnitofthermodynamictemperature
l Length,morft
LLength
mMilli
m Unitoflength,m;mass,kgorlbm
m Mass flowrate,kgs 1
MMega;mass
molUnitofamountofsubstance,mol nNano
NUnitofforce,newton pPico
p Pressure,Paorlbf
PPeta
P Power,WorBtuh 1
PaUnitofpressure,pascal
r Radius,m
R Thermalresistance,m2 KW 1 orhft2 1FBtu 1
radUnitofplaneangle,radian
s Entropy,Jg 1 orBtulbm 1
srUnitofsolidangle,steradian
TTera;time,s;temperature, 1C, 1F,K,orR
thermUnitofheatenergy,105.5MJor100,000Btu
tonRefrigerationton,12,000Btuh 1 or3.52kW
U Thermaltransmittance,Wm 2 K 1 orBtuh 1 ft 2 1F 1
VUnitofelectricpotential,potentialdifference, andelectromotiveforce,volt
V Volume,m3 orft3
Greekletters
D Difference
F Pump power,Worhp
Z Conversionef ficiency,%
l Wavelength, mm
m Micro
m Dynamicviscosity,Pas
Subscripts
w Width WUnitofpower,watt W Work x Distance,morft yYocto YYotta zZepto ZZetta
n Kinematicviscosity,m2 s 1;speci ficvolume, m 3 kg 1 orft3 lbm 1;frequency,cycles
s 1 ¼ hertz ¼ Hz
y Pumppower,Worhp
r Density,kgm 3 orlbm ft 3
O Unitofelectricresistance,ohm
bkBreakpower fl Fluid power keKineticenergy maxMaximum pPump;constantpressure pePotentialenergy vConstantvolume
Superscripts 1 Degree 0 Minute(angle)
1.1.1Introduction
Second(angle)
Whendealingwithengineeringandscientificrelationships,inordertoappreciatethemagnitudesofphysicalquantities,itis essentialtohaveasolidgraspofunits,andrecognizetwotypesofequations,namely,quantityequationsandnumerical equations.Bothtypesarefoundintextsandreferencebooks,andtheconceptofunitsandquantitiesisusefulinunderstanding theirrespectivefeatures.Inthischapter,wecoverthemainfeaturesofquantitiesandquantityequations,andprovidethemost importantunitsandconversionsrelatingtoenergy.Quantityequationsarealsocalledequationsbetweenquantities,orphysical equations.And,numericalequationsarealternativelycalledmeasureequations.Wealsointroducethetechniqueofdimensional analysis,whichisusedtoderivebasicphysicalrelationshipswithoutperformingafullanalysisofasystem.
1.1.2Quantities
In1954,the10thgeneralconferenceonweightsandmeasures(CGPM)decidedthataninternationalsystemshouldbederived fromsixbaseunitstoprovideforthemeasurementoftemperatureandopticalradiationinadditiontomechanicalandelectromagneticquantities.Sixbaseunitsrecommendedatthisconferencewerethemeter,kilogram,second,ampere,degreeKelvin (laterrenamedkelvin),andcandela.In1960,the11thCGPMnamedthesystemtheInternationalSystemofUnits,SIfromthe Frenchname,LeSystèmeInternationald'Unités [1].Later,theseventhbaseunit,themole,wasaddedin1971bythe14thCGPM [2].SIisthemodernformofthemetricsystem,andtodayisthemostwidelyusedmeasurementsystem.
Therefore,theInternationalSystemofQuantities(ISQ)isnowasystembasedonsevenbasequantities:length,mass,time, thermodynamictemperature,electriccurrent,luminousintensity,andamountofsubstance.Otherquantities,suchasarea,pressure, andelectricalresistanceareallderivedfromthesebasequantities.TheISQdefinesquantityasanyphysicalpropertythatcanbe measuredwiththeSIunits [3].Aquantitymayalsobeaphysicalconstant,suchasthegasconstant,orthePlanck’ s constant.Several hundredquantitiesareemployedtodescribeandmeasurethephysicalworld,andafewofthesequantitiesarelistedbelow [4]:
1.1.2.1RelationshipBetweenQuantities
Thestudyofphysicstoagreatextentcanbedefinedasthestudyofmathematicalrelationshipsamongvariousphysicalproperties.
Physicalquantitiesaredefined,asabove,whenthesepropertiesallowareasonablemathematicaldescription.Therelationshipof allotherquantitiescanbeestablishedintermsofafewbasequantitiesselectedproperly,eitherbydefinition,bygeometry,by physicallaw,orbyacombinationofthebasequantities.
Forinstance,pressureisaquantitythatisrelated,bydefinition,toaquantityforcedividedbyaquantityarea.Area,onthe otherhand,isaquantityrelated,bygeometry,totheproductoftwoquantitiesoflength.Moreover,forceisaquantityrelated(by Newton’ssecondlaw)tothequantitymasstimesthequantityacceleration.
Therelationshipsbetweenquantitiesareexpressedintheformofquantityequations.Wecanrelateevenanisolatedquantity, suchastemperaturetothequantitiespressure,volume,andmass.Wecanfurtherrelatethequantitieslengthandtimebyusingthe universalconstantandthespeedoflight.Therefore,ifwedefineourconceptscorrectly,wecanrelateanyquantitytoanyother quantity.Thustheequationarea ¼ length widthisaquantityequation,whichstatesthatthequantity(areaofarectangle)is equaltothequantity(length)timesthequantity(width).
1.1.2.2BaseQuantities
Inordertoreduceasetofquantityequations,wehaveto firstestablishanumberofso-calledbasequantities.Hence,base quantitiesarecalledthebuildingblocksuponwhichwedeveloptheentirestructureandrelationshipsofthephysicalworld.As mentionedearlier,theinternationalsystemofunits,orSI,makesuseofsevenbasequantities:mass(kg),length(m),time(s), temperature(K),electriccurrent(A),luminousintensity(cd),andamountofsubstance(mol).Thenumberofbasequantities,as wellastheirchoice,isquiteanarbitrarychoice;but,generally,weselectquantitiesthatareeasytounderstandandfrequentlyused, andforwhichaccurateandmeasurablestandardscanbeestablished.
1.1.2.3DerivedQuantities
Asmentionedintherelationshipsectionearlier,usingtheselectedbasequantitiesasbuildingblocks,derivedquantitiesare expressedasthosethatcanbedeductedbydefinition,geometry,orphysicallaw.Somederivedquantityexamplesarearea(equals theproductsoftwolengths),velocity(equalslength/time),andforce(equalsmass acceleration),pressure,power,etc.Wealso havewhatarecalledsupplementaryunits(asaclassofderivedunits),namely,theplaneangle(radian ¼ rad ¼ mm 1)andsolid angle(steradian ¼ sr ¼ m 2 m 2).
1.1.2.4MultiplesandSubmultiplesofQuantities
Notethatthemagnitudeofaquantitycanhaveanextremelylargerange.Inanefforttohandlesuchalargerange,theSIunit systemgenerated20prefixesshownin Table1
Table1 MultiplesandsubmultiplesinSIunitsystem
Prefix SymbolMultiplierExample
YottaY1024 5Ym ¼ 5yottameters ¼ 5 1024 m
ZettaZ1021 2Zm ¼ 2zettameters ¼ 2 1021 m
ExaE1018
7Em ¼ 7exameters ¼ 7 1018 m
PetaP1015 6PJ ¼ 6petajoules ¼ 6 1015 J
TeraT1012 5TW ¼ 5terawatts ¼ 5 1012 W
GigaG109 8GJ ¼ 8gigajoules ¼ 8 109 J
MegaM106 2MW ¼ 2megawatts ¼ 2 106 W
Kilok103 3km ¼ 3kilometers ¼ 3 103 m
Hectoh1006hL ¼ 6hectoliters ¼ 600L
Dekada102dam ¼ 2decameters ¼ 20m
Decid10 1 3dL ¼ 3deciliters ¼ 0.3L
Centic10 2 5cm ¼ 5centimeters ¼ 0.05m
Millim10 3 9mV ¼ 9millivolts ¼ 9 10 3 V
Micro m 10 6 5 mm ¼ 5micrometers ¼ 5 10 6 m
Nano n10 9 2ns ¼ 2nanoseconds ¼ 2 10 9 s
Picop10 12 3pJ ¼ 3picojoules ¼ 3 10 12 J
Femtof10 15 6fm ¼ 6femtometers ¼ 6 10 15 m
Attoa10 18 5aJ ¼ 5attojoules ¼ 5 10 18 J
zeptoz10 21 6zJ ¼ 6zeptojoules ¼ 6 10 21 J
yoctoy10 24 8yJ ¼ 8yoctojoules ¼ 8 10 24 J
1.1.2.5TypesofQuantityEquations
Theenergyofwind,thepressureatthebottomofanairorwatercolumn,theweightofanobject,andtheviscosityofaliquidare allphysicalquantitiesofnature.And,whethertheyaremeasuredornot,thesequantitiesarealwaysthereinteractingwitheach otheraccordingtofundamentallaws.Physicistsoftenexpresstheselawsintermsofquantityequationsbecausequantities conformtotheselaws.Quantityequationspossesstwoimportantfeatures: first,theyshowtherelationshipbetweenquantities, andsecond,theycanbeusedwithanysystemofunits.
Therearethreebasictypesofquantityequations:
1. Quantityequationsdevelopedfromthelawsofnature;forinstance,Newton’ssecondlawofmotion F ¼ ma
where F isthemagnitudeoftheforce, m isthemagnitudeofthemass,and a isthemagnitudeoftheacceleration.
2. Quantityequationsdevelopedfromgeometry;forinstance,areaofacircle
where A isthemagnitudeofthearea, p isthecoefficientbasedonthegeometryofacircle,and r isthemagnitudeoftheradius.
3. Quantityequationsdevelopedfromadefinition;forinstance,definitionofpressure
where p isthemagnitudeofthepressure, F isthemagnitudeoftheforce,and A isthemagnitudeofthearea.
Manyquantityequationscanbedevelopedasacombinationofthebasicquantityequationsgivenabove,andinallcases,we canuseanyunitswewanttodescribethemagnitudesoftherelevantphysicalquantities.
1.1.3DimensionalAnalysis
Dimensionalanalysisisquiteausefulmethodforderivinganalgebraicrelationshipbetweendifferentphysicalquantities,which reliesongoodphysicalintuitioninchoosingthedifferentappropriatephysicalvariables.Theideabehindthisanalysisisthateach variableisexpressedintermsofitsfundamentalunitsofmass M,length L,andtime T,etc.,raisedtosomearbitraryindex a,b,c, etc.Theseunknownindicesarethendeterminedbyequatingtheindicesoflikeunits [5].Onemightalsochooseforce,length,and mass asthebasedimensions,withassociateddimensions F, L, M,whichcorrespondstoadifferentbasis.Itmaysometimesbe usefultochooseoneoranotherextendedsetofdimensionalsymbols.Inelectromagnetism,forinstance,itmaybeadvantageous tousedimensionsof M, L, T,and Q,where Q isusedtorepresentthedimensionofelectriccharge.Anotherexampleisthat,for instance,inthermodynamics,thebasesetofdimensionsisoftenextendedtoincludeadimensionfortemperature, Y
Let’snowperformasimpledimensionalanalysisto findanexpressionforthehydrostaticpressureina fluid.Thehydrostatic pressureisdependentonthedensity r,thegravitationalacceleration g,anddepth h.Now,let’sassumeageneralalgebraicequation intheformof
where k isacoefficient(dimensionless),and a,b, and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeach symbolbyitsfundamentalphysicalunit,andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
Thenwecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforhydrostaticpressurecanbefound as p ¼ k r gh, wherethecoefficient k cannotbedeterminedfromdimensionalanalysisbecauseitisdimensionless. Moredimensionalanalysisexamplesareprovidedintheexamplessectionlater.
1.1.4UnitsandConversions
Thissection,asmodifiedafterASHRAE [6,7],referencestheStandardforMetricPractice,ASTMStandardE380-84 [8], asoneof the basicstandardsforSIusage [9–13] Table2 providesconversionfactorsroundedtothreeorfoursigni ficant figures for conversionbetweenSIandI–P.And Table3 providesconversionfactorsfordifferentphysicalquantitiesrelatedtoenergyfurther.
Table2
SIenergyrelatedunitsandconversions
Divide By Toobtain
Divide ByToobtain
ha 0.405acre J 1.36ft lbf (work)
kPa 100barJkg 1 2.99ft lbf lb 1 (specificenergy)
L 159barrel(42USgal,petroleum) W 0.0226ft lbf min 1 (power)
m3 0.159 L 3.79gallon(US,231in3)
kJ 1.055Btu,ITm3 0.00379gallon
kJm 3;JL 1 37.3Btuft 3 mLs 1 1.05gph kJL 1 0.279Btugal 1 Ls 1 0.0631gpm
W(mK) 1 1.731 Btufth 1 ft3 1FmLJ 1 0.0179gpmton 1 refrigeration Btuin(hft3 1F) 1 g 0.0648grain(1/7000lb)
W(mK) 1 0.144 (thermalconductivity,k) mgL 1 17.1grgal 1
W(m 1C) 1 gkg 1 0.143grlb 1 W 0.293Btuh 1 kW 9.81horsepower(boiler)
kJm 3 11.4Btuft 2 kW 0.746horsepower(550ft-lbf s 1)
GJ(ym2) 1 0.0000114 Btu(yft2) 1 mm 25.4a inch
Toobtainby Multiply Toobtain byMultiply
Wm 2 3.15Btu(hft2) 1 kPa 3.38inofmercury(60 F)
W(m2 K) 1 5.68 (overallheattransfercoef., U) Pa 249inofwater(60 F) (thermalconductance, C) mmm 1 0.833in/100ft,thermalexpansion
kJkg 1 2.33Btulb 1 mNm 113in lbf (torqueormoment)
kJ(kgK) 1 4.19 Btu(lb 1F) 1 (specificheat, C) mm2 645in2
kJ(kg 1C) 1 mL 16.4in3 (volume)
m3 0.0352bushel mLs 1 0.273in3 min 1 (SCIM) J 4.19calorie,grammm3 16,400in3 (sectionmodulus)
kJ 4.19calorie,kilogram;kilocaloriemm4 416,000in4 (sectionmoment)
mPa s 1.00a centipoise,viscosity, m ms 1 0.278kmh 1 (absolute,dynamic) MJ 3.60a kWh
mm2 s 1 1.00a centistokes,kinematicviscosity, n GJ(y m2) 1 0.0388 kWh(yft2)
Pa 0.100a dynecm 2 JL 1 2.12kWh/100cfm
W44.0EDRhotwater(150Btuh 1) N 9.81kilopond(kgforce)
W 70.3EDRstream(240Btuh 1) kN 4.45kip(1000lbf)
COP 0.293EERMPa6.89kipin 2 (ksi)
m 0.3048a ft m3 0.001a liter
mm304.8a ft mPa 133micronofmercury(60oF)
ms 1 0.00508ftmin 1,fpm km 1.61mile
ms 1 0.3048a fts 1,fps km 1.85mile/nautical
kPa 2.99ftofwater kmh 1 1.61mph
kPam 1 0.0981ftofwaterper100ftpipe ms 1 0.44mph
m2 0.0929ft2 kPa 0.100a millibar
m2 KW 1 kPa 0.133mmofmercury(601F)
m2 1CW 1 0.176ft2 h 1FBtu 1 Pa 9.80mmofwater(601F) (thermalresistance, R) kPa 9.80meterofwater
mm2 s 1 92900ft2 s 1,kinematicviscosity, n g28.3ounce(mass,avoirdupois)
L 28.3ft3 N 0.278ounce(forceorthrust)
m3 0.0283ft3 mL 29.6ounce(liquid,US)
mLS 1 7.78ft3 h 1,cfh mN m 7.06ounceinch(torqueormoment)
1. Ls 1 0.472ft3 min 1,cfm gL 1 7.49ounce(avoirdupois)pergallon
Ls 1 28.3ft3 s 1,cfs ng(s m2 Pa) 1 57.4 perm(permeance)
N m 1.36ft lbf (torqueormoment)
mL 473pint(liquid,US)
ng(s m Pa) 1 1.46 perminch(permeability)
kgm 3 16.0lbft 3 (density, r) pound
kgm 3 120lbgallon 1
kg 0.454lb(mass) mgkg 1 1.00a ppm(bymass)
g 454lb(mass) kPa 6.89psi
N 4.45lbf (forceorthrust) EJ 1.055quad
kgm 1 1.49lbft 1 (uniformload) L 0.946quart(liquidUS)
mPas 0.413lbm (ft h) 1 viscosity m2 9.29square(100sqft) (absolute,dynamic, m) mL 15tablespoon(approximately)
mPas 1490lbf (ft s) 1 viscosity mL 5teaspoon(approximately) (absolute,dynamic, m) MJ 105.5therm(US)
gs 1 0.126lbh 1 t(tonne);Mg 1.016 ton,long(2240lb)
kgs 1 0.00756lbmin 1 t(tonne);Mg 0.907 ton,short(2000lb) (Continued )
Table2 Continued
Divide By Toobtain Divide ByToobtain
kW 0.284lbofsteamperhour@2121FkW3.52ton,refrigeration(12,000Btuh 1) (1001C) Pa 133torr(1mmHg@01C)
Pa 47.9lbf ft 2 Wm 2 10.8wattpersquarefoot mPas47900lbf sft 2 viscosity m 0.9144a yd (absolute,dynamic, m) m2 0.836yd2 kgm 2 4.88lbft 2 m3 0.765yd3
Toobtainby Multiply Toobtain byMultiply aConversionfactorisexact.
Abbreviation:COP,coefficientofperformance;EDR,equivalentdirectradiation;EER,energyefficiencyratio;SCIM,standardcubicinchesperminute.
1.1.4.1UsefulUnitsinElectricity
1.1.4.1.1Coulomb
Inanelectriccircuit,theunitofelectricchargeinSIisthecoulomb,andhasthesymbolC.Anampere,whichhasthesymbolofA, isdefinedastheamountofchargetransportedthroughanycross-sectionofaconductorinonesecondbyaconstantcurrentofone ampere,andisequivalenttotheamountofchargeonabout6,241,510,000,000,000,000electrons.
1.1.4.1.2Volt
Inanelectriccircuit,theunitofelectricpotential,potentialdifference,andelectromotiveforceinSIisthevoltandhasthesymbol V.Ifandwhenweconsiderourhousewiringasplumbing,voltscanthenbeconsideredasameasureofthewaterpressure.One voltisthepotentialdifferencebetweentwopointsonaconductorwhenthecurrent flowingisoneampereandthepower dissipatedbetweenthepointsisonewatt.
Thevoltisaderivedunit,andintermsofbaseunitsitcanbeexpressedasfollows:
1.1.4.1.3Watt
Inanelectriccircuit,onewatt(joulespersecond)isacurrentofoneampereatapressureofonevolt.Intermsofbaseunits, Watt ¼ Js 1
1.1.4.1.4Ohm
Inanelectriccircuit,theunitofelectricalresistance(aderivedunit)inSIiscalledanohmandhasthesymbolof O.Oneohmis definedastheelectricalresistancebetweentwopointsonaconductorwhenaconstantpotentialdifferenceofonevolt,appliedto thesepoints,producesintheconductoracurrentofoneampere.Ohmisaderivedunit,andintermsofbaseunitsitcanbe expressedasfollows:
1.1.5RulesforUsingSIUnits
1.1.5.1Capitalization
Thenamesofunitsstartwithalowercaseletterwhenwritingtheunitsoutexceptforinatitleorthebeginningofasentence.The onlyexceptionis “degreeCelsius.” Unlesstheycomefromanindividual'sname(inwhichcasethe firstletterofthesymbolis capitalized),lowercaseisusedinwritingsymbolsforunits.TheonlyexceptionisLforliter.Symbolsfornumericalprefixes (multiplesandsubmultiples)arealsolowercase,exceptforthoserepresentingmultipliersof106 ormore,forinstance,mega(M), giga(G),tera(T),peta(P),exa(E),zetta(Z),andyotta(Y).Itmeansthatallprefixesarewritteninlowercasewhenspelledout. Lowercaseunits:m,kg,s,mol,etc. Uppercaseunits:A,K,Hz,Pa,C,etc. Symbolsratherthanself-styledabbreviationsshouldalwaysbeusedtorepresentunits. Correctusage:A,s. Incorrectusage:ampsec
1.1.5.2UseofPlurals
Rememberthatsymbolsareneverexpressedasplural.Thatis,an “ s ” isneveraddedtothesymboltodenoteplural.However, whenthenamesofunitsarespelledout,theyaremadepluralifthenumbertowhichtheyreferisgreaterthan1.Fractions,onthe otherhand,arealwayswrittenassingular.Pluralsareusedasrequiredwhenwritingunitnames.Forexample,henriesispluralfor henry.Thefollowingexceptionsarenoted:
Table3 Continued
10,000859810.23881761.1 41,86936,0004.186917373.5 5.67834.88235.6783
Singular:lux,hertz,siemens Plural:lux,hertz,Siemens
Example1: Correctandincorrectusages
Correctusage Incorrectusage 5kg 5kgs 5kilograms 5kilogram
5.57kg –
5.57kilograms 5.57kilogram
0.57kilogram 0.57kilograms
1.1.5.3UseofHyphenationandSpace
Alsorememberthatahyphenoraspaceisnotusedtoseparateaprefixfromthenameoftheunit.Aspace,however,isleft betweenasymbolandthenumbertowhichitrefers,withtheexceptionofthesymbolsfordegree,minute,andsecondofangles, andfordegreeCelsius.
Inthreecasesthe finalvowelintheprefixisomitted:megohm,kilohm,andhectare.
Example2: Correctandincorrectusages
Correctusage Incorrectusage
1.1.5.4UseofNumeralsandPeriods
Rememberthatscienti ficandtechnicalwritingisdifferentfromanyotherwritings,suchasnewspaper,magazine,andother writings.Inscientificandtechnicalwriting,numeralsareusedforallnumbersexpressingphysicalquantities;however,itisa commonpracticetowriteoutthenumbersfromonetonineandusenumeralsforothernumbersinnewspapers.Inordinary booksandmagazines,forinstance,wholenumbersfromonethroughninety-nine,andanyofthesefollowedby “hundred,” “thousand,”“million,”“billion,” etc.,arespelledout.Also,keepinmindthattheassociatednumberiswrittenasnumeralswhen theunitisrepresentedbyanabbreviationorsymbol.
PeriodsareneverusedafterSIsymbolsunlessthesymbolisattheendofasentence.
1.1.5.5UseofSymbolsforMathematicalOperations
Unitsarerepresentedbysymbols,notbytheirspelled-outnames,whentheunits(SI)areusedwithsymbolsformathematical operations.
Notestoremember
1.Whenwritingunitnamesasaproduct,alwaysuseaspace(preferred)orahyphen.
Correctusage:newtonmeterornewton-meter
2.Whenexpressingaquotientusingunitnames,alwaysusethewordperandnotasolidus(/).Thesolidusorslashmarkis reservedforusewithsymbols.
Correctusage:meterpersecond Incorrectusage:meter/second
3.Whenwritingaunitnamethatrequiresapower,useamodifier,suchassquaredorcubed,aftertheunitname.Forareaor volume,themodifiercanbeplacedbeforetheunitname.
Correctusage:millimetersquaredorsquaremillimeter
4.Whendenotingaquotientbyunitsymbols,anyofthefollowingareacceptedform:
Correctusage:m/sorms 1
Inmorecomplicatedcases,considerusingnegativepowersorparentheses.Foracceleration,usem/s2 orms 2 butnotm/s/s. Forelectricalpotential,usekg.m2/(s3 A)orkgm2 s 3 A 1 butnotkgm2/s3/A.
Example3: Correctandincorrectusages
Correctusage
Jkg 1
Jkg 1
1.1.6OverallExamples
Example4: Area
Incorrectusage
jouleskg 1 joulesperkilogram joules/kilogram
N.m newton.meter
newtonmeter newton-meter
Find:ShowtheunitofareainSI,andperformdimensionalanalysis.
Solution:
Areaequationisaquantityequationarisingfromgeometry;forexample,theareaequationforapipeisexpressedasfollows:
where A isthemagnitudeofareainm2,themagnitudeof p is3.14(dimensionless),and r isthemagnitudeofradiusinm.
Orinanotherexample,theareaforarectangleisexpressedasfollows:
where A isthemagnitudeofareainm2, w isthemagnitudeofwidthinm,and l isthemagnitudeoflengthinm.
Let’snowperformasimpledimensionalanalysisto findanexpressionforthearea.Theareaisdependentonthedimensionless number p andtheradius.So,
¼ kr a
where k isadimensionlessnumber,and a isthenumbertobedetermined.Now,wecanreplaceeachsymbolbyitsfundamental physicalunit,andhave L2 ¼ La
L isanindependentquantity;thereforewecanequatetheindicesonbothsides,andhavethefollowingequation
a ¼ 2
Consequently,theexpressionfortheareacanbefoundas A ¼ kra, wherethecoefficient k cannotbedeterminedfrom dimensionalanalysisbecauseitisdimensionless;however,fromgeometry,weknowthat k ¼ p Example5: Volume
Find:ShowtheunitofvolumeinSIandperformdimensionalanalysis.
Solution:
Volumeequationisaquantityequationarisingfromgeometry;forexample,thevolumeequationforapipeisexpressedasfollows:
Volume V ðÞ¼ pr 2 L
¼ p m2 m ðÞ
Volume V ðÞ¼ m3
where V isthemagnitudeofvolumeinm3,themagnitudeof p is3.14(dimensionless),and r isthemagnitudeofradiusinm.
Orinanotherexample,thevolumeforarectangularcross-sectionisexpressedasfollows:
Volume V ðÞ¼ w l h ¼ m m m
Volume V ðÞ¼ m3
where V isthemagnitudeofvolumeinm3, w isthemagnitudeofcross-sectionalwidthinm, l isthemagnitudeofcross-sectional lengthinm,and h isthemagnitudeofheight.
Let’snowperformadimensionalanalysisto findanexpressionforthevolumehavingatubularcross-sectionalarea.The volumeisdependentonthedimensionlessnumber p,theradius,andlengthofthetube.So,
V ¼ kr a Lb
where k isadimensionlessnumber,and a and b arethenumberstobedetermined.Now,wecanreplaceeachsymbolbyits fundamentalphysicalunit,andhave
L3 ¼ La Lb
L isanindependentquantity;wecanthereforeequatetheindicesonbothsides,andhavethefollowingequation a þ b ¼ 3
Intheearlierexample,itwasdeterminedthat a ¼ 2,sothisleaves b ¼ 1.Consequently,theexpressionforthevolumecanbe foundas V ¼ kra Lb,wherethecoefficient k cannotbedeterminedfromdimensionalanalysisbecauseitisdimensionless;however, fromgeometry,weknowthat k ¼ p;therefore, V ¼ kr2 L
Example6: Volume
Find:Determinetheunitofvolume(m3)inSIforagivenvolumeinI–Psystem.
Solution:
VolumeunitinI–Psystemisft3 andrememberthat1ft ¼ 0.3048m;then
Volume V ðÞ¼ ft 3 0 3048 m=1ft ðÞ3
Volume V ðÞ¼ 0 028317 m3
Example7: Mass
Find:Determinetheunitofmass(kg)inSIforagivenmassinI–Psystem.
Solution:
MassunitinI–Psystemislbm andrememberthat1lbm ¼ 0.45359kg;then
Mass m ðÞ ¼ lbm 0 45359kg =1lbm ðÞ
Mass m ðÞ¼ 0 45359 kg
Example8: Force
Find:Showthattheunitofforceisnewton(N)inSI,andperformdimensionalanalysis.
Solution:
TheunitofforceinSI,definedasthatforce,whichappliedtoamassof1kg,givesitanaccelerationof1ms 1.Newton’ s secondlawofmotion,aquantityequationestablishedfromthelawsofnature,isexpressedas:
Force F ðÞ¼ mass acceleration ¼ ma ¼ kg ðÞ ms 2 ¼ kgms 2
Force F ðÞ¼ N
where m isthemagnitudeofmassinkg, a isthemagnitudeofaccelerationinms 2,and F isthemagnitudeofforceinN. Theforceisdependentonthemassandtheacceleration.Now,let’sassumeageneralalgebraicequationforforceintheformof F ¼ ma ab
where a and b aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit,andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations 1 ¼ a and1 ¼ b
Then,wecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforforcecanbefoundas F ¼ ma.
Example9: Force
Find:Showthattheunitofforceisnewton(N)inSIforagivenforceinI–Psystem
Solution: ForceunitinI–Psystemislbf andrememberthat1lbm ¼ 0.45359kg,1ft ¼ 0.3048m,andgravitationalacceleration g is32.174 lbm s 2;then Force F ðÞ¼ 1lbf ¼ 1lbm 32
Force F ðÞ¼ 4 45 kgms 2 ¼ 4 45 N where g isthemagnitudeofgravitationalacceleration,and F isthemagnitudeofforce. NotethatinI–Psystem,anaccelerationof9.80665ms2 correspondsexactlyto32.174048fts2 asshownbelow: g ¼ 9 80665ms2 100cm=1m ðÞ= 12in=1ft ðÞ= 2 54cm=1in ðÞ¼ 32 174048fts2
Example10: Pressure
Find:Showtheunitofpressure(pascal)inSI,andperformdimensionalanalysis.
Solution:
Insolids,wedealwithstresses;inliquidsandgases,however,wedealwithpressure,whichisdefinedasthenormalcomponent offorceperunitarea.Thereforetheunitforpressureisaderivedunit,andhasthesymbolPa(pascal)inSI.Onepascalisthe pressureresultingfromaforceof1Nactinguniformlyoveranareaof1m2.So,thepressureequationisaquantityequation establishedfromadefinition,whichisexpressedasfollows:
ðpÞ¼ force=area ¼ F =A ¼
p ðÞ¼ Pa where F isthemagnitudeofforce(themasstimestheacceleration)innewton(N),and A isthemagnitudeofareainm2.
Thepressureisdependentonthemass,thegravitationalacceleration,andthearea.Now,let’sassumeageneralalgebraic equationforpressureintheformof
where a,b, and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit, andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
Then,wecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforpressurecanbefoundas p ¼ (mg)/A.
Example11: Pressure
Find:Showthattheunitofpressureispascal(Pa)inSIforagivenforceinI–Psystem.
Solution:
PressureunitinI–Psystemispsi(lbf in 2),andrememberthat1lbf ¼ 4.45kgms 2 ¼ 4.45N;1in ¼ 0.0254m;then
¼ 6894 8kgðÞ ms 2 m 2
Pressure p ðÞ¼ 6894 8Pa ¼ 6 89 kPa where F isthemagnitudeofforceand A isthemagnitudeofarea.
Example12: Work
Find:Showthattheunitofworkisjoule(J)inSI,andperformdimensionalanalysis.
Solution:
TheunitofworkorenergyinSIisjoule,whichhasthesymbol,J.Thisistheworkdonewhenthepointofapplicationofaforce of1Nisdisplaced1minthedirectionoftheforce.Onewatt-secondisequalto1J.Theworkequationisthenaquantityequation establishedfromadefinition,whichisexpressedasfollows:
Work ¼ force distance ¼ mass acceleration ðÞ distance ¼ W ¼ ma Dx ¼ kg ðÞ ms 2 ðÞ m ðÞ ¼ kgms 2 ðÞm
Work ¼ Nm ¼ J where W isthemagnitudeofworkinJ, m isthemagnitudeofmassinkg,and a isthemagnitudeofaccelerationinms 2,and Dx is thedistancetraveledinm.
Theworkisdependentonthemass,theacceleration,andthedistancetraveled,forinstance.Let’snowassumethatageneral algebraicequationforworkisintheformof
W ¼ ma ab Dxc
where a,b,and c aretheindices(numbers)tobedetermined.Now,wecanagainreplaceeachsymbolbyitsfundamentalphysical unit,andhave
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
¼ a; 1 ¼ b and1 ¼ c
Then,wecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforforcecanbefoundas W ¼ ma Dx
Example13: Energy
Find:Showthattheunitofenergyisjoule(J)inSI,andperformdimensionalanalysis.
Solution:
Energyisdefinedastheabilitytoperformwork,andasexpressedearlier,theunitofenergyinSIisjoule,whichhasthesymbol, J.So,theenergyequationisaquantityequationestablishedfromadefinition,whichisexpressedasfollows:
where m isthemagnitudeofmassinkg,and a isthemagnitudeofaccelerationinms 2,and Dx isthedistancetraveledinm. Inthiscase,theenergyisdependentonthemass,theacceleration,andthedistancetraveled.Let’snowassumethatageneral algebraicequationforenergyisintheformof
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanagainreplaceeachsymbolbyitsfundamentalphysical unit,andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
¼ a; 1 ¼ b and1 ¼ c
Then,wecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforenergycanbefoundas E ¼ ma Dx
Example14: Power
Find:Showthattheunitofpoweriswatt(W)inSI,andperformdimensionalanalysis.
Solution:
TheunitofpowerinSIiswattandhasthesymbol,W.Powerisdefinedastherateatwhichenergyisexpendedorworkdone. Thewattinthermodynamicsisdefinedas “thepowerwhichin1sgivesrisetoenergyofonejoule.” Inmechanicalterms,however, apowerofonewattcanmoveamassof1kgin1s,throughadistanceofonemeterwithsuchforcethatthekilogrammass’ s velocityattheendofthemeterwillbe1ms 1 greaterthanitwasatthebeginning.Inanelectriccircuit,ontheotherhand,one wattisacurrentofoneampereatapressureofonevolt.So,thepowerequationisaquantityequationestablishedfroma definition,whichisexpressedasfollows:
Power ¼ work =time; orenergygeneration=time; orenergyconsumption=time
SincetheunitofworkorenergyisJ,then
Power ¼ J s 1 ¼ W ¼ P ¼ Et 1 ¼ energy =time ¼ ma Dxt 1 where t isthetimeinseconds.Inthiscase,thepowerisdependentonthemass,theacceleration,thedistancetraveled,andthe timetakentotravel.Let’snowassumethatageneralalgebraicequationforpowerisintheformof
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit, andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
Then,wecansolveforand findthat a ¼ b ¼ c ¼ 1;consequently,theexpressionforpowercanbefoundas P ¼ F Dxt 1 ¼ ma Dxt 1
Example15: Volt
Find:Expresstheunitofvoltintermsofbaseunits.
Solution:
Asmentionedearlier,inanelectriccircuit,theunitofelectricpotential,potentialdifference,andelectromotiveforceinSIisvolt andhasthesymbolV.Onevoltisthepotentialdifferencebetweentwopointsonaconductingwirecarryingaconstantcurrentof oneampere,andthepowerdissipatedbetweenthepointsisonewatt.
Thevoltisaderivedunit,andintermsofbaseunitsitcanbeexpressedasfollows:
Example16: Radiant fluxdensity
Find:Howmanyunitsofradiant fluxdensity I (Wm 2)inSIareinagivenamountofBtuh 1 ft2?
Solution:
Radiant fluxdensityisdefinedastheamountofenergyreceivedonaunitsurfaceinunittime.
Radiantfluxdensity ðW m 2 Þ¼ðBtuh 1 ft 2 Þð1054 35JBtu 1 Þ h=3600s ðÞ ft =0 3048m ðÞ2
Radiantfluxdensity ðWm 2 Þ¼ 3 15 Wm 2
Example17: Boilerhorsepower
Find:HowmanykilowattsofpowerinSIarein1boilerhorsepower(bhp)inI–P?
Solution:
Rememberthatoneboilerhorsepoweristheenergyrateneededtoevaporate34.5lbm ofwaterat2121F(1001C)inonehour;therefore, itisequalto33,475Btuh 1.Aboilerhorsepowerisapproximately13timeslargerthanmechanicalhorsepower(engineoutput).
Alsorememberthat1Btu ¼ 1054.35J,and1h ¼ 3600s;therefore,
Boilerpower ¼ 1bhp ½ð33; 475Btuh 1 Þ=1bhp ð1054 35J=1BtuÞ 1h=3600s ðÞ
Boilerpower ¼ 9804W
Boilerpower ¼ 9 8kW
Example18: Horsepower
Find:HowmanykilowattsofpowerinSIarein1horsepower(hp)inI–P?
Solution:
Thehorsepower(hp)isaunitinI–Psystem,sometimesusedtoexpresstherateatwhichmechanicalenergyisexpended.Itwas originallydefinedas550foot-poundspersecond(ft-lbf s 1).
Rememberthat1lbf ¼ 4.45kgms 2 ¼ 4.45N,and1ft ¼ 0.3048m;then
Power ¼ð550ft lbf s 1 Þ½ 0 3048 m= 1ft ðÞð4 45kgms 2 Þ=1lbf
Power ¼ 746W
Power ¼ 0 746 kW
Example19: Refrigerationton
Find:HowmanyBtuh 1 andkWhofrefrigerationisprovidedby1tofrefrigeration?
Solution:
Rememberthat1Btu ¼ 1054.35J,1h ¼ 3600s,1lbm ice ¼ 1lbm ofliquidwater,latentheatoffusion ¼ 144Btulbm 1,and1 shortton ¼ 2000lbm
Refrigerationiscommonlyratedintons.1tofrefrigerationisthelatentheatoffusionneededtomelt1shortton(2000lbm)of icein24h.Therefore
1refrigerationton ¼ 2000lbm ice 144Btulb 1 m =24h
1refrigerationton ¼ 12; 000 Btuh 1
1refrigerationton ¼ 12; 000Btuh 1 1054 35JBtu 1 1 h=3600s ðÞ 1kJ=1000J ðÞ
1refrigerationton ¼ 3 52 kW
Example20: Energy
Find:ShowhowmanyMJofenergy1kWhisequalto.
Solution:
Rememberthat1MJofenergyisequalto106 Jofenergy,and1kWhisequalto1000Js 1.Therefore, 1kWh ¼ 1000Js 1 1h ðÞ 60min=1h ðÞ 60 s=1min ðÞ¼ 3;600;000J 1kWh ¼ 3;600;000J ðÞ = 1;000;000 J =1MJ ðÞ 1kWh ¼ 3 6MJ
Example21: Energy
Find:ShowhowmanyMJandkWhofenergy1therm(US)has.
Solution:
Thethermisaunitofheatenergyequalto100,000Btuunits.Itistheenergyequivalentofburningapproximately100ft3 (2.83m3)of naturalgas.Naturalgasmetersmeasurevolumeratherthanenergycontent;thereforenaturalgascompaniesuseathermfactortoconvert thevolumeofgasusedtoitsheatequivalent,andthencecalculatetheactualenergyuse.Pleaserememberthatnaturalgaswithahigher thanaverageconcentrationofbutane,ethane,orpropanehasahigherthermfactor,whileimpuritieslowerthethermfactor.
1therm ¼ 100;000Btu ðÞð1054 35J=BtuÞ MJ=106 J ¼ 105 5MJ
1therm ¼ð105 5MJÞ 1kWh=3 6MJ ðÞ¼ 29 3kWh
Example22: Potentialenergy
Find:Showthattheunitofpotentialenergyisjoule(J)inSI.
Solution:
Potentialenergy ¼ force elevation ¼ mass gravitationalacceleration ðÞ elevation
Epe ¼ mgh
¼ kg ðÞ ms 2 m ðÞ ¼ kgms 2 m
Epe ¼ Nm ¼ J where m isthemagnitudeofmassinkg, g isthemagnitudeofgravitationalaccelerationinms 2,and h istheelevationfromadatuminm. Adimensionalanalysiscaneasilybeperformedto findanexpressionforpotentialenergy,aswedidforworkandenergy examplesearlier.
Example23: Kineticenergy
Find:Showthattheunitofkineticenergyisjoule(J)inSI.
Solution:
Kineticenergy ¼ 0 5mass speed2
Eke ¼ 0 5 mu2 ¼ kg ðÞ ms 1 2
¼ kgms 2 m
Eke ¼ Nm ¼ J where m isthemagnitudeofmassinkg,and u isthemagnitudeofspeedinms 1
Adimensionalanalysiscaneasilybeperformedto findanexpressionforkineticenergy,aswedidforworkandenergyearlier.
Example24: Pressureenergy
Find:Showthattheunitofpressureenergyisjoule(J)inSI.
Solution:
Pressureenergy ¼ mass pressuredifference ðÞ=density ¼ m DP =r
¼ kg ðÞ Pa ðÞ= kgm 3
¼ kg ðÞ kgm 1 s2 = kgm 3 ¼ kgms 2 m
Pressureenergy ¼ Nm ¼ J
where m isthemagnitudeofmassinkg, DP isthemagnitudeofpressuredifferencebetweentwopointsinPa,and r isthe magnitudeofdensityinkgm 3
Again,adimensionalanalysiscaneasilybeperformedto findanexpressionforpressureenergy,aswedidforworkandenergyearlier.
Example25: Kinematicviscosity
Find:Showtheunitsofkinematicviscosity n inSI.
Solution:
Thequantityequationfordynamicviscosityisgivenasfollows: n ¼ dynamicviscosity =density ¼ m=r ¼ Ft =r ¼ Pas ðÞ= kgm 3 ¼ kgm 1 s 2 s= kgm 3
wherePa(pascal)isequaltokg(ms2) 1 , m isthemagnitudeofdynamicviscosityinPas,and r isthemagnitudeofdensityinkgm 3
Kinematicviscosityisdependentontheforce F,thetime t,andthedensity r.Now,let’sassumeageneralalgebraicequationin theformof
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolinkinematicviscositybyits fundamentalphysicalunit,andoverall,wewouldhave
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit,andhave
M, L,and T areindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
Then,wecansolveforand findthat a ¼ c ¼ ½,and b ¼ 0, whicharetheindices(numbers);consequently,theexpressionfor kinematicviscositycanbefoundas n ¼ Ft/r
Example26: Dimensionlessnumber
Find:ShowthattheReynoldsnumber Re isadimensionlessnumber.
Solution:
ThequantityequationforReynoldsnumberisgivenasfollows: Re ¼ ruD=m ¼ kgm 3 ms 1 m ðÞ = kgm 1 s2 s ¼ Dimensionless where r isthemagnitudeofdensityofthe fluidinkgm 3 , u isthemagnitudeofaveragevelocityofthe fluidinms 1 , D isthe diameterofthepipeinwhichthe fluid flowsinm,and m isthemagnitudeofdynamicviscosityinPa.s.
Example27: Pumphead
Find:Showthatthepumphead hp unitisminSI.
Solution: hp ¼ pumpingenergy ðÞ= gravitationalacceleration ðÞ¼ Ep =g ¼ Jkg 1 = ms 2 ¼ Nmkg 1 = ms 2 ¼ kgms 2 mkg 1 s2 m 1 hp ¼ m
whereJistheunitofenergyjouleinSI( ¼ force distance ¼ Nm),Nistheunitofforcenewton( ¼ kgms 2),and g isthe magnitudeofgravitationalacceleration9.81ms 2
Pumpheadisdependentonthepumpingenergy Ep andthegravitationalacceleration g.Now,let’sassumeageneralalgebraic equationintheformof:
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolinkinematicviscositybyits fundamentalphysicalunit,andoverall,wewouldhave
where a and b aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit,and have
M, L,and T areindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowing equations
Then,wecansolveforand findthat a ¼ 0and b ¼ 1,whicharetheindices(numbers);consequently,theexpressionforpump headcanbefoundas hp ¼ Ep/g.
Example28: Pumppower
Find:Showthatthepumppower y unitisWinSI.
Solution:
Pumppower y ðÞ¼ Ep ¼ kgs 1 Jkg 1
Pumppower h ðÞ¼ Js 1 ¼ W where m isthemagnitudeofmass flowrateinkgs 1,and Ep isthemagnitudeofpumpingenergyinJkg 1 Ifthepumphasaconversionefficiencyof Z,thenthepumpinputpower ybk canbecalculatedasfollows:
Pumpinputpower ¼ pumpbreakpower ybk ðÞ¼ pumpfluidpower =efficiency ¼ yfl =h where yfl isthepumpoutput(fluid)power,andtheefficiency Z isindecimals(i.e.,0.6isusedfor60%conversionefficiency). Adimensionalanalysiscaneasilybeperformedto findanexpressionforpumppower,aswedidforworkandenergy,and othersearlier.
Example29: Pump fluidpower
Find:Showthatthepump fluidpower Ffl unitisWinSI.
Solution:
Pumpfluidpower Ffl ðÞ¼ Js 1 ¼ W
where m isthemagnitudeofmass flowrateinkgs 1 , g isthemagnitudeofgravitationalaccelerationinms 2,and hp isthe magnitudeofpumpheadinm.
where a, b,and c aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolbyitsfundamentalphysicalunit, andhave
or
M, L,and T areallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowing equations
Then,wecansolveforand findthat
c ¼ 1;consequently,theexpressionforpump fluidpowercanbefoundas Ffl ¼ F Dxt 1 ¼ mghpump
Example30: Pumpbreakpower
Find:Showthatthepumpbreakpower Fbk unitisWinSI.
Fig.1 Relationshipsbetweenthermodynamictemperatureandtemperaturescales.
Solution:
Pumpbreakpower Fbk ðÞ¼ O o
¼ kgms 2 ms 1 ¼ Nms 1
Pumpbreakpower Ubk ðÞ¼ Js 1 ¼ W
where O isthemagnitudeoftorqueinkgms 2,and o isthemagnitudeofangularvelocityoftheshaftinms 1
Adimensionalanalysiscaneasilybeperformedto findanexpressionforpumpbreakpower,aswedidinthepreviousexample.
Example31: Temperature
Find:ShowwhatthetemperatureisinSIforathermodynamictemperatureof300K.
Solution:
Weknowthattemperature,aproperty,isrelatedtohotnessorcoldnessofanobject;however,itisdifficulttogiveanexact definitionoftemperature.Thezerothlawofthermodynamicsindicatesthatwhentwobodieshavetemperatureequalitywitha thirdbody,theninturntheyhaveequaltemperatureswitheachother.
Thermodynamictemperatureis,however,definedbythethirdlawofthermodynamicsinwhichthetheoreticallylowest temperatureisthezeropoint.Atthispoint(absolutezero),theparticleconstituentsofmatterhaveminimalmotionandcan becomenocolder.
Byde finition,thetemperatureindegreeCelsiusisthedifferencebetweenthethermodynamictemperatureandthethermodynamictemperatureof273.15K.Notethat,bydefinition,atemperatureintervalof11Cisequaltoatemperatureintervalof1K, and01C(a.k.a.theicepoint)correspondsto273.15K(Fig.1).Then,thetemperatureinSI(1C) canbeexpressedasfollows:
Example2: Temperature
Find:Determinethethermodynamictemperatureequivalentof550oC. Solution:
Thermodynamictemperatureisexpressedasfollows:
NotethatKwassubstitutedfor 1Cbecausebothunitsareidenticalasexpressedbefore(Fig.1).
Example 33: Temperature
Find:DeterminethetemperatureinFahrenheitforagiventemperatureof211C.
Solution:
Notethaticepointandboilingtemperatures0and1001ContheCelsiusscalecorrespondto32and2121F,respectively. ThereforetheCelsiustemperaturerangeof(100–01C) ¼ 1001CcorrespondsexactlytotheFahrenheittemperaturerangeof (212–321F) ¼ 1801F(Fig.1). (212–321F) ¼ (100–01C) ¼ (1801F ¼ 1001C); therefore,1.01C ¼ 1.81F.Furthermore,knowingthat 1C ¼ K,weobtainK ¼ 1.81F. Then,therelationshipbetweentheCelsiustemperature(1C)andFahrenheittemperature(1F)canbedefinedasfollows:
where321FagainisthefreezingtemperatureforwaterinFahrenheittemperaturescale,whichisequalto01CintheCelsiusscale (Fig.1).Then,thetemperature(1F) inthisexamplecanbedeterminedas:
TheabsolutetemperaturescalerelatedtotheFahrenheittemperaturescaleisknownastheRankinescaleandisdesignated R TherelationshipbetweentheRankineandFahrenheittemperaturescalesisexpressedasfollows: Rankine ¼ 1F 459 67
Example34: Temperature
Find:DeterminethetemperatureinSIforagiventemperatureof701F. Solution:
TherelationshipbetweentheCelsiustemperatureandtheFahrenheittemperatureisdefinedasfollows:
where321FisthefreezingtemperatureforwaterintheFahrenheittemperaturescale,whichisequalto01CintheCelsiusscale. Then,thetemperatureinSI(1C)canbedeterminedas:
Example35: Density
Find:Determinetheunit(kgm 3)ofdensityinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthatthedensityisdefinedasthemass m perunitvolume V.So,thedensityequationisaquantityequation establishedfromadefinition,whichisexpressedinI–Psystemasfollows:
r ¼ m=V ¼ lbm ft 3
Rememberthat: 1ft ¼ 0 3048m; and1lbm ¼ 0 45359kg r ¼ lbm 0:45359kg =1lbm ðÞ ½ = ft 3 0:3048m=1ft ðÞ3 q ¼ 16 0184 kgm 3
Densityisdependentonthemass m andthevolume V.Now,let’sassumeageneralalgebraicequationintheformof r ¼ ma =V b where a and b aretheindices(numbers)tobedetermined.Now,wecanreplaceeachsymbolindensitybyitsfundamental physicalunit,andoverall,wewouldhave
L and T areindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations 1 ¼ a and 3 ¼ 3b
Then,wecansolveforand findthat a ¼ b ¼ 1, whicharetheindices(numbers);consequently,theexpressionforkinematic viscositycanbefoundas r ¼ ma/Vb
Example36: Specificvolume
Find:Determinetheunit(m3 kg 1)ofspecificvolumeinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthatthespecificvolumeisdefinedasthevolume V perunitmass m,andisthereforeareciprocalofdensity. So,thespecificvolumeequationisaquantityequationestablishedfromadefinition,whichisexpressedinI–Psystemasfollows:
n ¼ 1=r ¼ ft 3 lb 1 m
Rememberthat: 1ft ¼ 0 3048m; and1lbm ¼ 0 45359kg
n ¼ ft 3 0 3048m=1ft ðÞ3 = lbm 0 45359kg =1lbm ðÞ ½
m ¼ 0:062428 m3 kg 1
Now,wecanreplaceeachsymbolinspecificvolumebyitsfundamentalphysicalunit,andoverallwewouldhave M 1 L3 ¼ M ðÞa L ðÞb where a and b aretheindices(numbers),whicharedeterminedas a ¼ 3and b ¼ 1,sospeci ficvolumehasadimensionofm3 kg 1 (inSI).
Example37: Specificheatorentropy
Find:Determinetheunit(J(kgK) 1)ofspecificheatinSIiftheunitisgiveninI–Psystem.
Solution:
Theconstantpressurespeci ficheat(Cp)andconstantvolumespecificheat(Cv)areusefulfunctionsforparticularlygases. Rememberthatthespeci ficheatisdefinedastheheatenergyrequiredtoraisethetemperatureofaunitmassofsubstanceone degree.So,thespecificheatequationisaquantityequationestablishedfromadefinition,whichisexpressedinI–Psystemas follows:
C ¼ Btulb 1 m 1F
Rememberthat: 1Btu ¼ 1054 35J; 1lbm ¼ 0 45359kg ; K ¼ 1 81F
C ¼ Btu1054 35J=1Btu ðÞ
¼ 4184 J= kgK ðÞ
So,inSIsystem,thespecificheatisdefinedastheheatenergy(J)requiredtoraisethetemperatureof1kgsubstance1K(or11C).
Example38: Enthalpy
Find:Determinetheunit(Jkg 1)ofenthalpyinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthattheenthalpyisdefinedastheheatenergyavailableperunitmassofasubstance.So,theenthalpyequationisa quantityequationestablishedfromadefinition,whichisexpressedinI–Psystemasfollows:
h ¼ Btulb 1 m
Rememberthat: 1Btu ¼ 1054 35J; and1lbm ¼ 0 45359kg
h ¼ Btu1054 35J=1Btu ðÞ ½ = lbm 0 45359kg =1lbm ðÞ
h ¼ 2324 5 Jkg 1
Example39: Entropy
Find:Determinetheunit(Jg 1)ofentropyinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthattheentropyisdefinedasameasureofthemoleculardisorder.Thehigherthedisorderofanysystem,thegreateris itsentropy;converselyahigherorderstatusofasystemgivesalowentropystatus.Boltzmannshowedthatthereexistedasimple relationshipbetweentheentropyofagivensystemofmoleculesanditsprobability(thermodynamic)ofoccurrence.So,theentropy equationisaquantityequationestablishedformadefinition,whichhasthesymbol s,andisexpressedinI–Psystemasfollows:
s ¼ Btulb 1 m
Rememberthat: 1Btu ¼ 1054:35J; and1lbm ¼ 0:45359kg
s ¼ Btu1054 35J=1Btu ðÞ ½ = lbm 1000g =1kg ðÞ 0 45359kg =1lbm ðÞ ½ ½
s ¼ 2 3244 Jg 1
Example40: Thermalconductivity
Find:Determinetheunit(W(mK) 1)ofthermalconductivityinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthatthethermalconductivityisdefinedastheamountofheatthatpassesthroughaunitareawhenthetemperature differencebetweenthetwosidesisonedegreeperunitdistance.So,thethermalconductivityequationisaquantityequation establishedfromadefinition,whichisexpressedinI–Psystemasfollows: k ¼ Btuh 1 ft 1F
Rememberthat: 1Btu ¼ 1054 35J; 1ft ¼ 0 3048m; K ¼ 1 81F; 1 h ¼ 3600s
k ¼ Btu1054 35J=1Btu ðÞ ½ = h3600s=1h ðÞ ft0 3048m=1ft ðÞ1F K =1 81F ðÞ
Example41: Heattransfercoefficient
Find:Determinetheunit(W(m2 K) 1)ofheattransfercoefficientinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthattheheattransfercoefficientisde finedastheamountofheatthatistransferredfrom/toaunitareaperunittime whenthetemperaturedifferencebetweenthesurfaceandtheambientisonedegree.So,theheattransfercoef ficientequationisa quantityequationestablishedfromadefinition,whichisexpressedinI–Psystemasfollows: h ¼ Btuh 1 ft 2 1F
Rememberthat: 1Btu ¼ 1054 35J; 1ft 2 ¼ 0 0929m2 ; K ¼ 1 81F; 1 h ¼ 3600s h ¼ Btu1054
Example42: Thermaltransmittance
Find:Determinetheunit(W(m2 K) 1)ofthermaltransmittanceinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthatthermaltransmittanceistheamountofheatthatpassesthroughanentirewall,ceiling,etc.,sectionofaunitarea perunittimewhenthetemperaturedifferencebetweentheaironthewarmsideandtheaironthecoldsideisonedegree.So,the thermaltransmittanceequationisaquantityequationestablishedfromadefinition,whichisexpressedinI–Psystemasfollows:
Rememberthat: 1Btu ¼ 1054 35J; 1ft 2 ¼ 0 0929m2 ; K ¼
Example43: Thermalresistance
¼ 5 68 W ðm2 KÞ– 1
Find:Determinetheunit(m2 KW 1 orm 2 1CW 1)ofthermalresistanceinSIiftheunitisgiveninI–Psystem.
Solution:
Rememberthatthermalresistanceistheresistanceofoneunitareatoheat flowthroughasubstanceperunittimewhenthe temperaturedifferencebetweenthetwosidesisonedegree,andhasthesymbolof R.Thermalresistanceisanadditivequantity; thatis,200 materialhastwicethe R-valueof100 .Anditdoesnotincludetheboundarylayerresistances.So,theheattransfer coefficientequationisaquantityequationestablishedfromadefinition,whichisexpressedinI–Psystemasfollows: R ¼ h ft 2 1FBtu 1
Rememberthat: 1Btu ¼ 1054 35J; 1ft 2 ¼ 0 0929m2 ; K ¼ 1 81C ¼ 1 81F; 1 h ¼ 3600s R ¼ h3600 s=1h ðÞ ft 2 0 0929m2 =1ft 2 1F K =1 81F ðÞ = Btu1054 35 J =1Btu ðÞ ½
R ¼ 0 176 m2 KW 1
Example44: Wavelength
Find:Calculatethemaximumwavelength lmax fortheSun’ssurfaceradiation.
Solution: Wien’sdisplacementlawstatesthatthewavelengthatwhichablackbodyemitsitsmaximumamountofradiationisinversely proportionaltoitsabsolutetemperatureinKelvin, lmax ¼ a/T,where l isin mm, a is2897 mmK,and T isinK.
Assuminganaveragesurfacetemperatureofapproximately6000K,wewouldhaveitsmaximumemissionat
lmax ¼ 2897 mmK =6000K
kmax ¼ 0 48 lm
Awavelengthofapproximately0.5 mmlieswithinthevisiblespectrum.
Example45: Frequency
Find:Determinethefrequencyofaradiationalwavelengthof0.5 mm.
Solution:
Wavelength(l)andfrequency(n)arerelated,andthisrelationshipcanformallybeexpressedthroughthespeedoflight c,as c ¼ ln,where c isthespeedoflight,whichhasavalueof3 108 ms 1 , l isthewavelength(mm),and n isthefrequency(cycles s 1,alsoknownasHz).Then,ifoneisknown,thentheothercaneasilybedeterminedusingthespeedoflight,whichisa constant.
Example46: Energycontentofasinglewavelengthsolarradiation
Find:Determinetheenergycontent E,ofasolarradiationfrequencyof6 1014 Hz(or0.5 mmwavelength).
Solution:
Solarradiationconsistsofphotons,whichcanbeconsideredaspacketsofenergy,andisrelatedtofrequency v as E ¼ hv, where E istheenergycontent(J),and h isthePlanckconstant(6 626 10 34 Js).
1.1.7ConcludingRemarks
Thischapterprovidedenergyunits,conversions,anddimensionalanalysis.Baseandderivedquantities,relationshipsbetween quantities,andquantityequationswerediscussed,alsocoveringthethreebasictypesofquantityequations:thequantityequations developedfromthelawsofnature,theequationsdevelopedfromgeometry,andtheequationsdevelopedfromadefinition.Then, the20multiplesandsubmultiplesintheSIunitsystemwerepresented.Anintroductionwasalsopresentedfordimensional analysis,whichisquiteausefulmethodforderivinganalgebraicrelationshipbetweendifferentphysicalquantities.Andthen,the StandardforMetricPractice,ASTMStandardE380-84,asoneofthebasicstandards,isreferencedforSIusage.Moreover, conversionfactorsforenergyrelatedunitsroundedtothreeorfoursignificant figuresforconversionbetweenSIandI–Pwere provided,aswellasconversionfactorsfordifferentphysicalquantitiesrelatedtoenergy.Andthechapterisconcludedwithsome illustrativeexamplesofunitconversionsanddimensionalanalyses.
References
[1] CGMP.ComptesRendusdela11eCGPM(1960);1961,p.87.
[2] CGMP.ComptesRendusdela11eCGPM(1971);1972,p.78.
[3] BIPM.Internationalvocabularyofmetrology – basic andassociatedterms(VIM).3rded.;2012.
[4] WildiT.Metricunitsandconversioncharts.Ametricationhandbookforengineers,technologists,andscientists.NewYork,NY:IEEEPress;1995.p.65–6.
[5] AndrewsJ,JelleyN.Energyscience:principles,technologies,andimpacts2007;NewYork,NY:OxfordUniversityPressInc.;2007.p.13–4.
[6] ASHRAE.Handbookoffundamentals.Atlanta,GA:AmericanSocietyofHeating,RefrigerationandAirConditioningEngineers,Inc.;1989.
[7] ASHRAE.SIGuideforHVAC&R.6thed.Atlanta,GA:AmericanSocietyofHeating,RefrigerationandAirConditioningEngineers,Inc.;1984.
[8] StandardsforMetricPractice.ASTMStandardE380.Philadelphia,PA:AmericanSocietyforTestingandMaterials;1993.
[9] TheInternationalSystemofUnits(SI).NationalBureauofStandardsSpecialPublication330.SuperintendentofDocuments.Washington,DC:U.S.Government Printing Office;2001.
[10] MetricPracticeGuide.CSAStandardCAN3-Z234-1.Rexdale,ON:CanadianStandardsAssociation;1973.
[11] ASMEGuide.ASMEorientationandguideforuseofmetricunits.NewYork,NY:AmericanSocietyofMechanicalEngineers;1982.
[12] ISO.SIunitsandrecommendationsfortheuseoftheirmultiplesandofcertainotherunits.Geneva:ISOStandard1000InternationalOrganizationforStandardization; 1992. AvailablefromAmericanNationalStandardsforMetricInstitute,NewYork,NY.
[13] HRAI.Supplementarymetricpracticeguidefortheheating,ventilating,refrigeration,airconditioning,plumbingandairpollutionequipmentmanufacturing industries. Etobicoke,ON:Heating,RefrigerationandAirConditioningInstituteofCanada.
RelevantWebsites
https://www.britannica.com/science/International-System-of-Units Brittanica. www.convertunits.com/SI-units.php ConvertUnits.com.
https://www.ic.gc.ca/eic/site/mc-mc.nsf/eng/lm00068.html GovernmentofCanada. https://www.nasa.gov/of fices/oce/f unctions/standards/isu.html NASA.
http://www.checklist.org.br/d/internationalsystemofunits.pdf NIST,U.S.DepartmentofCommerce. http://www.physics.nist.gov/cuu/Units/ NIST,U.S.DepartmentofCommerce. https://www.physics.info/system-international/ ThePhysicsHypertextbook.
1.2 HistoricalAspectsofEnergy
İlhamiYıldızandCraigMacEachern, DalhousieUniversity,Halifax,NS,Canada r 2018ElsevierInc.Allrightsreserved.
1.2.1Introduction
1.2.2PreindustrialMan
1.2.2.1.1Fireandearlyman
1.2.2.1.2Gunpowder
1.2.2.1.3Metallurgy
1.2.2.1.4Steamboilers
1.2.2.2.1Agriculture
1.2.2.2.2Transportation,hunting,andwarfare
1.2.2.3EarlyWindandHydro27
1.2.2.3.1Sailboats
1.2.2.3.2Windmills
1.2.2.3.3Waterwheels
1.2.3TheIndustrialRevolution
1.2.3.1.1Saverypump
1.2.3.1.3WattandBoulton–Wattsteamengines
1.2.3.1.4Solarreflectorsteamengine
1.2.3.2.1Thespinningjenny
1.2.3.2.3Thesewingmachine
1.2.3.3.1Naturalgas
1.2.3.3.2Coalmining
1.2.3.3.3Blastingcapsanddynamite
1.2.3.3.4Oildrilling
1.2.3.3.5Standardoil
1.2.3.4.1Discoveryofelectricity
1.2.3.4.1.1ThalesofMiletus
1.2.3.4.1.2WilliamGilbert
1.2.3.4.1.3OttovonGuerickeandCharlesFrançoisduFay
1.2.3.4.1.4PietervanMusschenbroek
1.2.3.4.1.5BenjaminFranklin
1.2.3.4.1.6LuigiGalvaniandAlessandroVolta
1.2.3.4.2Electromagnetism
1.2.3.4.3Fuelcells
1.2.3.4.4Incandescentbulb
1.2.3.4.5Warofthecurrents
1.2.3.5TransportationandMassProduction34
1.2.3.5.1Trainsandrailroads
1.2.3.5.2Internalcombustionengine
1.2.3.5.3Ethanol
1.2.3.5.4Automobiles
1.2.3.5.5Interchangeableparts
1.2.3.5.6Theassemblyline
1.2.3.5.7Ford’sModelT
1.2.3.5.8Hotairballoons
1.2.3.5.9Poweredairplanes
1.2.4Nonrenewables
1.2.4.1FossilFuelsandConventionalEnergySources36
1.2.4.1.1Coal
1.2.4.1.2Oil
1.2.4.1.3Naturalgas
1.2.4.1.4Nuclear fi ssion
1.2.5Renewables
1.2.5.1RenewableEnergySources39
1.2.5.1.1Hydro
1.2.5.1.1.1Small-scalehydro
1.2.5.1.1.2Large-scalehydro
1.2.5.1.3Geothermal
1.2.5.1.4Solar
1.2.5.1.5Biomassandbiofuels
1.2.5.1.6Tidal
1.2.5.1.7Pyrolysis
1.2.5.1.8Heatpumps
1.2.6.1.1Spacesolarpower
1.2.6.1.2GenerationIVnuclear fissionreactors
1.2.6.1.3Fusionpower
1.2.1Introduction
Thestoryofman’ssuccessandhiseventualdownfallisonethatrestslargelyontheshouldersofourcreativeexploitationand reimaginingofenergyanditsuses.Throughouthistorymanhasbeenabletoutilizeenergyinwaysotherspecieshavebeenunable tograsp,quicklydistinguishingmanasthealphaspeciesonplanetEarth.Ingenioususeofenergyhasledtoincreasedbrain development,grantedustheabilitytotravelgreatdistances,allowedforthemanufacturingofavarietyofproductsattremendous speed,andhelpedtopowerthemachinesthatinfluenceeverythinginlifefromhealthcaretocommunicationtoscienceand research.Despiteallthatman’scommandoverenergyhasgivenhim,therateatwhichenergyhasbeenexploitedhasleftmankind inacompromisingposition.Finiteresourcesarerapidlybeingdepletedandcarbonemissionscontinuetocauselarge-scale environmentalissues.Onceagainitwillbeuptomantoovercomethesechallengesifthespeciesistosurviveandthrive. Renewableenergysourcesofferoneanswertotheproblemandwithincreasedimplementationtheymay1daypowertheworld. Thisisthehistoryofhowmanandsocietyevolvedalongsideenergyandhowwe’vearrivedatthecurrentsituation.
1.2.2PreindustrialMan
Perhapsthemostinfluentialchangeinthedevelopmentofmodernmanwashisshifttowardtheuseofenergytocompletetasks onascalethatwaspreviouslyimpossible.Priortothe firstuseof fire,manwasasimplebeing,similartomanymodernapesin termsofenergyuse.Theyatefoodandusedthecalorieswithinthefoodtoperformwork.Thisworkgenerallycomprisedof attainingmorefood,protectingoneselffrompredators,andreproducing.Thisallchangedoncemanbegantouseenergysources otherthansimple,rawfood.Fireledtocookedfoodandprotectionfrompredators,theuseofanimalsmadeagricultureand transportationmoreefficient;soonsailboatsandwindmillsweretakingadvantageofwindenergyfortransportationandmilling. Regardlessofhowenergywasbeingusedandwhichsourceitcamefrom,thereisoneoverarchingthemelinkingthesetechnologiestogether.Theymadewhatweredifficultandtediousprocessesquickerandeasier,allowingmanmoretimetoperform othertasksandworktowardsolutionstomoreadvancedproblems.Itisundoubtedlythisconceptthatledtoman’srapid developmentasaspeciesanddrastictechnologicaladvanceintheyearsfollowingthe firstuseofenergy.
1.2.2.1Fire
Firecanmostaccuratelybedescribedasachemicalreactionthatoccursbetweenoxygen,heat,andafuelsource.Fireisnotan objectbutratherthevisibleoxidationthatoccursasaresultofrapidcombustion.Thisprocessisnotentirelydissimilarfromthe
rustingofmetalsorthebrowningofanapplecore.However,thecrucialdifferencebetweentheseoxidativeprocessesistherateat whichthereactiontakesplace.Heat,light,andsoundareallthebyproductsofthisrapidreactionandonesthatearlymantook greatadvantageofindevelopingasaspecies [1]
1.2.2.1.1Fireandearlyman
Theearliestknownexploitationofthenaturalenvironmentforenergyproductionbyhumanscomesintheformof fire.Some estimatesstatethatmanmayhavedevelopedanabilitytocontrolandmanipulate fireasearlyas1.6millionyearsago [2] Stratigraphicevidencegoesontosuggestthatasearlyas1millionyearsago,insitu fireswerebeingusedbyhominins [2].Fire offeredavarietyofadvantagestoearlymanincludingprotectionfrominsectsandpredators,warmth,aswellasproviding illuminationduringthenight.Withthatbeingsaid,perhapsthemostimportantadvantage fireprovidedearlymanwastheability tocookfood [3].Estimatessuggestthatpriortotheadventofcooking,earlymanwouldrequirebetween5.7and6.2hperday chewingatough, fibrousdietofplants,andrawmeat [4].Thistime-consumingprocessmeantthatwhenearlymanwasnot huntingandgatheringtheywouldbechewing.Thistimespentchewingrequiredlargeteethandjawmusclessimilartowhatwe mightobserveinmodernchimpanzees.Withamasteryofcookingandgeneticevolution,however,theseteethandjawmuscles begantoshrink,leavingmoreroomforthedevelopmentofearlyman’sbrain [3]
Theearliestmainstreamuseof fireforprocessesotherthancookingcomesintheformof “fire-stickfarming” [5].Fire-stick farmingwas firstobservedinthePaleolithicandMesolithicagesasameansofclearinglargeamountsofland [5].Landwascleared foravarietyofreasons,includingclearinggroundforpermanentortemporaryhumanhabitats,regeneratingplant-basedfood sources,facilitatingtravel,andevenwarfare [6].Fire-stickfarminghadtheeffectofreplacinglargeroldergrowthforestswithfaster growinggrassesandperennials,drasticallyreshapingthelandscapeofthetime.Theburningprocessincreasednutrientavailability, whichresultedinhigherplantyields [5].Withtheongoingextinctionofmegafaunaatthetime,earlymanwasforcedtoconvertto amoreplant-dependentdiet,reinforcingtheimportanceofthesenewfoundperennials [6].Thisprocessmaybetheearliestknown useofagriculturalpracticesbyman.
Inmoderntimesslashandburnorswiddenagriculturepracticescontinuetobeprevalentmethodsforlandclearingin agriculture.Thisprocessinvolvescuttingdownvegetationinanareaandsettingiton fire.Theideaisthatastheplantmaterial burnsitreleasesnutrientsintothenearbysoilresultinginhighlyfertileland.Thislandisthenusedforanumberofagricultural practicesuntilitisdeemednolongeracceptableduetosoildegradation.Currentestimatesstatethatthereareover200million peoplewhopracticeswiddenagricultureglobally [7]
1.2.2.1.2Gunpowder
ThediscoveryofgunpowderismostcommonlyattributedtoChinesealchemistsduringthe9thcenturyAD.Theactiveingredients forgunpowderwerediscoveredwhenanalchemistaccidentallydroppedcharcoalintoabowlofpotassiumnitrate(saltpeter).The combinationoftheingredientscausedthemixturetodeflagrateviolentlyand,thus,gunpowderwasborn.The firstwidelyused applicationofgunpowdercameintheformofcrude flamethrowersdevelopedbytheChineseinthemid-1000s.Theseweapons heldgunpowderinabambooorpapertubethatwasattachedtoanarrow.Thearrowswerethen firedfromabowwithdevastating effects [8].Duringthesametimeperiodadevicethatinmoderntimesisknownasagrenadewasalsodeveloped.Thisdevicewas describedasa “bursting fireball,” whichalsocontainedsmallbitsofporcelaintocausefurtherdestruction.Thesetwodesigns perfectlyharnessedtheexplosivepotentialofgunpowderandledtomanyfutureinventionsincludingrocketry,cannons,and firearms [9].Fromheretheknowledgeanduseofgunpowderspreadwest,throughtheMiddleEast,intoEuropeandeventuallyto EnglandwhereFranciscanmonkRogerBacontookupthetaskofimprovingontheexistingformula.Baconexperimentedwith variousproportionsofeachingredientandwasthe firsttonotehazelcharcoalasthebestvarietyforgunpowder.Baconalsomade theimportantdiscoverythatgunpowderwithhighernitratecontentwasmoreexplosive [8].Bacon’sworkdirectlyinfluencedthe implementationofthecannonand,inlateryears, firearmsintotheEnglishmilitary.
1.2.2.1.3Metallurgy
Thenextmajoradvancementintheexploitationof firewasseeninmetallurgy.WallpaintingsintheOldEmpireofMemphis suggestthatAncientEgyptiansutilizedtheintenseheatgeneratedby firetomeltandcastpuremetals.Thesepaintingsgoonto suggestthatancientEgyptiansalsodevelopedblowpipesandbellowstodelivermoreoxygentothe fires,demonstratingtheir knowledgeandcomfortwiththischemicalreaction [10]
Metallurgicalprocessesweregreatlyenhancedfollowingtheadventofcoke.Cokeisacoal-basedproductobtainedthroughthe destructivedistillationofcoal.Destructivedistillationisaprocess,wherebyafuelsourceisheatedtohightemperaturesinthe absenceofoxygen.Thisprocesshastheeffectofremovingmostofthevolatilecomponentsfoundinthecoal,resultinginacarbon massknownascoke [11].Cokingcoalallowedformuchlargerfurnacesandsubsequentlygreateroutput [10].Additionallycoke producesfarlesssmokethanconventionalcoal,leadingtosaferworkenvironments [11].Today,cokeisanessentialcomponentin theprocessingofironore.Withironbeingtheprimaryinputinsteelandmanyaluminumalloys,itisdifficulttosaywhatmodern manufacturingwouldlooklikewithouttheadventofcoke.
1.2.2.1.4Steamboilers
Inmoderntimes, fireseesextensiveuseinelectricityandheatgenerationthroughtheuseofsteamboilers.Oxygen-fed firesare usedtoboillargequantitiesofwaterwhosesteaminturndriveslargeturbines,generatingelectricity.Wasteheatfromthisprocess
canalsobecapturedandusedinavarietyofheatingprocesses;thisisknownascogeneration.Thesetopicswillbediscussed furtherinthefollowingsections [12]
1.2.2.2Animals
Theuseofanimalsforagriculture,transportation,andhuntingdatesbackthousandsofyears.Animals,suchascattle,horses, mules,donkeys,camels,elephants,anddogshaveallbeenusedforhumanbenefitthroughoutthistime [13].Byexploitingthe energyexpenditureoftheseanimals,mandevelopedtheabilitytoperformessentialtasksquickerandmoreefficiently.Thisledto greatercropyields,faster,andfurtherdistancestraveled,aswellasmorefruitfulhunts.
1.2.2.2.1Agriculture
SomeoftheearliestusesofanimalenergyinagricultureoccursintheMediterraneanregionsofEgyptandEthiopiaaround6000to 5000BC [14].Egyptianwallpaintingsandpapyrusrecordsshowtheuseofardplows,towedbyoxenasameansoftilling fields fortheplantingofcrops.Theardplowiscomposedofalongwoodenbeamattachedtoayokedpairofoxenatoneendandan almostperpendicularmetalshareattheother.Thissharewouldbepulledthroughthegroundbytheteamofoxen,thereby breakingupthepackedsoilallowingforeasierplantingandsuperiorplantgrowth [13].Anoperatorwouldwalkbehindtheplow controllingapairofhandlestoensuretheshareremaineduprightandinthesoil.TheentireprocessenabledtheEgyptianstoplow farmoreland,withfarlessmanpower.Ultimatelythismeantgreatercropyieldsandmorefoodtofeedtheirgrowingpopulation.
1.2.2.2.2Transportation,hunting,andwarfare
Theuseofhorsesfortransportationwas firstobservedaround3500BCbytheBotaipeopleofwhatisnowmodern-day Kazakhstan.TheBotaiutilizeddomesticatedhorsestogainaspeedadvantagewhenhuntingwildhorsesformeat.Additionally, horseswereusedasamoreefficientmeansofherdingsheep.Itisestimatedthatamancanherdaround200sheepwithagood herdingdog,butthisnumbercanbeincreasedto500ifthemanisonhorseback.Furthermore,itisthoughtthathorseswould havebeenusedasameansofquickentryandescapeduringtribalraidsonenemyencampments [15]
AstheuseofhorsesspreadacrossEuropeandAsia,webegintoseetheimplementationofanewformoftransport,thechariot. TheearliestknownuseofthechariotappearsinMesopotamiaaround3000BC [16].Withthatbeingsaid,itwasnotuntil1800BC thatthechariotwaspopularizedbytheAnatolians,whomayhavehelpedinshapingmoderntransportation [15].Theuseofthe chariotwasessentialinwarfareasitofferedhighmaneuverabilityandaplatformforrangedattacks.Essentialtothechariots successwastheuseofhorsesoronagersforpullingthecarts [16].Thiscombinationofanimallaboranddrawncartsfor transportationwasaconceptthatextendeduntiltheadventofthemodernautomobile.
Dogswerethe firstanimalstobedomesticatedbymanaroundtheendofthelasticeage.Atthistime,humansocietywasstill largelyahuntingandgatheringsociety,anddogsfacilitatedinthisprocess [17].Dogswereprimarilyemployedasameansof trackingwoundedpreyanddeliveringthekillingblowtopotentiallydangerousinjuredanimals.Thispartnershipledtogreater huntingefficiencyandsafetyresultinginmoreproductivehunts.Byusingdogstotrackwoundedanimals,manwasabletoexpend lessenergyandtimetrackinganimalsandmoretimehuntingfurtherprey [17]
1.2.2.3EarlyWindandHydro
1.2.2.3.1Sailboats
TheearliestknownuseofwindenergycomesintheformofcrudesailboatsdesignedandutilizedbytheEgyptiansbetween5000 and4000BC.Thesesailboatscomprisedofasinglesailattachedtothemastofwhatwaslittlemorethanahollowedlog [18] TheseboatshelpedEgyptiansmoveupanddowntheNileRiverandithasalsobeensuggestedthattheuseoftheseboatsdirectly impactedthespreadoftheNaqudaculturetoSouthernEgypt [18].Theimpactofthesailboatcontinuedtoincreaseandwiththis camegreatertechnologicaladvancement.Largersailsandcrewsbecamecommonandby2000BC,tradeintheMediterraneanwas highlydependentontheuseofthesailboat [19].By500BCthePhoeniciansandGreekshadpopularizedthetrireme,which combinedthebenefitsofhumanandwindenergyforevengreaterpropulsionthroughthewater [20].ByAD800theVikingswere readilyimplementinghydrodynamicallyoptimizedboatscapableofsailingfarfasterthanpreviousdesigns [21].Sailboats, throughcontinuedevolutionanddesignupgrades,becomeamajorpartofglobalization,worldtrade,andexplorationthroughout thenext1200years.TradethroughouttheMediterranean,EnglishChannel,BalticSea,andIndianandAtlanticOceanswouldnot havebeenpossiblewithouttheuseofwind-poweredsailboats.TheseboatswerealsoessentialinthediscoveryoftheAmericasand paintingthepictureoftheglobeasawhole.
1.2.2.3.2Windmills
Theearliestknownrecordofwindmillsdatesbackto400BCwhenaHindubookknownasthe Arthasastra ofKautilyasuggeststhe useofwindmillsforpumpingwater [22].This,however,istheonlymentionofsuchwindmillsinhistoryandis,therefore,difficult toconfirm.The firstconfirmedapplicationofwindturbinescomesfromHeronofAlexandriawhoimplementedaverticalwind turbineintothedesignofapipeorganduringthe1stcenturyAD [23].IthasbeensuggestedthatHeron’sreversalofconventional fanbladesmayhaveledtotheeventualimplementationofhorizontalwindturbinesinmidmillenniumEurope [24].The first knownimplementationofverticalaxiswindmillsonalarge-scalecomesfromthePersiansaroundAD800.ThePersiansutilized
thesewindmillsforthepurposesofgrindinggrain,poundingrice,andforirrigation [25].Thesesamewindmilldesignshavebeen foundasfareastasIndiasuggestingthattheywereefficientenoughtoimitate [26].The firsthorizontalaxiswindmillsappearin EuropebetweenAD1100and1200.Thesewindmillswereprimarilyimplementedforthepurposesofgrindinggrain,pumping water,andinthecaseoftheNetherlands,draining floodplainsforexpansion.Atthispoint,Europeanengineersalreadyhadan advancedknowledgeofgearingsystems.Withthistheyrealizedthatbyutilizinghorizontallypositionedbladesincombination withahorizontaltoverticalshafttransmissiongearingsystemtheycouldmaketheirwindmillsmoreefficient.Thiswasaconcept thatwasclearlyalreadyunderstoodbytheEuropeansbasedontheirimplementationoftheVitruvianwaterwheel [21].Thisdesign waspopularizedinEngland,Belgium,andNormandyandthroughitssuccessandefficiencyquicklyspreadtotheNetherlands, Germany,andDenmark [27].Bytheendofthe19thcenturythesewindmillswereachievingefficienciesofashighas5% [21]
1.2.2.3.3Waterwheels
The firstknownimplementationofhorizontalaxiswaterwheelscomesfromtheRomansbetween700and600BC [28].This waterwheelwasknownasanoriaandconsistedofbucketsthatcollectedwaterfromasurfacewatersource(usuallyastreamor river)andpoureditintoirrigationchannelsatgreaterpotential [29].Thesechannelshelpedtoprovidewatertonearbyfarmland, drasticallyincreasingyieldandproductivityinareasthathadconventionallyreliedononlyrainforwatering.Waterwheelsdriven bycamelsandoxenhavealsobeenemployedinAfghanistanandotherMiddleEasterncountriesforthepurposesofirrigation.To thisdaythereareregionsinSudanthatcontinuetoemploythismethodofirrigation [30].
By100BCtheuseofwaterwheelsformillingbeginstogainpopularitythroughoutGreece.Onceagainthismethodused bucketsofwaterthat filledupwiththe flowoftheriverandsubsequentlyrotatedthewaterwheel.Thechangeinweightcausedby the fillingandemptyingofthebucketscausedthewheeltorotatemoreefficiently.Thisrotationwastransferredfromthe horizontalaxisofthewheeltoaverticalshaft,whichinturndroveamillingstone.Thesemillingstoneswereusedprimarilyfor grindingwheatandcorninto floursforbreadmaking [29].Thismillingtechniquequicklygainedpopularityandbytheendofthe 1stcenturyAD,wasemployedasfareastasChina [29].AroundAD300theRomansmodifiedthedesignsothatthebucketscould beplacedjustbelowthesurfaceofthewater.Thisgreatlyimprovedtheefficiencyofthedesign [29].
ByAD1086therewereover5000watermillsinusethroughoutmainlandEnglandandbyAD1800thisnumberhadsurpassed 500,000.Millsatthistimewerenolongersimplybeingusedforgrindingcornandgrainthough.Thesewatermillshadbeen adaptedforavarietyofprocessesincludingpoweringbellowsforironproduction,grindingingredientsforpapermaking,sawing timber,crushingolivesforoliveoil,andinpoweringtextilefactories [29].
1.2.3TheIndustrialRevolution
Tothisday,theIndustrialRevolutionremainsthegreatesttimeperiodfortechnologicaladvancementinthehistoryofmankind. Eventoday,manyoftheprocessesthatallowformassproduction,rapidtransportation,andthatpowerourlivescanbecreditedto advancementsmadeduringthistimeinhumanhistory.TheIndustrialRevolutionbroughtmankindintotheeraoffossilfuelsand aworldofcheapandeasilyattainableenergy,moreabundantthananythingpreviouslydreamedof.Steamenginesgaveausefor thesefossilfuelsandtheirvarietyofapplicationshaddrasticeffectsonproductionandmanufacturing.Liquidfuelsallowedhomes tobelitatnightandforautomobilestobegintopopupandreplacetraditional,animal-drivenformsoftransportation.Before long,electricitywasmakingitswayintothehomesandof ficesofmillionsaroundtheworld,foreverchangingthewayhumanslive andwork.Incombination,alloftheseadvancementsledtobetterqualitiesoflife.Productswerecheaper,foodwasmorereadily available,andhealthcaredrasticallyadvancedwithnew findingsandinnovations.Regardlessofwhattheeffectwas,theoverarchingconsensusisthattheIndustrialRevolutionsparkedthisupturninhumanlifeandhashadagreaterimpactonmodernlife thananyotherperiodinhumanhistory.
1.2.3.1SteamEngine
1.2.3.1.1Saverypump
Perhapsthesinglemostcriticalinventionleadingtoindustrializationwastheadventofthesteamengine.The firststeamengine wasbuiltbyThomasSaveryin1698forthepurposeofremovingwaterfrommines.InSavery’swords,hismachinewas “anengine toraisewaterby fire. ” Savery’spumpoperatedbyvaporizingwatertogeneratesteamandusingthissteamto fillasecondarytank. Thenbyisolatingthesteamfromitssourceandallowingthesteamtocondenseavacuumwouldbecreated,whichwoulddraw waterfromwithinthemines.Thisdesignworkedwellbutwasextremelylimitedinthedepthatwhichitwaseffective.Themain issuewiththisdesignwasthatitcouldonlydrawwaterataround80ftbelowthesurface [31].Withtheminesofthetimeaiming togodeeperanddeeper,abetterpumpneededtobedeveloped.
1.2.3.1.2Newcomenatmosphericengine
Theyear1712sawtheinventionoftheatmosphericenginebyThomasNewcomen [32].Newcomen’sengineimprovedonSavery’ s designinthatitdidnotrelyonasteamvacuum.Newcomen’sdesignusedahorizontalbeamwithapivotinthemiddleweighted ononesideandincorporatedwithaboilerandpistonontheother.Theweightedsidewoulddrop,drivingthepistonupward,at thispoint,steamatnearatmosphericpressurewould fillthevoidinthecylinderleftbytherisingpiston.Coolwaterwouldthenbe
sprayedintothecylinder,quicklycondensingthesteamandtherebychangingthepressure,whichwouldpullthepistonback down.Thishadtheeffectofraisingtheweightedside,whichthroughanotherpistonmechanismdrovewatertothesurface.This automatedenginedrasticallyimprovedwaterremovalefficiencyandhadafargreateroperatingdepththanSavery’sdesign. Newcomen’sdesignwassorevolutionarythatitwouldbeanother63yearsbeforeabetterdesignwaspopularized [31]
1.2.3.1.3WattandBoulton– Wattsteamengines
In1776,JamesWattwasabletoimproveonNewcomen’sdesignfollowingacriticalobservation.Wattnotedthattherepeated heatingandcoolingofthecylinderwaswastingenergyandwouldleadtothemorerapiddeteriorationofthematerials.Basedon thisobservationhedevelopedhisowndesigninwhichthepistonandcylinderremainedhotatalltimesbyincorporatingan externalcondenser.Byalternatingtheopenandclosedphasesatthetopandbottomofthecylinder,steamisabletoenterthe cylinderinalternatesuccession,therefore,drivingthepistonupanddown.Asnewsteamentersfromthebottom,exhauststeam exitsthroughthetop,asthepistontravelsupward.Theprocessthenrepeatsitselfintheotherdirection.Theexhaustedsteam makesitswayfromthecylindertothecondenserwherethesteamiscondensedbackintowater.Thenewlycondensedwateris thenpumpedtoahotwatertankandrecirculatedbackthroughtheboiler.Bykeepingthepistonandcylinderhotatalltimes,less energywaswastedinreheatingandthethermalstressonthematerialwasreduced [31].In1782Wmodifiedhisengineto incorporateasunandplanetgearingsystemthatdrovea flywheel.This flywheelhadtheadvantageofprovidingsmoothand constantoutputasopposedtothepulsatingnatureofearlierdesigns [33].Thiscrucialdesignchangeiswhateventuallyledto steamenginesbecomingviableforthenewlyconstructedfactoriesthatwouldcometodrivetheIndustrialRevolution.
The finalmajoradvancementsinthesteamenginecamewiththeBoulton –Wattdoubleactingengine.Thegreatest improvementinthisdesigncameintheformofaparallelmotionmechanismthatassuredperfectalignmentofthepiston throughoutitscycle.Additionally,thismechanismallowedforworktobegeneratedontheupwardstroke,wherebeforethe upstrokesimplyservedtoresetthepiston.Wattwasfamouslynotedassayingthathewasmoreproudofthisinventionthanhe wasoftheengineitself [31].Thisdesignalsoincorporatedagovernorthatcouldbeusedtothrottlebacktheengineshouldless outputberequired.Bothofthesedesignchangesgreatlyimprovedtheviabilityoftheseenginesforfactoriesandmadethemmore attractiveasindooroptions [31].
1.2.3.1.4Solarre flectorsteamengine
In1860,FrenchinventorAugustineMouchotbecamefascinatedwiththeworldofsolarenergy.Mouchothadreadandheard storiesof “burningmirrors” capableoflighting fireatfargreaterspeedthananyoftheconventionalmethods.Mouchotrecognized thepotentialofsuchenergyandsetoutto findamorepracticaluseforit.ThedesignMouchotcameupwithisnotentirely dissimilarfrommodern-daysolardishconcentratingcollectors.Mouchot’sdesignorientedmirrorsonaconcavedisktowarda centralabsorbertube.Thisheatgeneratedonthetubewasthenusedtoboilwaterandthesteaminturndroveaturbine.While thereweresomewhofeltthatMouchot’sinventionwouldmeanunlimitedfreeenergytherealitywasthattheenergyproduced wasnotonparwiththesteamenginesavailableatthetime.France’sclimatesimplydidnotlenditselfwelltosolarenergy; however,Mouchotdemonstratedthattheprospectforimplementationinhotterregionswascertainlythere [34]
1.2.3.2Textiles
1.2.3.2.1Thespinningjenny
Inthemid-1700s,spinningwasalongandarduoustask,performedbyindividualsknownasspinners.Spinnersusedaspinning wheeltowindasinglestrandofcotton fiberintoayarn.Thisprocessinvolvedmanuallytwistingtheyarnandensuringtheyarn remainedtautuntilitwaswoundontothespindle.EnterJamesHargreaves,aBritishcarpenterandweaverwhowasattemptingto findawayinwhichtooptimizethistime-consumingprocess.Hargreaveshadbeenattemptingtoutilizemultiplespinnersatonce byholdingallofthethreadsinthislefthand,however,hequicklyranintodifficultieswhenitcametotwistingtheyarn.Thiswas duetothehorizontalpositioningofthespindles,whichHargreavesingeniouslyremarkedfollowingtheobservationofatoppled spinningwheel,whichcontinuedtospinandoperate.In1764,Hargreavesusedthisobservationtodevelophisspinning jenny,whichutilizedverticallypositionedspindlestowindeightcottonthreadsatonce.Thepositionofthespindlesallowed forthethreadtobetwistedautomaticallyaswellasensuringthethreadsremainedtaut.Thiscleverdesigncouldbeoperated byasingleperson,drasticallyreducingtimeandenergyinput.Hargreaveswentontodevelopa16-threadversionofthejenny andlaterinventorsmodifiedthedesigntobedrivenbyanexternalengine.Thespinningjennydrasticallychangedthetextile industrybyreducinglabordemands,whileincreasingoutput,andisoftenconsideredasthemachinethatbegantheIndustrial Revolution [35].
1.2.3.2.2Thecottongin
Duringthelate1700s,cottonwasavaluedproduct,however,notinthesamewayitistoday.Themainissuewithcottonwasthat seedsembeddedinthecotton fibersrequiredseparating,aprocessthatatthistimecouldonlybedonebyhand.AmericanEli Whitneyrecognizedthatifabettermethodforseparatingtheseedsfromthe fiberscouldbedevelopedthencottoncouldseea globalupturninvalue.WiththeAmericanSouthbeingoneofthemajorglobalproducersofcotton,anyproductionadvantage wouldbemassivefortheregion.In1794,Whitneydevelopedandpatentedamachinehecalledthecottongin,whichwascapable ofremovingembeddedseedfromrawcotton fibers.Thecottonginoperatedbyloadingrawcotton fibersintoahopperwherethey
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