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[null,"Berechnung der Mischungstemperatur"]
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[null,"Voraussetzung:",null,"keine Aggregatszustandsänderung"]
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[null,"Abgabemenge eines Boilers in für eine bestimmte Temperatur"]
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[null,"Fassungvermögen Boiler",null,100,"l = kg"]
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[null,"Material","J/(kg*K)","kJ*kg^(−1)*K^(−1)"]
[null,"Aluminium",{"v":896,"d":"896.00 "},{"$f":"C3/1000","v":{"v":0.896,"d":"0.90 "}}]
[null,"Argon",{"v":523,"d":"523.00 "},{"v":0.523,"d":"0.52 "}]
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[null,"Wassererwärmung"]
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[null,"Ausgangstemperatur",{"v":12,"d":"12.00 "},"°C"]
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[null,"Stoff","Wasser"]
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[null,"Masse",{"v":100,"d":"100.00 "},"kg"]
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[null,"Wärmemenge"]
[null,"∆Q (erforderliche Wärmemenge)",{"$f":"C9*C10*C6","v":{"v":10455000,"d":"10,455,000.00 "}},"Joule"]
[null,"W",{"$f":"C13/(3.6*(10^6))","v":{"v":2.904166666666667,"d":"2.90 "}},"kWh"]
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[null,"Dauer für das Aufwärmen"]
[null,"Leistungsaufnahme",2,"kW"]
[null,"∆t",{"$f":"C14/C17","v":{"v":1.4520833333333334,"d":"1.45 "}},"h",{"$nulls":6},4.68]
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[null,"Kosten für das Aufwärmen"]
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[null,"Kosten gesamt",{"$f":"C22*C14","v":{"v":58.083333333333336,"d":"58.08 "}},"Cent"]

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[null,"Bereitstellungsenergieverbrauch von Boilern"]
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[null,"Volumen",{"v":100,"d":"100.00 "},"Liter"]
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[null,null,{"$f":"C11*30/100","v":{"v":9.24,"d":"9.24 "}},"Euro / Monat",null,{"$f":"F11*30/100","v":{"v":0.924,"d":"0.92 "}},"Euro / Monat"]
[null,null,{"$f":"C11*365/100","v":{"v":112.42,"d":"112.42 "}},"Euro / Jahr",null,{"$f":"F11*365/100","v":{"v":11.242,"d":"11.24 "}},"Euro / Jahr"]
[null,null,{"$f":"C13*10","v":{"v":1124.2,"d":"1,124.20 "}},"Euro / 10 Jahre",null,{"$f":"F13*10","v":{"v":112.42000000000002,"d":"112.42 "}},"Euro / 10 Jahre"]
[]
[null,"Teilfrage 1: Um wieviel ist der Boiler binnen der 24h kühler geworden"]
[]
[null,"Anfangstemperatur",{"v":51.74318507890961,"d":"51.74 "},"°C",null,"(unbekannt)"]
[null,"Endtemperatur",{"v":65,"d":"65.00 "},"°C gem. EN 60379:2005"]
[null,"∆T",{"$f":"C19-C18","v":{"v":13.256814921090388,"d":"13.26 "}},"°C (Temperaturabnahme = Lösung)"]
[]
[null,"Stoff","Wasser"]
[null,"spezifische Wärmekapazität",{"$f":"SUMIF(Tabelle1[Material],C22,Tabelle1[J/(kg*K)])","v":{"v":4182,"d":"4,182.00 "}},"J/(kg*K)"]
[null,"Masse",{"$f":"C4","v":{"v":100,"d":"100.00 "}},"kg"]
[]
[null,"Wärmemenge"]
[null,"∆Q (erforderliche Wärmemenge)",{"$f":"C23*C24*C20","v":{"v":5544000,"d":"5,544,000.00 "}},"Joule"]
[null,"W",{"$f":"C27/(3.6*(10^6))","v":{"v":1.54,"d":"1.54 "}},"kWh"]
[]
[]
[null,"Teilfrage 2: Berechnung der Proportionalitätskonstante"]
[null,"unter Verwendung des Newtonschen Abkühlungsgesetzes"]
[]
[]
[]
[null,"Umgebungstemperatur",{"v":20,"d":"20.00 "}]
[null,"Temperatur zu t=0 (T0)",{"$f":"C19","v":{"v":65,"d":"65.00 "}}]
[null,"Dauer in Minuten (X)",{"$f":"24*60","v":{"v":1440,"d":"1,440.00 "}}]
[null,"Proportionalitätskonstante (k)",{"v":0.00024235305737649,"d":"0.000242353057376 "}]
[]
[null,"Temperatur zu t=X (T(t))",{"$f":"C36+(C37-C36)*EXP(-C39*C38)","v":{"v":51.74305899626268,"d":"51.74 "}}]
[{"$nulls":11},"Abgeführte Wärmemenge durch die Behälterwand"]
[]
[null,"Teilfrage 3: Berechnung der Abkühlung bei höherer Ausgangstemperatur"]
[null,"unter Verwendung des Newtonschen Abkühlungsgesetzes"]
[]
[]
[]
[null,"Umgebungstemperatur",{"$f":"C36","v":{"v":20,"d":"20.00 "}}]
[null,"Temperatur zu t=0 (T0)",{"v":80,"d":"80.00 "}]
[null,"Dauer in Minuten (X)",{"$f":"24*60","v":{"v":1440,"d":"1,440.00 "}}]
[null,"Proportionalitätskonstante (k)",{"$f":"C39","v":{"v":0.00024235305737649,"d":"0.000242353057376 "}}]
[]
[null,"Temperatur zu t=X (T(t))",{"$f":"C49+(C50-C49)*EXP(-C52*C51)","v":{"v":62.32407866168357,"d":"62.32 "}}]
[]
[null,"Teilfrage 4: Berechnung des Energieaufwandes bei höherer Ausgangstemperatur",{"$nulls":9},"http://www.schweizer-fn.de/waerme/waermeabstrahlung/waermeabstrahlung.php"]
[]
[null,"Anfangstemperatur",{"$f":"C54","v":{"v":62.32407866168357,"d":"62.32 "}},"°C"]
[null,"Endtemperatur",{"$f":"C50","v":{"v":80,"d":"80.00 "}},"°C gem. EN 60379:2005"]
[null,"∆T",{"$f":"C59-C58","v":{"v":17.675921338316428,"d":"17.68 "}},"°C (Temperaturabnahme)"]
[]
[null,"Stoff","Wasser"]
[null,"spezifische Wärmekapazität",{"$f":"SUMIF(Tabelle1[Material],C62,Tabelle1[J/(kg*K)])","v":{"v":4182,"d":"4,182.00 "}},"J/(kg*K)"]
[null,"Masse",{"$f":"C4","v":{"v":100,"d":"100.00 "}},"kg"]
[]
[null,"Wärmemenge"]
[null,"∆Q (erforderliche Wärmemenge)",{"$f":"C63*C64*C60","v":{"v":7392070.30368393,"d":"7,392,070.30 "}},"Joule"]
[null,"W",{"$f":"C67/(3.6*(10^6))","v":{"v":2.053352862134425,"d":"2.053352862 "}},"kWh"]
[]
[]
[null,"Teilfrage 5: Berechnung des Wärmeübertragungskoeffizienten"]
[]
[null,"Oberfläche Boiler"]
[null,"Breite",{"v":700,"d":"700.00 "},"mm",{"$f":"C74/1000","v":{"v":0.7,"d":"0.70 "}},"m"]
[null,"Höhe",{"v":1585,"d":"1,585.00 "},"mm",{"$f":"C75/1000","v":{"v":1.585,"d":"1.59 "}},"m"]
[null,"Tiefe",{"v":815,"d":"815.00 "},"mm",{"$f":"C76/1000","v":{"v":0.815,"d":"0.82 "}},"m"]
[null,"Oberfläche (A)",{"$f":"2*C74*C75+2*C74*C76+2*C75*C76","v":{"v":5943550,"d":"5,943,550.00 "}},"mm²",{"$f":"2*E74*E75+2*E74*E76+2*E75*E76","v":{"v":5.943549999999999,"d":"5.94 "}},"m²"]
[]
[null,"Fassungsvolumen",{"$f":"C4","v":{"v":100,"d":"100.00 "}},"kg"]
[null,"Eigengewicht",{"v":50,"d":"50.00 "},"kg"]
[null,"Gesamtmasse (m)",{"$f":"C80+C79","v":{"v":150,"d":"150.00 "}}]
[]
[null,"spezfifische Wärmekapazität (c) ",{"$f":"C63","v":{"v":4182,"d":"4,182.00 "}},"J/(kg*K)"]
[]
[null,"Wärmeübertragungskoeffizient (α)",0.02557866475288506]
[]
[null,"Proportionalitätskonstante (k)",{"$f":"(C85*E77)/(C83/1000*C81)","v":0.000242353057376072}]

{"sheet":"Durchflussmenge","index":6,"n_rows":36,"n_cols":4,"rows_kept":36,"merged":[[1,1,1,6],[11,1,11,6],[21,1,21,3]]}
[]
[null,"Warmwasserleistung; Durchflussmenge"]
[]
[null,"Durchflussmenge",{"v":10,"d":"10.00 "},"L/min = kg/min"]
[null,null,{"$f":"C4/60","v":{"v":0.16666666666666666,"d":"0.17 "}},"L/sec = kg/min"]
[]
[null,"Masse (Badewannengröße)",{"v":100,"d":"100.00 "},"L"]
[]
[null,"Dauer",{"$f":"C7/C4","v":{"v":10,"d":"10.00 "}},"min"]
[]
[]
[null,"Warmwasserleistung"]
[]
[null,"Ausgangstemperatur",{"v":12,"d":"12.00 "},"°C"]
[null,"Endtemperatur",{"v":40,"d":"40.00 "},"°C"]
[null,"∆T",{"$f":"C15-C14","v":{"v":28,"d":"28.00 "}},"°C"]
[]
[null,"Stoff","Wasser"]
[null,"spezifische Wärmekapazität",{"$f":"SUMIF(Tabelle1[Material],C18,Tabelle1[J/(kg*K)])","v":{"v":4182,"d":"4,182.00 "}},"J/(kg*K)"]
[null,"Masse",{"$f":"C7","v":{"v":100,"d":"100.00 "}},"kg"]
[]
[null,"Wärmemenge"]
[null,"∆Q (erforderliche Wärmemenge)",{"$f":"C19*C20*C16","v":{"v":11709600,"d":"11,709,600.00 "}},"Joule"]
[null,"W",{"$f":"C23/(3.6*(10^6))","v":{"v":3.252666666666667,"d":"3.25 "}},"kWh"]
[]
[null,"Energieverbrauch in kW"]
[null,"∆t",{"$f":"C9","v":{"v":10,"d":"10.00 "}},"min"]
[null,null,{"$f":"C27/60","v":{"v":0.16666666666666666,"d":"0.17 "}},"h"]
[null,"Leistungsaufnahme",{"$f":"C24/C28","v":{"v":19.516000000000002,"d":"19.52 "}},"kW"]
[]
[]
[]
[]
[null,"Kosten für das Aufwärmen"]
[null,"Strompreis",{"v":20,"d":"20.00 "},"Cent / kWh"]
[null,"Kosten gesamt",{"$f":"C29*C28*C35","v":{"v":65.05333333333334,"d":"65.05 "}},"Cent"]

{"sheet":"Abkühlungsgesetz","index":7,"n_rows":13,"n_cols":4,"rows_kept":13,"merged":[[1,1,1,6]]}
[]
[null,"Newtonsches Abkühlungsgesetz"]
[]
[]
[]
[]
[null,"Umgebungstemperatur",null,{"v":20,"d":"20.00 "}]
[null,"Temperatur zu t=0 (T0)",null,{"v":60,"d":"60.00 "}]
[null,"Dauer in Minuten (X)",null,{"v":120,"d":"120.00 "}]
[null,"Proportionalitätskonstante (k)",null,{"$f":"-LN(1/3)/90","v":{"v":0.012206803207423442,"d":"0.012206803207423 "}}]
[]
[null,"Temperatur zu t=X (T(t))",null,{"$f":"D7+(D8-D7)*EXP(-D10*D9)","v":{"v":29.244816991341796,"d":"29.24 "}}]
[null,"Abkühlung um °C",null,{"$f":"D8-D12","v":{"v":30.755183008658204,"d":"30.76 "}}]

{"sheet":"Grafik Abkühlungsgesetz","index":8,"n_rows":112,"n_cols":4,"rows_kept":112,"merged":[[1,1,1,6],[10,1,10,2]]}
[]
[null,"Newtonsches Abkühlungsgesetz"]
[]
[]
[]
[]
[null,"Umgebungstemperatur",null,{"v":15,"d":"15.00 "}]
[null,"Temperatur zu t=0 (T0)",null,{"v":40,"d":"40.00 "}]
[null,"Proportionalitätskonstante (k)",null,{"v":0.007635689632153786,"d":"0.007635689632154 "}]
[]
[null,"Temperaturentwicklung"]
[null,"nach Zeiteinheiten","Temperatur"]
[null,1,{"$f":"$D$7+($D$8-$D$7)*EXP(-$D$9*B13)","v":{"v":39.809834704727926,"d":"39.809834704727900 "}}]
[null,{"$f":"B13+1","v":2},{"$f":"$D$7+($D$8-$D$7)*EXP(-$D$9*B14)","v":{"v":39.62111592303689,"d":"39.621115923036900 "}},{"$f":"C13-C14","v":{"v":0.18871878169103695,"d":"0.188718781691037 "}}]
[null,{"$f":"B14+1","v":3},{"$f":"$D$7+($D$8-$D$7)*EXP(-$D$9*B15)","v":{"v":39.4338326518596,"d":"39.433832651859600 "}},{"$f":"C14-C15","v":{"v":0.18728327117728583,"d":"0.187283271177286 "}}]
[null,4,{"v":39.247973971824834,"d":"39.247973971824800 "},{"v":0.18585868003476946,"d":"0.185858680034769 "}]
[null,5,{"v":39.06352904662076,"d":"39.063529046620800 "},{"v":0.18444492520407607,"d":"0.184444925204076 "}]
[null,6,{"v":38.88048712236321,"d":"38.880487122363200 "},{"v":0.1830419242575445,"d":"0.183041924257545 "}]
[null,7,{"v":38.6988375269686,"d":"38.698837526968600 "},{"v":0.18164959539461023,"d":"0.181649595394610 "}]
[null,8,{"v":38.51856966953177,"d":"38.518569669531800 "},{"v":0.1802678574368315,"d":"0.180267857436831 "}]
[null,9,{"v":38.339673039708444,"d":"38.339673039708400 "},{"v":0.17889662982332766,"d":"0.178896629823328 "}]
[null,10,{"v":38.16213720710245,"d":"38.162137207102400 "},{"v":0.17753583260599726,"d":"0.177535832605997 "}]
[null,11,{"v":37.98595182065761,"d":"37.985951820657600 "},{"v":0.1761853864448355,"d":"0.176185386444836 "}]
[null,12,{"v":37.81110660805421,"d":"37.811106608054200 "},{"v":0.17484521260340102,"d":"0.174845212603401 "}]
[null,13,{"v":37.63759137511008,"d":"37.637591375110100 "},{"v":0.1735152329441334,"d":"0.173515232944133 "}]
[null,14,{"v":37.46539600518622,"d":"37.465396005186200 "},{"v":0.17219536992385542,"d":"0.172195369923855 "}]
[null,15,{"v":37.29451045859701,"d":"37.294510458597000 "},{"v":0.1708855465892114,"d":"0.170885546589211 "}]
[null,16,{"v":37.1249247720248,"d":"37.124924772024800 "},{"v":0.16958568657221207,"d":"0.169585686572212 "}]
[null,17,{"v":36.95662905793901,"d":"36.956629057939000 "},{"v":0.16829571408578659,"d":"0.168295714085787 "}]
[null,18,{"v":36.78961350401972,"d":"36.789613504019700 "},{"v":0.1670155539192919,"d":"0.167015553919292 "}]
[null,19,{"v":36.62386837258547,"d":"36.623868372585500 "},{"v":0.16574513143424952,"d":"0.165745131434250 "}]
[null,20,{"v":36.45938400002558,"d":"36.459384000025600 "},{"v":0.16448437255989035,"d":"0.164484372559890 "}]
[null,21,{"v":36.29615079623672,"d":"36.296150796236700 "},{"v":0.16323320378886308,"d":"0.163233203788863 "}]
[null,{"$f":"B33+1","v":22},{"v":36.13415924406372,"d":"36.134159244063700 "},{"v":0.16199155217299932,"d":"0.161991552172999 "}]
[null,23,{"v":35.973399898744745,"d":"35.973399898744700 "},{"v":0.16075934531897218,"d":"0.160759345318972 "}]
[null,24,{"v":35.813863387360584,"d":"35.813863387360600 "},{"v":0.15953651138416092,"d":"0.159536511384161 "}]
[null,25,{"v":35.65554040828818,"d":"35.655540408288200 "},{"v":0.1583229790724019,"d":"0.158322979072402 "}]
[null,26,{"v":35.49842173065832,"d":"35.498421730658300 "},{"v":0.15711867762986031,"d":"0.157118677629860 "}]
[null,27,{"v":35.34249819381744,"d":"35.342498193817400 "},{"v":0.15592353684088067,"d":"0.155923536840881 "}]
[null,28,{"v":35.18776070679348,"d":"35.187760706793500 "},{"v":0.15473748702395795,"d":"0.154737487023958 "}]
[null,29,{"v":35.03420024776591,"d":"35.034200247765900 "},{"v":0.15356045902757387,"d":"0.153560459027574 "}]
[null,30,{"v":34.88180786353966,"d":"34.881807863539700 "},{"v":0.15239238422624624,"d":"0.152392384226246 "}]
[null,31,{"v":34.730574669023156,"d":"34.730574669023200 "},{"v":0.1512331945165073,"d":"0.151233194516507 "}]
[null,32,{"v":34.58049184671026,"d":"34.580491846710300 "},{"v":0.15008282231289627,"d":"0.150082822312896 "}]
[null,33,{"v":34.43155064616617,"d":"34.431550646166200 "},{"v":0.14894120054408688,"d":"0.148941200544087 "}]
[null,34,{"v":34.28374238351728,"d":"34.283742383517300 "},{"v":0.14780826264889413,"d":"0.147808262648894 "}]
[null,35,{"v":34.13705844094479,"d":"34.137058440944800 "},{"v":0.14668394257248707,"d":"0.146683942572487 "}]
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[null,45,{"v":32.73020693398005,"d":"32.730206933980000 "},{"v":0.1359005441577068,"d":"0.135900544157707 "}]
[null,46,{"v":32.595340132506635,"d":"32.595340132506600 "},{"v":0.13486680147341445,"d":"0.134866801473414 "}]
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[null,48,{"v":32.32867636430837,"d":"32.328676364308400 "},{"v":0.13282284612984085,"d":"0.132822846129841 "}]
[null,49,{"v":32.196863850008654,"d":"32.196863850008700 "},{"v":0.13181251429971752,"d":"0.131812514299718 "}]
[null,50,{"v":32.06605398233703,"d":"32.066053982337000 "},{"v":0.13080986767162273,"d":"0.130809867671623 "}]
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[null,52,{"v":31.80741173791702,"d":"31.807411737917000 "},{"v":0.12882739663280418,"d":"0.128827396632804 "}]
[null,53,{"v":31.679564281281007,"d":"31.679564281281000 "},{"v":0.1278474566360117,"d":"0.127847456636012 "}]
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