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GreenhouseEarth-thermodynamicanalysis HelmutUllmann
initialsituation
Inthelast150years,globaltemperatureshaveincreasedbyabout1degree.Duringthe sameperiod,theconcentrationofcarbondioxideintheairincreasedfrom280to400ppmby volume.ThemeasuredCO-temperature-timerelationshipleadstothesuspicionthatmanmadeCOemissionsfromtheuseoffossilfuelsduringtheIndustrialRevolutionwerethe causeofthetemperatureincrease.Man-madeCOisostracizedasaclimatekiller.Asa result,zero-emissionstargetsanddecarbonizationforclimateprotectionare politicallyenforced,whichcanleadtodeindustrializationandimpoverishmentofsociety.
Here,anassessmentiscarriedoutusingphysical-chemicaldataontheheatstorage capacityofthegases.
sunexposure
Withitsatmosphere,theoceancurrentsandthewatercycle,theearthformsakindof thermostat.Temperaturedeviationsof1to2Cperyearcorrespondto0.1to0.2%ofthe globalsurfacetemperatureof288K.Whilethetemperatureatthetopoftheatmosphereis -18Caccordingtosatellitemeasurements,theearth'ssurfacemeasuresanaverageof +15C.Thedifferenceof33degreesiscalledthegreenhouseeffect.
Attheouteratmosphereoftheearth,ataheightofapprox.20km,thesolarradiation hasapowerdensityof1.35kW/m(=solarconstant).Onitswaythroughtheatmosphere, solarradiationisweakenedbyreflectionandabsorption,dependingonthepathlengthand theangleofincidence.Attheearth'ssurface,thepowerofsolarradiation2isstilla maximumof1kW/m ,dependingongeographicallatitude,altitude,weatherandtimeof dayandyear.Athigherlatitudes,thepeakvalueislimitedtomiddayandthemonthsof JuneandJuly.Atthe60thdegreeoflatitudethisis2to900W/minsummer ,
ThespectrumofsolarradiationrangesfromUVthroughthevisiblerangetoIRwith increasingwavelength.Thehighest-energyUVradiationisalreadyabsorbedin thestratosphereinchemicalreactionswiththeformationanddecompositionofozone. OnlyaboutatenthofUVradiationreachestheearth'ssurface.
Visiblelightisreflectedbycloudsandparticulatematterintheatmosphere,onlyabouthalf ofwhichreachestheearth'ssurface.Thermalradiation(IR)isabsorbedbywater vapour,byaerosolsandbytracegases(CO,CHandothers)intheatmosphere.Onlyabout halfoftheIRradiationreachestheground.
Accordingtovarioussources,onaverageabout60to75%oftheradiatedenergy reachestheearth'ssurface,withthespectraldistributionshiftinginfavorofthelong-wave components.Thenumbersvarywidelydependingontheweather,humidityand regionalairpollution.
HeatstorageEarth'satmosphere
Attheearth'ssurface,theabsorbedsolarradiationisabsorbedinsolidsandwaterand convertedintoheat.Mostoftheheatistransferredtoairmoleculesonheatedroof surfaces,concretehighways,housewalls,farmlandandbodiesofwater.Heated airislessdenseandrises.Heatspreadsthroughconvection,aircurrents,highandlow pressureareasintheatmosphere.
Thecapacityofgasestoabsorbheatisdescribedbytheirheatcapacity.
Table1containscollectedmeasurementsofthemolarheatcapacitiesCp.Heatiskinetic energy(kineticenergyE)oftheparticles.Theseriesofnoblegases(Table1a)showsthat Cpisindependentofthemassoftheparticles,andtheenergythatcanbeabsorbed correspondstothekineticortranslationalenergy.
IndiatomicgasessuchasNandO,vibrationalenergyintheformofrotationaland oscillatorydegreesoffreedominthestructureofthemoleculescanbeactivatedas potentialenergyEinadditiontothekineticenergybyhigh-energyradiationorhigh temperatures.Themaximumabsorbableenergypermoleisaboutathirdpotgreaterthan formonatomicgases(Tab.1b).
Duetotheirmolecularstructure,triatomicandpolyatomicgasmoleculessuchas HO(upto5%inthe atmosphere)andtracegasessuchasCOshowadditionaldegreesoffreedomintheir spectrumintheformofrotational,oscillatinganddeformationvibrations,theirmolarheat capacityisaroundoneanotherfifthcomparedtothediatomicgases(Table1c).The vibrationsinthemoleculeresonatewiththeenergyofIRphotons,theycanabsorb4.5such andalsoemitthemagain.
CHandothers(intotallessthan0.05%byvolumeintheatmosphere)
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Theabsorbedenergyisthesumofkineticandpotentialenergy,consideringthe translationalenergyaskineticandthevibrationalenergyinthemolecularstructure aspotentialenergy.Theindividualpartscanchangeintoeachother,theirsum remainsconstant:E=E+E.pot
Theenergyretentioninthegreenhouseearthiseffectedbyallgascomponentsaccording totheirmolarheatcapacityandconcentrationintheatmosphere.Mostoftheenergyis containedinthemaincomponentsoftheatmosphere,nitrogenandoxygen.For watervapour,at3%inair,itwouldbe37.2x0.03partsoftheenergycontentofthe atmosphere.Theratiooftheenergycontentofairtowatervaportotracegaseswouldthen beabout100:35:0.07.Thisrelationshipisnotchangedbythelowtemperaturedependency oftheCpvalues.Even1%argonintheairwouldcontributemoretoheatretentionthanCO.
Thecontributionofthewatercycleisalwaysfargreaterthantheenergycontentinthesmall proportionoftracegases,whichisdifficulttoquantifybecauseofitsdependenceonair humidityandonvariousstatesofmatterwiththeirconversionenergies.
Theradiativebalance–theearth'sreflection
Solarradiationandearthradiationshouldbalanceeachotherout.Thebalanceisonlybalancedas longastherearenochangesinthesolarorplanetaryparameters,whichhashappenedseveraltimesin thehistoryofourplanet:therewerewarmandiceages,grasslandsbecamedeserts.Butevenwith constantcosmicparameters,theradiationbalanceisbalancedneitherdailynorannually,sometimesonly afterthousandsofyears.
Howdoesheatgetbackintospace?Theexchangeofenergywithspacecanonlytakeplacevia electromagneticradiation.Only15to30%oftheenergyisreflectedbackfromtheearth'ssurfaceas IRradiation.Mostofthestoredenergyiskineticenergyofthegasmolecules.Inordertorestore theenergybalancebetweenincomingandoutgoingradiation,theenergywouldhavetoescapeinto spacewiththegasmolecules,buttheseareheldtoearthbygravity.
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Heatmustthereforebeconvertedintoelectromagneticradiation.The3-andpolyatomicgasesHOand thetracegasesCOCHandothersactasconverters,whichcanemittheirpotentialenergystoredin molecularvibrationsasIRphotons.
ResonancesbetweenvibrationalenergyandIRphotonsarepossible,astheenergyvaluesareinthe rangeofIRphotonenergies(Table2).Theenergyvaluespermoleculein7milli-electronvoltsare recalculated
1mole=6.02x10molecules
1eV=1.602x10J
Itcanbeassumedthatincollisionswithgasmoleculesofacertainenergy,molecular vibrationscanbegeneratedandstoppedandconvertedintophotons.
Onlyinthiswayisitpossibletoconvertthekineticenergyintoelectromagneticradiationand thustheenergybalancebetweenincomingandoutgoingradiation.Thetracegasesreferredtobyclimate researchas"greenhousegases"wouldthenbeseenascatalystsforthereductionofheat andtheemissionofelectromagneticradiation.Theexchangeofkineticenergywithvibrational energyinthemoleculesofagasmixtureisathermodynamicprocess.A congestionofatypeofenergyinapartofthewholeisafterthe2.
Nottobeexpectedfromthefirstlawofthermodynamics.
Thedensityoftheatmosphereandthusitsheatcontentdecreasewithincreasingaltitude.TheIR photonsareemittedinalldirections.Inclimateresearch,thereturnradiationinthedirectionofthe earthisusedasanargumenttocalculatevaluesfora"radiativeforcing"asthecauseofthe temperatureincreaseduetothe"greenhousegases".Inthedirectionofearth,however,theIRrays encounterahigherdensityofabsorbingmoleculesthaninthedirectionofspace,sothat transportintospaceshouldbefavoredovertransportbacktoearth.
Conclusions
TheEarth'satmosphereactslikeagreenhousebystoringsolarenergy.Allgasesinthe atmosphereareinvolvedinenergystorageaccordingtotheirmolarheatcapacitiesand concentrations.Nitrogenandoxygenasthemaincomponentsoftheaircarrythelargestshareof thestoredenergy.
Theenergycontentofwaterintheatmospherevariesoverawiderange,butisfargreater thanthatoftracegases.
Theenergycontentofthetracegasescarbondioxide,methane,etc.islowduetotheirlow concentration.Accordingtothethermodynamicanalysis,carbondioxidecannotcauseheat accumulation.
Watervaporandthetracegaseshaveacatalyticfunctioninconvertingthermalenergyinthe airintoelectromagneticradiation.Theyplayanimportantroleinmaintainingtheradiationbudget.
N.Leitgeb,rays,waves,fields,ThiemeVerlag,1990,p.196
6thIPCCAssessmentReport,March2023
Tablecollectionchemistry/de.wikibooks.org
G.Kortüm,Introductiontochemicalthermodynamics,VerlagChemie,Basel1981
Czeslik,H.Seemann,R.Winter,basicknowledgeofphysicalchemistry,ViewegandTeubner,
GWVspecialistpublishers,Wiesbaden2010
earthobservatory.nasa.gov/features/EnergyBalance/page7.php
H.Ullmann,Thegreenhouseeffect-amolecularanalysis.
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