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{"sheet":"Inhalt","index":0,"n_rows":44,"n_cols":1,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
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["Verbrennung"]
["VLE"]
["WatStoff"]
["Tabelle1"]
["Tabelle2"]

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[3.9999999999999251E-2,1.0617803933821283E-3,9.3593206192558245E-2,0.90534501358639641,3.872360179760078E-3,0.17066928670705908,0.82545835311318094]
[2.9999999999999249E-2,4.9037445865243159E-4,7.3444666553650326E-2,0.92606495908476372,1.8247920933053292E-3,0.13665194471062295,0.86152326319607164]
[1.9999999999999248E-2,1.5988133157615844E-4,5.1361872736561252E-2,0.94847824597237507,6.0800540395799878E-4,9.7660858442240497E-2,0.90173113615380152]
[9.9999999999992473E-3,2.2129327816936534E-5,2.7023467911409159E-2,0.97295440276839484,8.6182636075173729E-5,5.262142889662607E-2,0.94729238846729868]

{"sheet":"Behälter","index":2,"n_rows":35,"n_cols":15,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["Füllvolumen von Kugelbehältern, horizontalen und vertikalen zylindrischen Behältern mit elliptischen Böden"]
[]
["Kugelbehälter","standard","numerisch","Formel","Füllhöhe","Radius","Länge","Bodenhöhe",null,null,"standard","numerisch","Formel"]
["Radius r",{"$f":"10-F4","v":1},null,null,50,9]
["Füllhöhe",{"$f":"2*B4*(100-E4)/100","v":1}]
["Füllvolumen",{"$f":"kugelBehVol(B5,B4)","v":2.0943951023931957},{"$f":"IntSimpBehF(B5,0,10,B4,0,0,\"Kugel\")","v":2.0943951023931953},{"$f":"KugelPrismoid(B5,B4)","v":2.0943951023931953}]
["TotalVolumen",{"$f":"B6/(D7+1E-20)","v":0.50000000000000011},{"$f":"IntSimpBehF(B4,0,10,B4,0,0,\"Kugel\")*2","v":4.1887902047863905},{"$f":"4/3*PI()*B4^3","v":4.1887902047863905}]
[]
["Horizontal Behälter Ellipse",null,null,null," ",null,null,null,null,"Ellipse vertikal"]
["Radius",{"$f":"10-F10","v":1},null,null,50,9,8,0,null,"Füllvolumen",{"$f":"VertikalEllipse(B13,B10,0,B12)","v":2.0943951023931957},{"$f":"IntSimpBehF(B13,0,100,B10,0,B12,\"EllipseVertikal\")","v":2.0943951023931953},{"$f":"K10/(M11+1E-20)","v":0.50000000000000011}]
["Länge",{"$f":"10-G10","v":2},null,null,null,null,null,null,null,"TotalVolumen",{"$f":"VertikalEllipse(B10*2,B10,0,B12)","v":4.1887902047863914},{"$f":"IntSimpBehF(B10*2,0,4,B10,0,B12,\"EllipseVertikal\")","v":4.1887902047863905},{"$f":"4/3*PI()*B10*B10*B12","v":4.1887902047863905}]
["Bodenhöhe",{"$f":"B10*(100-H10)/100","v":1}]
["Füllhöhe",{"$f":"2*B10*(100-E10)/100","v":1},null,null,null,null,null,null,null,"Kreisabschnitt",{"$f":"Kreisabschnitt(B13,B10)","v":1.5707963267948966},{"$f":"IntSimpBehF(B13,0,1000,B10,0,0,\"Kreisabschnitt\")","v":1.5707890651069958}]
["Füllvolumen",{"$f":"B18+K10","v":5.2359877559829888},{"$f":"C18+L10","v":5.2359732326071864},{"$f":"B14/(D15+1E-20)","v":0.50000000000000011},null,null,null,null,null,"Kreisabschnitt Prismoid",{"$f":"KreisPrismoid(B13,B10)","v":1.5833333333333333}]
["TotalVolumen",{"$f":"B19+K11","v":10.471975511965978},{"$f":"C19+L11","v":10.471893351787063},{"$f":"D19+M11","v":10.471975511965976},null,null,null,null,null,"Kreisab. D",{"$f":"KreisabschnittD(B13,B10)","v":1.5707963705062866}]
[null,null,null,null,null,null,null,null,null,"Kreisab. B",{"$f":"KreisabschnittB(B13,B10)","v":1.5707963267948966}]
["Horizonal Behälter flach"]
["Füllvolumen",{"$f":"HorizontalZylinder(B13,B10,B11,0)","v":3.1415926535897931},{"$f":"IntSimpBehF(B13,0,1000,B10,B11,0,\"HorizontalZylinder\")","v":3.1415781302139916},{"$f":"B18/(D19+1E-20)","v":0.5}]
["TotalVolumen",{"$f":"HorizontalZylinder(2*B10,B10,B11,0)","v":6.2831853071795862},{"$f":"IntSimpBehF(B10*2,0,1000,B10,B11,0,\"HorizontalZylinder\")","v":6.2831031470006735},{"$f":"B10*B10*PI()*B11","v":6.2831853071795862}]
[]
["Vertikal Behälter Ellipse",null,null,null,null,null,null,null,null,"Ellipsenhälfte horizontal"]
["Radius",{"$f":"10-F22","v":1},null,null,61,9,8,40,null,"Füllvolumen",{"$f":"HorizontalEllipse(B25,B22,0,B24)","v":1.2566370614359172},{"$f":"IntSimpBehF(L24,0,100,B22,0,B24,\"EllipseHorizontal\")","v":1.2566370614359175},{"$f":"K22/(M23+1E-20)","v":1}," "," "]
["Länge",{"$f":"10-G22","v":2},null,null,null,null,null,null,null,"TotalVolumen",{"$f":"HorizontalEllipse(B24,B22,0,B24)","v":1.2566370614359172},{"$f":"IntSimpBehF(B24,0,100,B22,0,B24,\"EllipseHorizontal\")","v":1.2566370614359175},{"$f":"2*PI()*B22*B22*B24/3","v":1.2566370614359172}," "," "]
["Bodenhöhe",{"$f":"B22*(100-H22)/100","v":0.6},null,null,null,null,null,null,null,"Bodenfüllhöhe",null,{"$f":"IF(B25<B24,B25,B24)","v":0.6}]
["Füllhöhe ges.",{"$f":"(B23+B24)*(100-E22)/100","v":1.014}]
["Füllvolumen",{"$f":"B30+K22","v":3.8578757786082662},{"$f":"C30+L22","v":2.5572564200220906},{"$f":"B26/(D27+1E-20)","v":0.51166666666666671}]
["TotalVolumen",{"$f":"B31+K23","v":7.5398223686155035},{"$f":"C31+L23","v":4.3982297150257068},{"$f":"D31+M23","v":7.5398223686155035}]
[]
["Vertikal Behälter flach"]
["Füllvolumen",{"$f":"VertikalZylinder(B32,B22,B23,B24)","v":2.601238717172349},{"$f":"IntSimpBehF(B32,0,100,B22,B23,0,\"VertikalZylinder\")","v":1.3006193585861732},{"$f":"B30/(D31+1E-20)","v":0.41400000000000003}]
["TotalVolumen",{"$f":"VertikalZylinder(B22,B22,B23,B24)","v":6.2831853071795862},{"$f":"IntSimpBehF(B22,0,100,B22,B23,0,\"VertikalZylinder\")","v":3.1415926535897896},{"$f":"B22*B22*PI()*B23","v":6.2831853071795862}]
["Füllhöhe Zylinder:",{"$f":"IF(B25<B24,0,B25-B24)","v":0.41400000000000003}]
[]
[]
[" "]

{"sheet":"Beisp1a","index":3,"n_rows":20,"n_cols":11,"rows_kept":20,"cut":false,"hidden":false,"merged":[]}
["Einheitentabelle ",null,"wird nicht benötigt"]
["Nr.","Arbeit","Wert für 1 J",null,null,null,null,null,"Nr.","Arbeit","Wert für 1 J"]
[1,"Btu",9.47817E-4,null," ",null,null,null,1,"Btu",9.47817E-4]
[2,"kBtu",9.47817E-7," "," "," "," "," ",2,"kBtu",9.47817E-7]
[3,"MMBtu",9.4781700000000002E-10,null,null,null,null,null,3,"MMBtu",9.4781700000000002E-10]
[4,"J",1,null,null,null,null,null,4,"J",1]
[5,"kJ",1E-3,null,null,null,null,null,5,"kJ",1E-3]
[6,"MJ",9.9999999999999995E-7,null," ",null,null,null,6,"MJ",9.9999999999999995E-7]
[7,"cal",0.2388458966,null,null,null,null,null,7,"cal",0.2388458966]
[8,"kcal",2.3884589660000001E-4,null,null," ",null,null,8,"kcal",2.3884589660000001E-4]
[9,"Mcal",2.3884589000000002E-7,null,null,null,null,null,9,"Mcal",2.3884589000000002E-7]
[10,"Ws",1,null,null,null," ",null,10,"Ws",1]
[11,"Wh",2.7777777799999997E-4,null,null,null,null,null,11,"Wh",2.7777777799999997E-4]
[12,"kWh",2.7777770000000001E-7,null,null,null,null,null,12,"kWh",2.7777770000000001E-7]
[13,"MWh",2.7777776999999999E-10,null,null,null,null,null,13,"MWh",2.7777776999999999E-10]
[14,"PSh",3.7250599999999999E-7,null,null,null," ",null,14,"PSh",3.7250599999999999E-7]
[]
[]
[null," "]
[null,null,null,null,null,null,null,null,"Kap1a"]

{"sheet":"Bilanz","index":4,"n_rows":30,"n_cols":13,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Massenbilanz einer Mischung"]
[]
[]
["Beispiel 1",null,null,"Menge 1",2,3]
[null,null," ","%","%","%","mges","mi","Kontrolle"]
[null,null,"Stoff1",0.1,0.6,0.2,100,{"$f":"MMULT(MINVERSE(D6:F8),G6:G8)","v":322.22222222222229},{"$f":"$D$9*D6+$E$9*E6+$F$9*F6","v":100.00000000000001},null,null,null," "]
[null,null,2,0.2,0.3,0.4,150,55.555555555555543,{"$f":"$D$9*D7+$E$9*E7+$F$9*F7","v":150.00000000000006}]
[null,null,3,0.7,0.1,0.4,300,172.22222222222234,300.00000000000006]
[null,null,"mi",{"$f":"H6","v":322.22222222222229},{"$f":"H7","v":55.555555555555543},{"$f":"H8","v":172.22222222222234},{"$f":"SUM(G6:G8)","v":550},{"$f":"SUM(H6:H8)","v":550.00000000000023}]
[]
[]
[]
["Beispiel 2: m(ges)=m(Lösung)-m(Extra)"]
[null,null,null,"Menge 1",2,3,4,5]
[null,null," ","%","%","%","%","%","m(Matrix)","Matrix","m(Extra)","m(ges)"]
[null,null,"Stoff1",0.1,0.6,0.2,0.5,0.2,100,{"$f":"MMULT(MINVERSE(D16:F18),I16:I18)","v":322.22222222222229},{"$f":"G19*G16+H19*H16","v":40.700000000000003},{"$f":"G19*G16+H19*H16+I16","v":140.69999999999999}]
[null,null,2,0.2,0.3,0.4,0.3,0.5,150,55.555555555555543,{"$f":"G19*G17+H19*H17","v":49.5},{"$f":"G19*G17+H19*H17+I17","v":199.5}]
[null,null,3,0.7,0.1,0.4,0.2,0.3,300,172.22222222222234,{"$f":"G19*G18+H19*H18","v":30.8},{"$f":"G19*G18+H19*H18+I18","v":330.8}]
[null,null,"m",{"$f":"J16","v":322.22222222222229},{"$f":"J17","v":55.555555555555543},{"$f":"J18","v":172.22222222222234},55,66,{"$f":"SUM(I16:I18)","v":550},null,{"$f":"SUM(K16:K18)","v":121},{"$f":"SUM(L16:L18)","v":671}]
[]
[]
[]
["Beispiel 3: 6*6 Matrix"]
[null,null," ","x1m1","x1m2","x3m3","x4m4","x5m5","mges","mi"]
[null,null,"x1",0.1,0.6,0.2,0.5,0.2,140.69999999999999,{"$f":"MMULT(MINVERSE(D25:H29),I25:I29)","v":322.22222222222229}]
[null,null,"x3",0.2,0.3,0.4,0.3,0.5,199.5,55.5555555555555]
[null,null,"x4",0.7,0.1,0.4,0.2,0.3,330.8,172.22222222222234]
[null,null,"x5",0,0,0,1,0,55,55]
[null,null,"x6",0,0,0,0,1,66,66]
[null,null,"mi",{"$f":"J25","v":322.22222222222229},{"$f":"J26","v":55.5555555555555},{"$f":"J27","v":172.22222222222234},{"$f":"J28","v":55},{"$f":"J29","v":66}]

{"sheet":"Biot-Savart","index":5,"n_rows":312,"n_cols":4,"rows_kept":312,"cut":false,"hidden":false,"merged":[]}
["Magnetfeld nach Biot-Savart und Simpson"]
["Einzelberechnung"]
["R [m]",0.5]
["I [A]",5]
["x [m]",0]
["z [m]",0.1]
["n",10]
["Hx",{"$f":"IntSimpBSF(B7,B5,B6,B3,B4,1)","v":-2.9065570816738596E-17}]
["Hy",{"$f":"IntSimpBSF(B7,B5,B6,B3,B4,2)","v":3.9286300838329995E-18}]
["Hz",{"$f":"IntSimpBSF(B7,B5,B6,B3,B4,3)","v":4.7143301715909631}]
[]
["Feldstärkevektoren"]
["Nr.","x","z"]
[1,0,0.1," "]
[null,-1.2330731942319487E-19,0.12000000000000001]
[]
[2,0,0.2]
[null,0,0.22]
[]
[3,0,0.30000000000000004]
[null,-5.9006137730797111E-19,0.32000000000000006]
[]
[4,0,0.4]
[null,-4.8835384958916295E-19,0.42000000000000004]
[]
[5,0,0.5]
[null,-5.2614303292348643E-19,0.52]
[]
[6,0,0.60000000000000009]
[null,-7.0899564892876519E-19,0.62000000000000011]
[]
[7,0,0.70000000000000007]
[null,-9.4731932536835598E-19,0.72000000000000008]
[]
[8,0,0.8]
[null,-7.8093312493771093E-19,0.82000000000000006]
[]
[9,0,0.9]
[null,-1.0150504607480139E-18,0.92]
[]
[10,0,1]
[null,-3.1196444232509562E-18,1.02]
[]
[11,0.1,0.1]
[null,0.10119800420278174,0.11996408740539165]
[]
[12,0.1,0.2]
[null,0.10212751441631164,0.21988652011811988]
[]
[13,0.1,0.30000000000000004]
[null,0.10269415485778874,0.31981770747594823]
[]
[14,0.1,0.4]
[null,0.10295510135101328,0.41978047967075727]
[]
[15,0.1,0.5]
[null,0.10301292718761934,0.51977175434204326]
[]
[16,0.1,0.60000000000000009]
[null,0.10295408089504408,0.61978063209469147]
[]
[17,0.1,0.70000000000000007]
[null,0.10283587558359943,0.71979792437793289]
[]
[18,0.1,0.8]
[null,0.10269222131495688,0.81981797023893455]
[]
[19,0.1,0.9]
[null,0.1025418693687519,0.91983781490266003]
[]
[20,0.1,1]
[null,0.10239461026310223,1.0198561285674688]
[]
[21,0.2,0.1]
[null,0.20267334065377993,0.11982052597053994]
[]
[22,0.2,0.2]
[null,0.20459535570761336,0.21946490960473503]
[]
[23,0.2,0.30000000000000004]
[null,0.20564033748268545,0.31918818889529221]
[]
[24,0.2,0.4]
[null,0.20604937187086056,0.41906318703596129]
[]
[25,0.2,0.5]
[null,0.20608158256358905,0.51905293556180387]
[]
[26,0.2,0.60000000000000009]
[null,0.20591428376708834,0.61910552923952533]
[]
[27,0.2,0.70000000000000007]
[null,0.20565230007279142,0.71918466845914009]
[]
[28,0.2,0.8]
[null,0.20535378069208379,0.81927010722079852]
[]
[29,0.2,0.9]
[null,0.20504967723453699,0.91935202211209466]
[]
[30,0.2,1]
[null,0.20475569693107759,1.0194263570105087]
[]
[31,0.30000000000000004,0.1]
[null,0.30499230477073153,0.119366901999962]
[]
[32,0.30000000000000004,0.2]
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[]
[33,0.30000000000000004,0.30000000000000004]
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[]
[34,0.30000000000000004,0.4]
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[]
[35,0.30000000000000004,0.5]
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[]
[36,0.30000000000000004,0.60000000000000009]
[null,0.30884197340456454,0.61793932847998989]
[]
[37,0.30000000000000004,0.70000000000000007]
[null,0.30840424455446908,0.7181485171148686]
[]
[38,0.30000000000000004,0.8]
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[]
[39,0.30000000000000004,0.9]
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[]
[40,0.30000000000000004,1]
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[]
[41,0.4,0.1]
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[]
[42,0.4,0.2]
[null,0.41251462329277466,0.21560077574481293]
[]
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[]
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[]
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[]
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[]
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[]
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[]
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[]
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[]
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[]
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[]
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[]
[54,0.5,0.4]
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[]
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[]
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[]
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[]
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[]
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[]
[60,0.5,1]
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[]
[61,0.60000000000000009,0.1]
[null,0.61717596781462292,8.9753726061097189E-2]
[]
[62,0.60000000000000009,0.2]
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[]
[63,0.60000000000000009,0.30000000000000004]
[null,0.61919250084815336,0.30562564762437489]
[]
[64,0.60000000000000009,0.4]
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[]
[65,0.60000000000000009,0.5]
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[]
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[]
[67,0.60000000000000009,0.70000000000000007]
[null,0.61545920475780114,0.71268908933912845]
[]
[68,0.60000000000000009,0.8]
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[]
[69,0.60000000000000009,0.9]
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[]
[70,0.60000000000000009,1]
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[]
[71,0.70000000000000007,0.1]
[null,0.71353087093095313,8.5271947452229477E-2]
[]
[72,0.70000000000000007,0.2]
[null,0.71912017787686222,0.19413324638687193]
[]
[73,0.70000000000000007,0.30000000000000004]
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[]
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[60,0]
[80,40]
[]
[70,0]
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[]
[80,0]
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[]
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[]
[]
[]
[]
[]
[]
[null,"Einstellung in Listbox1"]
[]
[]
[]
[null,"Einstellung in Listbox2"]
[]
[]
[]
[]
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[2,"kBtu",9.47817E-7]
[3,"MMBtu",9.4781700000000002E-10]
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[12,"kWh",2.7777770000000001E-7]
[13,"MWh",2.7777776999999999E-10]
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["Fourier-Reihe als Lösung des 2. Fick'schen Gesetzes am Beispiel der instationären Wärmeleitung eines Stabes"]
[]
["Eingabe"]
["Stelle x",2]
["Zeit z",4]
["Schrittzahl",70]
[]
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[null,null,null,2.6,0.01,20.933373741047639,4,25.759657619148509,10,28.906928733530247,50,33.405164072544736]
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[null,null,null,2.8,0.01,22.932161568878577,4,32.256126161817988,10,34.277581413894445,50,36.673563481319796]
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["Lösen eines Gleichungssystem nach Gauß-Jordan"]
[]
["Zahl der Gleichungen N",null,3]
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["Schrittweises Lösen einer Matrix","Eingangsdaten"]
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[null,"Vertauschen","Zeile i1 = 2 Zeile i2 = 2"]
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[null,null,null,null,"df2dx1",null,{"$f":"MethanisierungF(F5,F6,F7,F8,F9,F10,F11,F12,F13,F14,F15,F18,11)","v":1236.285612728004},null,null,null,null,null,null,null,0.69999999999999896,-9.2612843318827807,-15.021517827292705,null,0.22,-0.93074426867052473,-2.2765199158096863]
[null,null,null,null,"df1dx2",null,{"$f":"MethanisierungF(F5,F6,F7,F8,F9,F10,F11,F12,F13,F14,F15,F18,12)","v":618.19372675411796},null,null,null,null,null,null,null,0.71999999999999897,-8.8465021262837364,-14.238711525225536,null,0.222,-0.43543965086097813,-1.0650771730551192]
[null,null,null,null,"df2dx2",null,{"$f":"MethanisierungF(F5,F6,F7,F8,F9,F10,F11,F12,F13,F14,F15,F18,13)","v":1512.1723776535453},null,null,null,null,null,null,null,0.73999999999999899,-8.0397067424579571,-12.807865183036483,null,0.224,0.12348326419860456,0.302046695508146]
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[null,null,null,null,"Schritte",50,{"$f":"G16*G16","v":3.8180867812696971E-28},null,null,null,null,null,null,null,0.77999999999999903,2.3762916907858891,3.6707158115912861,null,0.22800000000000001,1.4881430755080309,3.640314188282737]
[null,null,null,null,null,null,{"$f":"G17*G17","v":6.1846694969327326E-28},null,null,null,null,null,null,null,0.79999999999999905,-40.666042609029695,-61.422630196999975,null,0.23,2.3329269683508151,5.707036840962104]
[null,null,null,null,null,null,{"$f":"SUM(G24:G25)","v":1.000275627820243E-27},null,null,null,null,null,null,null,0.81999999999999895,-20.040302425298375,-29.40051323489832,null,0.23200000000000001,3.3232262334436644,8.1299078347837934]
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[null,"T[Cel]","T[K]","K1",null,null,null,null,null,null,null,null,null,null,0.87999999999999901,-17.524131967291105,-22.006005464273024,null,0.23799999999999999,7.6724176348682818,18.772039670063485]
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["3D Darstellung eines Würfels"]
["Grundkoordinaten",null,null,null,"Aktuelle Koordinaten",null,null,null,"Drehfunktionen"]
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[1,1,-1,null,{"$f":"MMULT(A6:C6,$E$17:$G$19)","v":0.25256240669465857},1.4558954325976932,-0.90364856004188809,null,0,{"$f":"COS(J4)","v":0.93969262078590843},{"$f":"SIN(J4)","v":0.34202014332566871}]
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[null,null,null,null,0.25256240669465857,1.4558954325976932,-0.90364856004188809]
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[null,null,null,null,null,null,null,null,null,null," ",null,null,"z","Draufsicht",null,null,null,{"$f":"F4","v":-1.0329541333041079}]
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[null,null,null,null,{"$f":"E9","v":-0.67550370598824372},0.39016652361756871,{"$f":"G9","v":1.5464361697284275},null,null,null,null,null,null,"Betrachter X = Drehung um die X-Achse"]
[null,null,null,null,1.0905407371307343,1.0329541333041079,0.86239588307709003,null,null,null,null,null,null,"Betrachter Y = Drehung um die Y-Achse"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,"Kombinationsmatrix = Multiplikation aller 3 Betrachter"]
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[null,null,null,null,{"$f":"E27","v":-0.25256240669465857},{"$f":"F27","v":-1.4558954325976932},0.90364856004188809,null,null,null,null,null,null," "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"manuelle Berechung der Drehung der X-Achse"]
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[]
[null,null,null,null,{"$f":"E24","v":0.67550370598824372},{"$f":"F24","v":-0.39016652361756871},-1.5464361697284275]
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["Nullstellensuche nach dem Halbschrittverfahren (Zweiersuche, Bisection) + Regula Falsi"]
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[]
["Eingabe"," "]
["Grenzwert A",1]
["Grenzwert E",2]
["Toleranz EP",9.9999999999999995E-8]
[null," "]
["Zwischenergebnis"]
["Grenzwert A",1.4142135620117187,null,"Y1",1.0221268276211504E-9]
["Grenzwert E",1.4142137527465819,null,"Y2",-5.3845757008730288E-7]
["Mittelwert M",1.4142136573791504,null,"Y3",-2.6871771297010127E-7]
[]
["Endergebnis"]
["Mittelwert",1.4142136096954345]
["Regula Falsi",1.4142135623730951]
["Schrittzahl",21]

{"sheet":"Interpolation","index":18,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"IntWärme","index":19,"n_rows":37,"n_cols":18,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["Instationäre Wärmeleitung eines Quaders"]
[]
["z-Ebene",5,"↗","a=",1]
["Intervall",10,null,"h=",1]
["Zeit",0.79999999999999993,null,"dt=",0.01]
[null,null,null,"Anzeigen",1]
["xy-Matrix"]
[null,"y  →",1,2,3,4,5,6,7,8,9,10,11]
["x  ↓",null,10,10,10,10,10,10,10,10,10,10,10]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[null,"Zwischenergebnisse"]
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[" "," "]
[" "," "]

{"sheet":"Kinetik","index":20,"n_rows":111,"n_cols":13,"rows_kept":111,"cut":false,"hidden":false,"merged":[]}
["Kinetische Reaktionsgleichungen numerisch lösen"]
[]
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[0.99000000000000066,0.13532607744362568,8.6062627614814313E-2,0.77861129494155989,-2.7065215488725138E-3,-1.5966098318682021E-3,4.3031313807407158E-3,0.99999999999999989,null,0.22396843702475921,0.13415638821883047,0.64187517475641021,0.99999999999999989]
[1.0000000000000007,0.13261955589475316,8.4466017782946115E-2,0.78291442632230057,-2.6523911178950631E-3,-1.5709097712522423E-3,4.2233008891473054E-3,0.99999999999999978,null,0.22060891046938785,0.13248505021599574,0.64690603931461621,0.99999999999999978]

{"sheet":"Kompression","index":21,"n_rows":11,"n_cols":9,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
["Kompressions und Expansionsvorgänge"]
[null,"Eingabe",null,"Ausgabe",null,"   arr Index"]
["Variable","Eingang (1)","Ausgang (2)","Eingang (1)","Ausgang (2)"]
["Druck P [bar]",1.01325,4,{"$f":"KompressorF(B4,B5,B6,C4,C5,C6,B8)","v":1.01325},4,0]
["Temperatur T [°C]",20,0,20,160.8340027049075,1,null,"  "," "]
["Volumen V [m3]",1000,0,1000,375.00792319695341,2]
["Arbeit W [J]"," "," ",0,121695423.1969534,3,null," "]
["kappa",1.4,null,null,null," "]
["n (Mole)"," ",null,null,{"$f":"MolGasF(B4,B5,B6)","v":41570.924267819108}," "]
[]
[" ",null,null,"W=",{"$f":"8.31*(E5-B5)/(B8-1)*E9","v":121629307.95269503}]

{"sheet":"Kubische Gleichung","index":22,"n_rows":49,"n_cols":34,"rows_kept":49,"cut":false,"hidden":false,"merged":[]}
[null,"Lösung einer kubischen Gleichung"]
[null,"Kubische Gleichung:",null,{"$f":"IF(AND(F4=0,F5=0,F6=0),\"\",IF(G6>0,\"(Cardanische Formel)\",\"(casus irreducibilis)\")&\"             \")","v":"(casus irreducibilis)             "},null,"p",{"$f":"(3*F5-F4*F4)/9","v":-10.444444444444445},null,{"$f":"G2*3","v":-31.333333333333336},null,null,"über Zielwertsuche",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX(AE:AE,MATCH(ROW(),AF:AF,0))","v":{"$error":"#N/A"}},0]
[null,"ax³ + bx² + cx + d = 0","a=",0.05," ","q",{"$f":"(2*F4^3/27-F4*F5/3+F6)/2","v":7.2962962962962976},{"$f":"MIN(5,MAX(H4:H6))","v":0},{"$f":"G3*2","v":14.592592592592595},null,0.61956163095105865,{"$f":"D3*K3^3+D4*K3^2+D5*K3+D6-D7","v":-2.6443470281488386},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX(AE:AE,MATCH(ROW(),AF:AF,0))","v":{"$error":"#N/A"}},0]
[null,"allgemeine Form der","b=",0.4," ",{"$f":"D4/D$3","v":8},null,{"$f":"IF(MOD(F4,1)=0,0,LEN(F4)-FIND(\",\",F4))","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE4,AE4)=1)*(MAX(AF$2:AF3)+1)","v":0},{"$f":"INDEX(AE:AE,MATCH(ROW(),AF:AF,0))","v":{"$error":"#N/A"}},0]
[null,"kubischen Gleichung ","c=",-0.5," ",{"$f":"D5/D$3","v":-10},null,{"$f":"IF(MOD(F5,1)=0,0,LEN(F5)-FIND(\",\",F5))","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE5,AE5)=1)*(MAX(AF$2:AF4)+1)","v":0},{"$f":"INDEX(AE:AE,MATCH(ROW(),AF:AF,0))","v":{"$error":"#N/A"}},0]
[null,{"$f":"IF(AND(D7=0,D3=1),\"\",\"x³ \"&IF(F4<0,\"- \",\"\")&IF(F4>0,\"+ \",\"\")&IF(F4=0,\"\",IF(ABS(F4)=1,\"x² \",ROUND(ABS(F4),H3)&\"x² \"))&IF(F5>0,\"+ \",IF(F5<0,\"- \",\"\"))&IF(ABS(F5)=1,\"x \",IF(F5<>0,ROUND(ABS(F5),H3)&\"x \",\"\"))&IF(F6>0,\"+ \",IF(F6<0,\"- \",\"\"))&IF(F6<>0,ROUND(ABS(F6),H3),\"\")&\" = 0\")","v":"x³ + 8x² - 10x - 50 = 0"},"d=",-2.5," ",{"$f":"D6/D$3-D7/D$3","v":-50},{"$f":"ROUND((G3)^2+(G2)^3,9)","v":-1086.1111111109999},{"$f":"IF(MOD(F6,1)=0,0,LEN(F6)-FIND(\",\",F6))","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE6,AE6)=1)*(MAX(AF$2:AF5)+1)","v":0}]
[null,{"$f":"IF(B6=\"\",\"\",\"(Normalform)\")","v":"(Normalform)"},null,0,{"$f":"IF(D7=0,\"\",\"  =  e \")","v":""},null,"r","gamma",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE7,AE7)=1)*(MAX(AF$2:AF6)+1)","v":0}]
[null,{"$f":"IF(D3=0,\"Tabelle quadr. Gleichung verwenden !\",IF(OR(D10=\"falsch\",D11=\"falsch\",D12=\"falsch\"),\"Höhere \"&IF(B13<>\"\",\"bzw. automatische \",\"\")&\"Rundung (Zelle B12) einstellen.\",\"\"))","v":""},null,null,null,null,{"$f":"ABS(G2)^0.5","v":3.2317865716108862},{"$f":"ACOS(G3/G8^3)","v":1.3529170156572403},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE8,AE8)=1)*(MAX(AF$2:AF7)+1)","v":0}]
[null,{"$f":"IF(D3<0,\"- \",\"\")&IF(D3=0,\"\",IF(ABS(D3)=1,\"x³ \",ABS(ROUND(D3,5))&\"x³ \"))&IF(D4<0,\"- \",\"\")&IF(D4>0,\"+ \",\"\")&IF(D4=0,\"\",IF(ABS(ROUND(D4,5))=1,\"x² \",ABS(D4)&\"x² \"))&IF(D5>0,\"+ \",IF(D5<0,\"- \",\"\"))&IF(ABS(D5)=1,\"x \",IF(D5<>0,ABS(ROUND(D5,5))&\"x \",\"\"))      &IF(D6>0,\"+ \",IF(D6<0,\"- \",\"\"))&IF(D6<>0,ABS(D6),\"\")&\" = \"&IF(D7<0,\"- \",\"\")&ABS(D7)","v":"0,05x³ + 0,4x² - 0,5x - 2,5 = 0"},null,null,{"$f":"IF(ISTEXT(C11),\"\",IF(OR(MOD(C10,1)>0,MOD(C11,1)>0,MOD(C12,1)>0),\"\",\"= diophantische Gleichung\"))","v":""},null,null,{"$f":"IF(MOD(ROUND(F10,6),1)=0,6,16)","v":16},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE9,AE9)=1)*(MAX(AF$2:AF8)+1)","v":0}]
[null,"x2 =     ",{"$f":"IF(AND(F4=0,F5=0,F6=0),0,ROUND(IF(G$6>0,(-G3+(G3*G3+(G2^3))^0.5)^(1/3)+(-G3-(G3*G3+(G2^3))^0.5)^(1/3)-F4/3,F10),IF(B13<>\"\",B13,IF(G6>0,H10,H9))))","v":-2.1976529424680602},{"$f":"IF(ROUND(C10^3+F4*C10^2+F5*C10+F6,5)=0,\"OK\",\"falsch\")","v":"OK"},{"$f":"\"Extrema bei X = \"&ROUND(MIN(H13,H14),4)&\" und X = \"&ROUND(MAX(H13,H14),4)","v":"Extrema bei X = -5,8985 und X = 0,5651"},{"$f":"G10-G11-F4/3","v":-2.197652942468062},{"$f":"-2*G8*COS(H8/3-60*PI()/180)","v":-5.3483555693258493},{"$f":"IF(MOD(ROUND((-G3+(G3*G3+(G2^3))^0.5)^(1/3)+(-G3-(G3*G3+(G2^3))^0.5)^(1/3)-F4/3,6),1)=0,6,16)","v":{"$error":"#NUM!"}},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE10,AE10)=1)*(MAX(AF$2:AF9)+1)","v":0}]
[null,"x3 =     ",{"$f":"IF(AND(F4=0,F5=0,F6=0),0,IF(G$6>0,\"komplexe Wurzel\",ROUND(F11,IF(B13<>\"\",B13,H11))))","v":2.6816889026591801},{"$f":"IF(OR(C11=\"\",G$6>0),\"\",IF(ROUND(C11^3+F$4*C11^2+F$5*C11+F$6,5)=0,\"OK\",\"falsch\"))","v":"OK"},{"$f":"\"Wendepunkt bei X = \"&ROUND(-G14/(G13*2),4)","v":"Wendepunkt bei X = -2,6667"},{"$f":"-G10-F4/3","v":2.6816889026591828},{"$f":"-2*G8*COS(H8/3)","v":-5.8173692935244539},{"$f":"IF(MOD(ROUND(F11,6),1)=0,6,16)","v":16},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE11,AE11)=1)*(MAX(AF$2:AF10)+1)","v":0}]
[null,"x1 =     ",{"$f":"IF(AND(F4=0,F5=0,F6=0),0,IF(G$6>0,\"komplexe Wurzel\",ROUND(F12,IF(B13<>\"\",B13,H12))))","v":-8.4840359601911199},{"$f":"IF(OR(C12=\"\",G$6>0),\"\",IF(ROUND(C12^3+F$4*C12^2+F$5*C12+F$6,5)=0,\"OK\",\"falsch\"))","v":"OK"},null,{"$f":"G11-F4/3","v":-8.4840359601911199},null,{"$f":"IF(MOD(ROUND(F12,6),1)=0,6,16)","v":16},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(COUNTIF(AE$3:AE12,AE12)=1)*(MAX(AF$2:AF11)+1)","v":0}]
[null,null,null,null,null,"erste Ableitung",{"$f":"3*D3","v":0.15000000000000002},{"$f":"IF(G13=0,-(G15-G16)/G14,IF(ISERROR((-G14+(G14*G14-4*G13*(G15-G16))^0.5)/(G13*2)),\"komplexe Wurzel\",(-G14+(G14*G14-4*G13*(G15-G16))^0.5)/(G13*2)))","v":0.56511990494421938}]
[null,{"$f":"IF(B13<>\"\",B13&\" Rundungsstellen manuell\",\"automatische Rundung\")","v":"automatische Rundung"},null,"Grafik",null,null,{"$f":"2*D4","v":0.8},{"$f":"IF(OR(G13=0,4*G13*(G15-G16)-G14*G14=0),\"es gibt nur eine Lösung\",IF(ISERROR((-G14-(G14*G14-4*G13*(G15-G16))^0.5)/(G13*2)),\"komplexe Wurzel\",(-G14-(G14*G14-4*G13*(G15-G16))^0.5)/(G13*2)))","v":-5.8984532382775523}]
[null,null,null,"x-Werte von:",-10,null,{"$f":"D5","v":-0.5}]
[null,null,null,"x-Werte bis:",5]
[]
[]
[null,"Quelle:  http://www.excelformeln.de/tips.html?welcher=37",null,null,null,null,"x","y"]
[null,"                                                                W a l t e r   F R I C K E,   M o n h e i m   (W F)","",null,null,null,{"$f":"+E15","v":-10},{"$f":"$D$3*G20^3+$D$4*G20^2+$D$5*G20+$D$6-$D$7","v":-7.5}]
[null,null,null,null,null,null,{"$f":"G20+($E$16-$E$15)/29","v":-9.4827586206896548},{"$f":"$D$3*G21^3+$D$4*G21^2+$D$5*G21+$D$6-$D$7","v":-4.4253044405264728}]
[null,"x1= Lösung Links",null,null,null,null,-8.9655172413793096,-1.8976792816433594]
[null,"x2 = Lösung Mitte",null,null,null,null,-8.4482758620689644,0.12439009389479416]
[null,"x3 = Lösung Rechts",null,null,null,null,-7.9310344827586192,1.6824183033334705,null,"Quelle: http://www.excel4managers.de/index.php?page=excel"]
[null,null,null,null,null,null,-7.413793103448274,2.8179199639181629,null,"Lösung mit der Funktion KubischeGleichungF",null,null,"Hilfe"]
[null,null,null,null,null,null,-6.8965517241379288,3.5724096928943396,null,"x3",{"$f":"KubischeGleichungF(D3,D4,D5,D6)","v":2.6816889026591824},null,"1. K25:K30 markieren"]
[null,null,null,null,null,null,-6.3793103448275836,3.9874021075074833,null,"x1",-8.4840359601911235,null,"2. KubischeGleichungF aufrufen, Parameter wählen"]
[null,null,null,null,null,null,-5.8620689655172384,{"$f":"$D$3*G28^3+$D$4*G28^2+$D$5*G28+$D$6-$D$7","v":4.1044118250030746},null,"x2",-2.1976529424680682,null,"3. Ergebnis steht in K26. F2, Strg+Shift+Enter,  Bereich ziehen"]
[null,null,null,null,null,null,-5.3448275862068932,3.9649534626265925,null,"p",-31.333333333333332,null,"Sie können auch den Bereich nach der Berechnung markieren und dann F2, Strg+Shift+Enter wählen"]
[null,null,null,null,null,null,-4.827586206896548,3.6105416376235153,null,"q",14.592592592592593]
[null,null,null,null,null,null,-4.3103448275862029,3.0826909672393255,null,"D",-1086.1111111111111]
[null,null,null,null,null,null,-3.7931034482758581,2.4229160687194993]
[null,null,null,null,null,null,-3.2758620689655134,1.6727315593095184,null,"Berechnung mit der Normalform"]
[null,null,null,null,null,null,-2.7586206896551686,0.87365205625486331,null,"x3",{"$f":"KubischeGleichungF(1,8,-10,-50)","v":2.6816889026591824},null,null,{"$f":"KubischeGleichungF(D3,D4,D5,D6)","v":2.6816889026591824}]
[null,null,null,null,null,null,-2.2413793103448238,6.7192176801011083E-2,null,"x1",-8.4840359601911235,null,null,-8.4840359601911235]
[null,null,null,null,null,null,-1.7241379310344791,-0.70513346180655723,null,"x2",-2.1976529424680682,null,null,-2.1976529424680682]
[null,null,null,null,null,null,-1.2068965517241343,-1.4018102423223628,null,"p",-31.333333333333332,null,null,-31.333333333333332]
[null,null,null,null,null,null,-0.68965517241378949,-1.9813235475009261,null,"q",14.592592592592593,null,null,14.592592592592593]
[null,null,null,null,null,null,-0.17241379310344462,-2.4021587600967673,null,"D",-1086.1111111111111]
[null,null,null,null,null,null,0.34482758620690024,-2.6228012628644066]
[null,null,null,null,null,null,0.8620689655172451,-2.6017364385583654]
[null,null,null,null,null,null,1.3793103448275899,-2.2974496699331635]
[null,null,null,null,null,null,1.8965517241379346,-1.668426339743321]
[null,null,null,null,null,null,2.4137931034482794,-0.67315183074335971]
[null,null,null,null,null,null,2.9310344827586241,0.72988847431220094]
[null,null,null,null,null,null,3.4482758620689689,2.5822091926688397]
[null,null,null,null,null,null,3.9655172413793136,4.9253249415720379]
[null,null,null,null,null,null,4.4827586206896584,7.8007503382672709]
[null,null,null,null,null,null,5.0000000000000036,11.250000000000027]

{"sheet":"LLE","index":23,"n_rows":102,"n_cols":20,"rows_kept":102,"cut":false,"hidden":false,"merged":[]}
["x1","y1","gamma1","gamma2","gamma=gamma1/gamma2","gE/RT=x1ln(gamma1)+x2ln(gamma2)","gE/RT=Ax1x2","g/RT=(x1ln(x1)+x2ln(x2))+Ax1x2",null,null,null,null,"A_Porter:",3,null,"A/RT",{"$f":"N1/8.314/298","v":1.2108628931873624E-3}]
[0,{"$f":"YF(C2,D2,$N$2,A2)","v":0},{"$f":"Gamma1PorterF($N$1,A2)","v":20.085536923187668},{"$f":"Gamma2PorterF($N$1,A2)","v":1},{"$f":"C2/D2","v":20.085536923187668},{"$f":"A2*LN(C2)+(1-A2)*LN(D2)","v":0},{"$f":"$N$1*A2*(1-A2)","v":0},{"$f":"A2*LN(A2)+(1-A2)*LN(1-A2)+A2*LN(C2)+(1-A2)*LN(D2)","v":{"$error":"#NUM!"}},null,"xLLE","yLLE",null,"alpha12",3]
[0.01,{"$f":"YF(C3,D3,$N$2,A3)","v":0.36435592706094128},{"$f":"Gamma1PorterF($N$1,A3)","v":18.92152191744692},{"$f":"Gamma2PorterF($N$1,A3)","v":1.0003000450045003},{"$f":"C3/D3","v":18.915846312255031},{"$f":"A3*LN(C3)+(1-A3)*LN(D3)","v":2.9699999999999976E-2},{"$f":"$N$1*A3*(1-A3)","v":2.9699999999999997E-2},{"$f":"A3*LN(A3)+(1-A3)*LN(1-A3)+A3*LN(C3)+(1-A3)*LN(D3)","v":-2.6301534354847368E-2},null,7.0000000000000007E-2,0.74874365162984591,null,null,null,null,"Anleitung:","Werte in N1 oder N2 ändern",null,null,"Alle Grafiken werden automatisch generiert"]
[0.02,{"$f":"YF(C4,D4,$N$2,A4)","v":0.52168438724566879},17.83566313883647,1.0012007202880864,{"$f":"C4/D4","v":17.814273179612197},{"$f":"A4*LN(C4)+(1-A4)*LN(D4)","v":5.879999999999995E-2},5.8799999999999998E-2,{"$f":"A4*LN(A4)+(1-A4)*LN(1-A4)+A4*LN(C4)+(1-A4)*LN(D4)","v":-3.9239113279732049E-2},null,{"$f":"1-J3","v":0.92999999999999994},{"$f":"K3","v":0.74874365162984591}]
[0.03,0.608857807777481,16.822209375648974,1.0027036482827156,16.776850672139865,8.7300000000000086E-2,8.7299999999999989E-2,-4.7442168179766667E-2]
[0.04,0.66386332811558557,15.875864500175322,1.0048115384541396,15.7998429482604,0.11519999999999998,0.1152,-5.2744147734173005E-2,null,0]
[0.05,0.7014418559526685,14.991749253459909,1.0075281954445339,14.879731724872835,0.14249999999999993,0.14250000000000002,-5.6015243345872656E-2,null,1]
[0.06,0.72851018384581234,14.16536640679252,1.010858530520097,14.013203607733612,0.16919999999999996,0.16919999999999999,-5.7767522500604532E-2]
[7.0000000000000007E-2,0.74874365162984591,13.392568987985568,1.0148085763718544,13.197138159658353,0.19529999999999989,0.1953,-5.8338946921691587E-2]
[0.08,0.76427562201648169,12.66953129047014,1.0193855053321235,12.428596663577546,0.22080000000000002,0.2208,-5.7969371768587373E-2]
[0.09,0.7764292072617619,11.992722410241335,1.0245976510836627,11.704811539980856,0.24570000000000006,0.24570000000000003,-5.6837823097497985E-2]
[0.1,0.78606843994764464,11.358882080001457,1.0304545339535169,11.023176380641601,0.27000000000000007,0.27000000000000007,-5.508297339144811E-2]
[0.11,0.79378137617541711,10.764998591762339,1.0369668898990494,10.381236562731845,0.29369999999999996,0.29370000000000002,-5.2815336918666161E-2]
[0.12,0.79998204145261609,10.208288618922452,1.0441467033097327,9.7766804095289039,0.31680000000000008,0.31679999999999997,-5.012499127270955E-2]
[0.13,0.8049702999694599,9.6861787666493289,1.0520072437650141,9.2073308658822519,0.33930000000000005,0.33929999999999999,-4.7086706288603654E-2]
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{"sheet":"Makro","index":24,"n_rows":7,"n_cols":9,"rows_kept":7,"cut":false,"hidden":false,"merged":[]}
["Makro"]
[]
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{"sheet":"Masseinheiten","index":25,"n_rows":13,"n_cols":19,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["Masseinheiten umrechnen am Beispiel der Reynoldsgleichung"]
[]
["Variable","Wert","Maßeinheit","Umrechnungsfaktor","Wert in SI","SI-Einheiten","Listen-Adresse",null,null,"Einheitenliste"]
["Dichte",1000,"kg/m³",{"$f":"MasseinheitenF(C4,G4)","v":0},{"$f":"B4*D4","v":0},"kg/m³","J5"," ",null,"Dichte","Faktoren","Geschwindigkeit","Faktoren","Durchmesser","Faktoren","Dyn. Vis.","Faktoren","Masse"]
["Geschwindigkeit",10,"m/s",{"$f":"MasseinheitenF(C5,G5)","v":0},{"$f":"B5*D5","v":0},"m/s","L5",null,null,"kg/m³",1,"m/s",1,"m",1,"kg/m.s",1,"kg",1]
["Durchmesser",100,"mm",0,0,"m","N5",null,null,"g/cm³",1E-3,"km/h",{"$f":"1/3.6","v":0.27777777777777779},"dm",0.1,"g/m.s",1000,"g",1E-3]
["Dyn. Viskosität",1,"Pa.s",{"$f":"MasseinheitenF(C7,G7)","v":0},0,"kg/m.s","P5",null,null,"kg/dm³",1E-3,"m/min",{"$f":"1000/60","v":16.666666666666668},"cm",0.01,"kg/cm.s",100,"mg",9.9999999999999995E-7]
["Reynold",{"$f":"E4*E5*E6/E7","v":{"$error":"#DIV/0!"}},null,null,null,null,null,null,null,"g/dm³",1,"cm/s",{"$f":"1000/36","v":27.777777777777779},"mm",1E-3,"g/cm.s",0.1,"d. Pfund",0.5]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pa.s",1,"Zentner",50]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"N.s/m²",1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"mPa.s",1000]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"cP",1000]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"g/cm.s",10]

{"sheet":"Matrix","index":26,"n_rows":32,"n_cols":18,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Matrixmultiplikation mit MMULT und manuel"]
[null,null,"Matrix a"]
[" ",null,"Spalte k=1","Spalte k=2","Spalte k=3",null,null,"Matrixregel:",null,null,null,null,null,null,null,null,{"$f":"MMULT(C4:E5,C8:D10)","v":12},-6]
["Zeile i=1",null,1,2,3,null,null,null,null,null,null,null,null,null,null,null,39,-12]
["Zeiel i=2",null,4,5,6]
[]
[null,null,"Matrix b"," "]
["Zeile i=1",null,6,-1," "]
["Zeiel i=2",null,3,2," "]
["Zeiel i=3",null,0,-3]
[]
["Zeile i=1",null,{"$f":"MMULT(C4:E5,C8:D10)","v":12},-6]
["Zeile i=2",null,39,-12]
[]
["Formel mmult in C12 eintragen. C12:D13 markieren"]
["F2, STRG+UMSCHALT+EINGABE"]
[]
[]
[]
[]
["Formel",null,null,null,null,"i= Zeile","j=Spalte für c",null,"Schema nach Falk"]
["Matrixregel beachten ",null,null,null,null,"k=Spalte für a und b",null,null,null,null,"b11","b12"]
[null,null,null,null,null,"n = kmax",null,null,null,null,"b21","b22"]
[null,null,null,null,null,null,null,null,null,null,"b31","b32"]
[null,null,null,null,null,null,null,"a11","a12","a13","c11","c12"]
[null,null,null,null,null,null,null,"a21","a22","a23","c21","c22"]
[]
[]
[]
["Rechenregel"]
[null,null,"c11 = a11*b11+a21*b21+a23*b32",null,null,{"$f":"C4*C8+D4*C9+E4*C10","v":12}," ","c12=a11*b12+a12*b22+a13*b32",null,null,{"$f":"C4*D8+D4*D9+E4*D10","v":-6}]
[null,null,"c21=a21*b11+a22*b21+a23*b31",null,null,{"$f":"C5*C8+D5*C9+E5*C10","v":39},null,"c22=a21*b12+a22*b22+a23*b32",null,null,{"$f":"C5*D8+D5*D9+E5*D10","v":-12}]

{"sheet":"Menüs","index":27,"n_rows":13,"n_cols":8,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["1. Start des Add-Ins \"Menuleiste\""]
[]
[]
[1,"J",1,10,9.4781700000000002E-9,"MMBtu",9.4781700000000002E-10,10]
[]
["2. Add-Ins \"User\""]
[]
[]
["3. Add-Ins, User, Menü anklicken"]
[]
["4. Es erscheint:"]
[]
["5. Makro \"Menulöschen\""]

{"sheet":"Mischung","index":28,"n_rows":41,"n_cols":16,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["Konzentrationsberechnung von Gemischen "]
["1. Datenzeile:",37,null,"<---"]
[]
["Mischen1"]
["Lösung","Menge","Konz. %"]
[1,10,{"$f":"B6/$B$16*100","v":2.604166666666667}]
[2,50,{"$f":"B7/$B$16*100","v":13.020833333333334}]
[3,80,20.833333333333336]
[4,12,3.125]
[5,45,11.71875]
[6,99,25.78125]
[7,1,0.26041666666666663]
[8,25,6.510416666666667]
[9,57,14.84375]
[10,5,1.3020833333333335]
["Summe:",{"$f":"SUM(B6:B15)","v":384}]
[null,null,null,null,null,null,null,null,null,null,null,"P41 "]
["Mischungsmengen2 berechnen",null,null,null,null,null,null,null,null,"Mischen2"]
[null,"Grad",2,null,null,null,null,null,null,"Lösung","L1","L2","mi [kg]","xGemisch"]
[null,"Konz. der 2 Lösungen",null,"Erg. mLi","mi [kg]","xGemisch",null,null,null,"mi [kg]",600,400,{"$f":"SUM(K20:L20)","v":1000},{"$f":"M20","v":1000}]
[null,0.05,0.1,599.99999999999977,{"$f":"F21*$F$23","v":70},7.0000000000000007E-2,null,null,null,"x1,i",0.05,0.1,{"$f":"$K$20*K21+$L$20*L21","v":70},{"$f":"M21/$N$20","v":7.0000000000000007E-2}]
[null,{"$f":"1-B21","v":0.95},{"$f":"1-C21","v":0.9},399.99999999999989,{"$f":"F22*$F$23","v":929.99999999999989},{"$f":"1-F21","v":0.92999999999999994},null,null,null,"x2,i",{"$f":"1-K21","v":0.95},{"$f":"1-L21","v":0.9},{"$f":"$K$20*K22+$L$20*L22","v":930},{"$f":"1-N21","v":0.92999999999999994}]
[null,null,null,null,"mges:",1000,null,null,null,null,null,null,{"$f":"SUM(M21:M22)","v":1000},{"$f":"SUM(N21:N22)","v":1}]
[]
[]
["Mischungsmengen3 berechnen",null,null,null,null,null,null,null,null,"Mischen3"]
[null,"Grad",3,null,null,null,null,null,null,"Lösung","L1","L2","L3","mi [kg]","xGemisch"]
[null,"Konzentrationen der 3 Lösungen",null,null,"Erg. mLi","mi [kg]","xGemisch",null,null,"mi [kg]",22,110,88,{"$f":"SUM(K28:M28)","v":220},{"$f":"N28","v":220}]
[null,0.1,0.3,0.6,22,{"$f":"G29*$G$32","v":88},0.4,null,null,"x1,i",0.1,0.3,{"$f":"1-K29-L29","v":0.60000000000000009},88,{"$f":"N29/$O$28","v":0.4}]
[null,0.3,0.4,0.3,110.00000000000006,{"$f":"G30*$G$32","v":77},0.35,null,null,"x2,i",0.3,0.4,{"$f":"1-K30-L30","v":0.29999999999999993},{"$f":"$K$28*K30+$L$28*L30+$M$28*M30","v":77},{"$f":"N30/$O$28","v":0.35}]
[null,0.6,0.3,0.1,88.000000000000014,{"$f":"G31*$G$32","v":55},0.25,null,null,"x3,i",{"$f":"1-K29-K30","v":0.60000000000000009},{"$f":"1-L29-L30","v":0.29999999999999993},{"$f":"1-M29-M30","v":9.9999999999999978E-2},55,{"$f":"N31/$O$28","v":0.25}]
[null,null,null,null,{"$f":"SUM(E29:E31)","v":220.00000000000006},"mges:",220,null,null,null,null,null,null,{"$f":"SUM(N29:N31)","v":220},{"$f":"SUM(O29:O31)","v":1}]
[]
["Mischungsmengen4 berechnen",null,null,null,null,null,null,null,null,"Mischen4"]
[null,"Grad",4,null,null,null,null,null,null,"Lösung","L1","L2","L3","L4","mi [kg]","xGemisch"]
[null,"Konzentrationen der 4 Lösungen ",null,null,null,"Erg. mLi","mi [kg]","xGemisch",null,"mi [kg]",20,110,90,50,{"$f":"SUM(K36:N36)","v":270},{"$f":"O36","v":270}]
["x1,i",0.17,0.39,0.45,0.33,22.000000000000114,{"$f":"$G$41*H37","v":102.74000000000001},0.38051851851851853,null,"x1,i",0.17,0.39,0.45,0.33,{"$f":"$K$28*K37+$L$28*L37+$M$28*M37+$N$36*N37","v":102.74000000000001},{"$f":"O37/$O$36","v":0.38051851851851853}]
["x2,i",0.3,0.42,0.28000000000000003,0.28999999999999998,109.99999999999996,{"$f":"$G$41*H38","v":91.94},0.3405185185185185,null,"x2,i",0.3,0.42,{"$f":"1-K38-L38","v":0.27999999999999997},0.28999999999999998,{"$f":"$K$28*K38+$L$28*L38+$M$28*M38+$N$36*N38","v":91.94},{"$f":"O38/$O$36","v":0.3405185185185185}]
["x3,i",0.15,0.05,0.12,0.21,87.999999999999957,29.86,0.11059259259259259,null,"x3,i",0.15,0.05,0.12,0.21,{"$f":"$K$28*K39+$L$28*L39+$M$28*M39+$N$36*N39","v":29.86},{"$f":"O39/$O$36","v":0.11059259259259259}]
["x4,i",0.38,0.14000000000000001,0.15,0.17,49.999999999999858,45.460000000000022,{"$f":"1-H37-H38-H39","v":0.16837037037037045},null,"x4,i",{"$f":"1-K37-K38-K39","v":0.38},{"$f":"1-L37-L38-L39","v":0.14000000000000001},0.15000000000000008,0.16999999999999996,{"$f":"$K$28*K40+$L$28*L40+$M$28*M40+$N$36*N40","v":45.460000000000008},{"$f":"O40/$O$36","v":0.16837037037037039}]
[null,null,null,null,null,"mges:",270,{"$f":"SUM(H37:H40)","v":1},null,null,null,null,null,null,{"$f":"SUM(O37:O40)","v":270},1]

{"sheet":"Molekül","index":29,"n_rows":72,"n_cols":45,"rows_kept":72,"cut":false,"hidden":false,"merged":[]}
["Modellierung und Potentialberechnung des Wassermoleküls",null,null,null,null,null,null,null,null,10,null,null,null,null,null,null,null,null,null,20,null,null,null,null,null,null,null,null,null,30]
[]
[null,"Kartesisch [pm]",null,null,null,null,"Kartesisch aktuell [pm]",null,null,"Polar",null,"Res.","Winkel",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Grad","Matrix",null,null,null,"x',y',z'"]
["Nr","x0","y0","z0","r","Ladung","x","y","z","phi","theta",null,"x-Achse (alpha)",30,null,null,null,null,null,"F",null," ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,1,0,0,1,{"$f":"MMULT(AO4:AQ6,AR4:AR6)","v":1}]
[1,0,-0.58709999999999996,0.75749999999999995,{"$f":"SQRT(B5*B5+C5*C5+D5*D5)","v":0.95838022725847172},1,{"$f":"DrehungxyzF(B5,C5,D5,$N$4,$N$6,$N$8,1)","v":0.34632662135953896},{"$f":"DrehungxyzF(B5,C5,D5,$N$4,$N$6,$N$8,2)","v":-0.34970893915832191},{"$f":"DrehungxyzF(B5,C5,D5,$N$4,$N$6,$N$8,3)","v":0.82234675728092199},{"$f":"PhiF(H5,G5)","v":-45.278420974887773},{"$f":"ThetaF(I5,E5)","v":30.900661621513443},null," ",null,null,null,null,null,null,{"$f":"CoulombF(F5,$N$12,G5,H5,I5,$N$10)","v":7.802895279082502E-16},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AN4/180*PI()","v":0.3490658503988659},0,{"$f":"COS(AN5)","v":0.93969262078590843},{"$f":"SIN(AN5)","v":0.34202014332566871},1.5,2.0935792178302002]
[2,0,-0.29354999999999998,0.37874999999999998,{"$f":"SQRT(B6*B6+C6*C6+D6*D6)","v":0.47919011362923586},-2,0.17316331067976948,-0.17485446957916095,0.411173378640461,{"$f":"PhiF(H6,G6)","v":-45.278420857337977},{"$f":"ThetaF(I6,E6)","v":30.900661721402564},null,"y-Achse (beta)",30,null,null,null,null,null,{"$f":"CoulombF(F6,$N$12,G6,H6,I6,$N$10)","v":-2.5868253708902657E-15},null,null,null,null,null,null,null,null,"alpha","SF","Beta","SF","Gamma","SF",null,null,null,null,null,null,0,{"$f":"-SIN(AN5)","v":-0.34202014332566871},{"$f":"COS(AN5)","v":0.93969262078590843},2,1.3663550265833138]
[3,0,0,0,0,8,0,0,0,0,90,null," "," ",null,null,null,null,null,1.6341825424393017E-14,null,null,null,null,null,null,null,null,36,-8.6841675158913015E-2,36,-0.20703930328644701,36,-8.566354235536526E-2]
[4,0,0.5,0,0.5,-4,0.10825317547305484,0.43750000000000006,-0.21650635094610965,76.102113182586194,{"$f":"ThetaF(I8,E8)","v":115.65890619339747},null,"z -Achse(gamma)",30,null,null,null,null,null,-2.1789100565857361E-14,null,null,null,null,null,null,null,null,72,0.54587755768077884,72,-0.45865636880233601,72,0.53795104255047976,null,null,null,null,null,30,{"$f":"COS(AN9)","v":0.86602540378443871},0,{"$f":"SIN(AN9)","v":0.49999999999999994},{"$f":"AS4","v":1},{"$f":"MMULT(AO8:AQ10,AR8:AR10)","v":1.5492029170760955}]
[5,0,-0.58709999999999996,-0.75749999999999995,0.95838022725847172,1,-0.60054837864046084,-0.67771606084167801,-0.31390324271907816,-48.454702171591755,109.11923916855783,null,null,null,null,null,null,null,null,6.2393864070353385E-16,null,null,null,null,null,null,null,null,108,1.2445923123303384,108,-0.45865636880233601,108,1.1197989503127934,null,null,null,null,null,{"$f":"AN8/180*PI()","v":0.52359877559829882},0,1,0,{"$f":"AS5","v":2.0935792178302002},2.0935792178302002]
[6,0,-0.29354999999999998,-0.37874999999999998,0.47919011362923586,-2,-0.30027418932023042,-0.33885803042083901,-0.15695162135953908,-48.454702100187056,109.1192391478333,null,"Abstand der Referenzladung auf y-Achse [pm]",1,null,null,null,null,null,-2.1419663061222933E-15,null,null,null,null,null,null,null,null,144,1.8001397045730296,144,-0.20703930328644762,144,1.7086671868543171,null,null,null,null,null,null,{"$f":"-SIN(AN9)","v":-0.49999999999999994},0,{"$f":"COS(AN9)","v":0.86602540378443871},1.3663550265833138,0.68329816360971174]
["Nullpunkt",0,0,0,0,null,0,0,0,0,90,null,null,null,null,null,null,null,"S",{"$f":"SUM(T5:T10)","v":-8.7718386498651194E-15},null,null,null,null,null,null,null,null,180,1.6615470579415994,180,0.1246629656283073,180,1.9821883513361185]
["Reserve"," "," "," "," "," "," "," "," "," "," ",null,"Ladung",{"$f":"P12-10","v":1},null,11,null,null," "," ",null,null,null,null,null,null,null,null,216,1.6832233084422252,216,0.39237297107178681,216,1.602017194279884,null,null,null,null,null,40,{"$f":"COS(AN13)","v":0.76604444311897801},{"$f":"-SIN(AN13)","v":-0.64278760968653925},0,{"$f":"AS8","v":1.5492029170760955},{"$f":"MMULT(AO12:AQ14,AR12:AR14)","v":-0.15896849522863499}]
[" "," "," "," ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,252,1.7749509262834235,252,0.54210863089031269,252,1.4038316463463947,null,null,null,null,null,{"$f":"AN12/180*PI()","v":0.69813170079773179},{"$f":"SIN(AN13)","v":0.64278760968653925},{"$f":"COS(AN13)","v":0.76604444311897801},0,{"$f":"AS9","v":2.0935792178302002},2.5995831660349586]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,324,0.47177494155394623,324,0.39237297107178681,324,0.47030397972819959]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,360,-0.13046477630190978,360,0.1246629656283065,360,-0.13322634579899675]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Blasengröße"]
[null,"x","y","z",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Definitionen nach Bartsch:"]
[null,{"$f":"1+G5","v":1.3463266213595388},{"$f":"1+H5","v":0.65029106084167809},1.822346757280922,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[null,{"$f":"1+G6","v":1.1731633106797694},0.82514553042083905,1.411173378640461]
[null,1,1,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"z","               P (r;phi;teta)"]
[null,1.1082531754730549,1.4375,0.78349364905389041,null,null," "]
[null,0.39945162135953916,0.32228393915832199,0.68609675728092179,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[null,0.69972581067976958,0.66114196957916094,0.84304837864046089,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"teta"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,null,null,"y"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"phi"," "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null," "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"winkel alpha dreht sich um die x-Achse"]
[null,null,"winkel theta dreht sich um die y-Achse"]
[null,null,"winkel phi dreht sich um die z-Achse"]

{"sheet":"Molgewicht","index":30,"n_rows":13,"n_cols":28,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
["Berechnen des Molgewichts aus der Summenformel",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Atomtabelle"]
["Beispiele",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Nr.","Atom ","Atomgewicht"]
["Formel","MG [g/mol]","Name",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,"C",12]
["CCl4",{"$f":"MolgewichtF(A4)","v":0},"Tetrachlorkohlenstoff",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,"H",1]
["H2O",0,"Wasser",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,"S",32]
["C6H6",0,"Benzol",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,"N",14]
["C2H6O",0,"Ethanol, Methylether",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,"O",16]
["C2H5OH",0,"Ethanol, Methylether",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,"Cl",35.5]
["CH3OCH3",0,"Methylether"]
["C2H5OC2H5",0,"Ethylether"]
["Cl2CCCl2",0,"Tetrachlorethylen"]
["C6H5CH3",0,"Toluol"]
["C10H8",0,"Naphthalin"]

{"sheet":"Newton","index":31,"n_rows":28,"n_cols":3,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Nullstellensuche nach dem Newton-Raphson Verfahren"]
[]
["a",1]
["b",1]
["y0",10]
[null," "]
["Lfd Nr.","x","p"]
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[null," "]

{"sheet":"Polymer","index":32,"n_rows":207,"n_cols":7,"rows_kept":207,"cut":false,"hidden":false,"merged":[]}
["Polymerisation und die Poisson- sowie Schulz-Flory-Verteilung"]
[]
["α (U)",null,0.99]
["ν",null,100]
["mode",null,0]
[null,null,"Poisson","Poisson","Poisson","Schulz-Flory","Schulz-Flory"]
["P","P-1","wp","Excel","VBA","wp","VBA"]
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{"sheet":"Polynom","index":33,"n_rows":5,"n_cols":3,"rows_kept":5,"cut":false,"hidden":false,"merged":[]}
["Polynom in Excel und in VBA"]
[]
["Zelle:",1,{"$f":"1+2*B3+3*B3*B3","v":6}]
["VBA:",1,{"$f":"Polynomf(B4)","v":6}]
[null," "," "]

{"sheet":"Regression","index":34,"n_rows":28,"n_cols":15,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Lineare Regression aus Meßdaten"]
["y = a + bx"]
["a",2]
["b",3]
[" "," "]
["Ldf Nr.","x","y","Fehler","y_ideal","y-Regr",null,null,null,null,null,null,null,"ySolver","(y - ySolver)2"]
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[2,2,9.34,1.34,{"$f":"$B$3+$B$4*B8","v":8},{"$f":"$I$25+$I$26*B8","v":9.826751879699243},null,null,null,null,null,null,null,{"$f":"$L$25+$L$26*B8","v":9.8267516744624821},{"$f":"(C8-N8)^2","v":0.23692719259203029}]
[3,3,15.59,4.59,11,12.85507518796992,null,null,null,null,null,null,null,12.855074881270097,7.4798154050597736]
[4,4,12.45,-1.55,14,15.883398496240599,null,null,null,null,null,null,null,15.883398088077714,11.788222431215704]
[5,5,21.81,4.8099999999999996,17,18.911721804511277,null,null,null,null,null,null,null,18.911721294885332,8.400019452521148]
[6,6,21.53,1.53,20,21.940045112781952,null,null,null,null,null,null,null,21.940044501692945,0.16813649336861489]
[7,7,20.32,-2.68,23,24.968368421052631,null,null,null,null,null,null,null,24.968367708500558,21.607322353430728]
[8,8,27.55,1.55,26,27.99669172932331,null,null,null,null,null,null,null,27.996690915308179,0.19953277381885781]
[9,9,28.91,-0.09,29,31.025015037593988,null,null,null,null,null,null,null,31.025014122115792,4.4732847367492328]
[10,10,40.909999999999997,8.91,32,34.053338345864667,null,null,null,null,null,null,null,34.053337328923412,47.013822984935082]
[11,11,35.72,0.72,35,37.081661654135345,null,null,null,null,null,null,null,37.081660535731025,1.8541194145673054]
[12,12,32.11,-5.89,38,40.109984962406017,null,null,null,null,null,null,null,40.109983742538638,63.99973988088253]
[13,13,48.980000000000004,7.98,41,43.138308270676696,null,null,null,null,null,null,null,43.138306949346259,34.125377698056262]
[14,14,49.29,5.29,44,46.166631578947374,null,null,null,null,null,null,null,46.166630156153872,9.7554391814473824]
[15,15,46.95,-0.05,47,49.194954887218053,null,null,null,null,null,null,null,49.194953362961492,5.0398156018720996]
[16,16,55.9,5.9,50,52.223278195488732,null,null,null,null,null,null,null,52.223276569769105,13.518295182408828]
[17,17,62.01,9.01,53,55.25160150375941,null,null,null,null,null,null,null,55.251599776576718,45.675973579967838]
[18,18,48.96,-7.04,56,58.279924812030089,null,"Regression mit VBA",null,null,"Solver",null,null,58.279922983384338,86.860964416215609]
[19,19,66.09,7.09,59,61.308248120300767,null,"a=",3.7701052631578875,null,"a=",3.7701052608472505,null,61.308246190191952,22.86516949761382]
[20,20,59.78,-2.2200000000000002,62,64.336571428571446,null,"b=",3.0283233082706777,null,"b=",3.0283232068076158,null,64.336569396999565,20.762324669672967]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(O7:O26)","v":405.9479054887513}]
[null,null,null,null,null,null," "]

{"sheet":"RungeKutta","index":35,"n_rows":19,"n_cols":8,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Runge Kutta als Funktion: D5 anklicken, auf fx klicken"]
["Vergleich mit Euler und Theorie"]
["A = x0",0]
["E =Xende",1]
["y0",1,null,{"$f":"RungeK4(B3,B4,B5,B6)","v":1.6487206103294629},"Runge-Kutta","Abweichung",{"$f":"($D$6-D5)/$D$6*100","v":4.0053505525618434E-5},"%"]
["2^N Schritte",3,{"$f":"2^3","v":8},{"$f":"EXP(0.5)","v":1.6487212707001282},"theoretisch"]
[]
[]
["Euler:"]
["x","y","Δx","Funktion","Nr. "]
[0,1,0.125,{"$f":"A11*B11","v":0},0]
[{"$f":"A11+C11","v":0.125},{"$f":"B11+D11*$C$11","v":1},0.125,0.125,1]
[0.25,1.015625,0.125,0.25390625,2]
[0.375,1.04736328125,0.125,0.39276123046875,3]
[0.5,1.0964584350585937,0.125,0.54822921752929688,4]
[0.625,1.1649870872497559,0.125,0.72811692953109741,5]
[0.75,1.256001703441143,0.125,0.94200127758085728,6]
[0.875,1.3737518631387502,0.125,1.2020328802464064,7]
[1,1.524005973169551,0.125,1.524005973169551,8,"Abweichung",{"$f":"($D$6-D19)/$D$6*100","v":7.5643651687478348},"%"]

{"sheet":"Simpson","index":36,"n_rows":15,"n_cols":9,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Integration nach Simpson. Anwendung in I7, Fx anklicken"]
[]
["Lfd. Nr.","x","Rechteck",null,"Trapez",null,null,"VBA-Lösung"]
[1,1,{"$f":"B4^2*0.2","v":0.2},null,1,0,null,"Anfang",1]
[2,1.2,0.28799999999999998,null,{"$f":"(B5+B4)/2","v":1.1000000000000001},{"$f":"E5^2*0.2","v":0.24200000000000005},null,"Ende",3]
[3,1.4,0.39199999999999996,null,{"$f":"(B6+B5)/2","v":1.2999999999999998},{"$f":"E6^2*0.2","v":0.33799999999999991},null,"n",10]
[4,1.6,0.51200000000000012,null,1.5,0.45,null,"Integral",{"$f":"IntSimpF(I5,I4,I6)","v":8.6666666666666661}]
[5,1.8,0.64800000000000013,null,1.7000000000000002,0.57800000000000018]
[6,2,0.8,null,1.9,0.72199999999999998]
[7,2.2000000000000002,0.96800000000000019,null,2.1,0.88200000000000012]
[8,2.4,1.1519999999999999,null,2.2999999999999998,1.0579999999999998]
[9,2.6,1.3520000000000003,null,2.5,1.25]
[10,2.8,1.5679999999999998,null,2.7,1.4580000000000002]
[11,3,null,null,2.9,1.6820000000000002]
["Summe:",null,{"$f":"SUM(C4:C13)","v":7.88},null,null,{"$f":"SUM(F5:F14)","v":8.66}]

{"sheet":"SLE","index":37,"n_rows":107,"n_cols":10,"rows_kept":107,"cut":false,"hidden":false,"merged":[]}
["Fest-Flüssiggleichgewicht"]
["Stoff",null,"Tm [°C]","hm [J/mol]"]
[1,"1,2-Dichlorethan",-35.5,8750.4]
[2,"Benzol",5.53,9958.7000000000007]
[]
["x1","T1[°C]","T2 [°C]","T2-T1",null,"T","T [K]","x2","1-x2","x1"]
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[0.19,-100.31501498344599,-7.4945999814290758,-7.4945999814290758]
[0.2,-98.846749668715347,{"$f":"SLETF(A27,$D$3,$C$3,$D$4,$C$4,2)","v":-8.2245348648000345},-8.2245348648000345]
[0.21,{"$f":"SLETF(A28,$D$3,$C$3,$D$4,$C$4,1)","v":-97.426797620077878},{"$f":"SLETF(A28,$D$3,$C$3,$D$4,$C$4,2)","v":-8.959575647882275},{"$f":"SLETF(A28,$D$3,$C$3,$D$4,$C$4,0)","v":-8.959575647882275}]
[0.22,-96.051200101524586,-9.6998348666514858,-9.6998348666514858]
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[0.32,-84.133330490003999,-17.4172962901483,-17.4172962901483]
[0.33,-83.082906210605302,-18.223671545562297,-18.223671545562297]
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[0.35,-81.041465590938742,-19.857432433648057,-19.857432433648057]
[0.36,-80.048487869855109,{"$f":"SLETF(A43,$D$3,$C$3,$D$4,$C$4,2)","v":-20.685192250769006},-20.685192250769006]
[0.37,{"$f":"SLETF(A44,$D$3,$C$3,$D$4,$C$4,1)","v":-79.072821688998232},{"$f":"SLETF(A44,$D$3,$C$3,$D$4,$C$4,2)","v":-21.520467801688653},{"$f":"SLETF(A44,$D$3,$C$3,$D$4,$C$4,0)","v":-21.520467801688653}]
[0.38,-78.113661201749295,-22.363466939271234,-22.363466939271234]
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{"sheet":"Steigung","index":38,"n_rows":34,"n_cols":9,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Steigung und Minimum einer Funktion, numerisch"]
[]
["a",1]
["b",2]
["c",0.5]
[" "]
[]
["Lfd. Nr.","x","y","1. Ableitung","2. Ableitung","y'","y''"]
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[5,5,5.4721359549995796,0.44721359549995793,-4.4721359549995794E-2,0.44721381908311741,-4.4721415462845471E-2]
[6,6,5.8989794855663558,0.40824829046386302,-3.4020690871988585E-2,0.40824843222799245,-3.4020720406260807E-2]
[7,7,6.2915026221291814,0.37796447300922725,-2.6997462357801944E-2,0.37796456939395284,-2.6997479573765304E-2]
[8,8,6.6568542494923806,0.35355339059327379,-2.2097086912079612E-2,0.35355345951393247,-2.2097097709774971E-2]
[9,9,7,0.33333333333333331,-1.8518518518518517E-2,0.33333338492957409,-1.8518525655963458E-2]
[10,10,7.324555320336759,0.31622776601683794,-1.5811388300841896E-2,0.31622780539328232,-1.5811393241165206E-2]
[]
["Funktionswerte an der Stelle x=1",null,null,null," "," ",null,"Funktion","Differenz"]
["x1=",0.99,"y1=",{"$f":"Steigf($B$3,$B$4,$B$5,B21)","v":2.9899748742132397},"a=",{"$f":"G26","v":1.7499796865395183},"y'=",{"$f":"G27+2*G28","v":1.0000125005462905},{"$f":"(D23-D21)/(B23-B21)","v":1.0000125005469087}]
["x2=",1,"y2=",{"$f":"Steigf($B$3,$B$4,$B$5,B22)","v":3},"b=",{"$f":"G27","v":1.5000281263746729},"y''=",{"$f":"2*G28","v":-0.50001562582838233},{"$f":"(D23-2*D22+D21)/((0.5*(B23-B21))^2)","v":-0.50001562582391212}]
["x3=",1.01,"y3=",3.0099751242241779,"c=",-0.25000781291419116]
[]
[null,"Große Matrix",null,null,"Kleine Matrix","Matrix","VBA","y-Kontrolle"]
[1,1,{"$f":"B21","v":0.99},{"$f":"C26^2","v":0.98009999999999997},{"$f":"D21","v":2.9899748742132397},{"$f":"MMULT(MINVERSE(B26:D28),E26:E28)","v":1.7499796865395183},1.7499796865395183,{"$f":"$F$26+$F$27*C26+$F$28*D26","v":2.9899748742150285}," "]
[2,1,{"$f":"B22","v":1},{"$f":"C27^2","v":1},{"$f":"D22","v":3},1.5000281263746729,1.5000281263746729,{"$f":"$F$26+$F$27*C27+$F$28*D27","v":3.000000000001819}," "]
[3,1,1.01,1.0201,{"$f":"D23","v":3.0099751242241779},-0.25000781291237217,-0.25000781291419116,{"$f":"$F$26+$F$27*C28+$F$28*D28","v":3.0099751242260271}," "]
[]
["Inverse Matrix",5050.0000000005211,-10050.000000001042,5000.0000000005211]
[null,-9999.0000000010423,20000.000000002085,-10000.000000001042]
[null,4950.0000000005211,-9950.0000000010423,5000.0000000005211]
[]
[" "]

{"sheet":"Verbrennung","index":39,"n_rows":17,"n_cols":12,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["Verbrennungsberechnung"]
["Eingabe Brennstoff",null,null,null,"Ergebnisse Luft",null,null,"Ergebnisse Rauchgas",null,null,"Sonstiges"]
["Auswahl",{"$f":"IF(B4=1,\"Formel\",\"Gew. %\")","v":"Formel"},{"$f":"IF(C10<>100,\"Fehler\",\"OK\")","v":"OK"},null," "," "]
["Elemente",1,0,"kg","O2-Bedarf [kg]",373.33333333333337,null,"Rauchgas ","kg",null,"Brennstoff"," "]
["C",2,80,80,"Luftbedarf [kg]",1777.7777777777781,null,"CO2 ",293.33333333333331," ","Molgewicht [kmol/kg]",30]
["H",6,20,20,null,null,null,"H2O",180]
["S",null,null,0," ",null," ","SO2",0]
["N",null,null,0,null,null,null,"N2",1404.4444444444448]
["O",null,null,0,null,null,null,"Gesamt",{"$f":"SUM(I5:I8)","v":1877.7777777777781}]
["Menge [kg]",100,{"$f":"SUM(C5:C9)","v":100},{"$f":"SUM(D5:D9)","v":100}]
["Bildungsenthalpie [kJ/kg]",-2788.49,null,null,null,null,null,"Heizwert [kJ/kg]",-47602.143333333341]
[]
[]
[]
["Modul","Verbrennung"]
[]
[null," "]

{"sheet":"VLE","index":40,"n_rows":41,"n_cols":9,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["Dampf-Flüssiggleichgewicht"]
[]
["Verdampfungsgrad","D/G=",0.8," ","Konvergenz",7.1946463583180258E-5,null,"Schritte:",100]
["Stoff"," α","xi0","xi","α*x","yi",null,"K=yi/xi","xi,R"]
[1,5,0.05,2.6850283973514615E-2,{"$f":"B5*D5","v":0.13425141986757308},{"$f":"E5/$E$15","v":5.4070670205338567E-2},{"$f":"IF(((F5-D5)>0),\"y ist größer\",\"y ist kleiner\")","v":"y ist größer"},{"$f":"F5/D5","v":2.0137839234279387},{"$f":"(C5-$C$3*F5)/(1-$C$3)","v":3.3717319178645726E-2}]
[2,4.8,0.06,3.4199685259610466E-2,0.16415848924613022,6.611594530761504E-2,{"$f":"IF(((F6-D6)>0),\"y ist größer\",\"y ist kleiner\")","v":"y ist größer"},{"$f":"F6/D6","v":1.933232566490821},{"$f":"(C6-$C$3*F6)/(1-$C$3)","v":3.5536218769539822E-2}]
[3,4.2,0.1,6.4654556138482477E-2,0.27154913578162643,0.10936825681155794,"y ist größer",1.6915784956794686,6.2526972753768215E-2]
[4,3.9,0.2,0.13772691669541948,0.53713497511213593,0.21633475551833706,"y ist größer",1.570751460273792,0.13466097792665183]
[5,3.5,0.03,2.2641516992604489E-2,7.9245309474115705E-2,3.1916586045209187E-2,"y ist größer",1.4096487463995571,2.2333655819163238E-2]
[6,3.2,0.1,8.1363619214498167E-2,0.26036358148639416,0.10486319892868413,"y ist größer",1.2888217109938809,8.0547204285263491E-2]
[7,2.9,0.14499999999999999,0.12799416294520802,0.37118307254110322,0.149496500826372,"y ist größer",1.1679946755882042,0.12701399669451194]
[8,1.7,0.04,5.3535439629274137E-2,9.1010247369766026E-2,3.6654994604086936E-2,"y ist kleiner",0.68468653396549917,5.3380021583652265E-2]
[9,1.4,0.2,0.30739495180438059,0.43035293252613283,0.17332756338423896,"y ist kleiner",0.56385949855982287,0.3066897464630442]
[10,1,{"$f":"1-SUM(C5:C13)","v":7.4999999999999956E-2},0.14363886734700743,0.14363886734700743,5.7851528368560369E-2,"y ist kleiner",0.40275678468558773,0.1435938865257583]
[null,null,null,{"$f":"SUM(D5:D14)","v":0.99999999999999978},{"$f":"SUM(E5:E14)","v":2.4828880307519845},{"$f":"SUM(F5:F14)","v":1.0000000000000002},null,null,{"$f":"SUM(I5:I14)","v":0.99999999999999922}]
[" ",null,{"$f":"IF(C14<0,\"Fehler: Summe xi >1\",\"OK\")","v":"OK"}]
[]
[]
[" α1",3]
[" ","x1","x2"," αx1"," Σαx","y1","Diagonale"]
[0,0,{"$f":"1-B21","v":1},{"$f":"$B$19*B21","v":0},{"$f":"D21+C21","v":1},0,{"$f":"B21","v":0}]
[1,0.05,{"$f":"1-B22","v":0.95},{"$f":"$B$19*B22","v":0.15000000000000002},{"$f":"D22+C22","v":1.1000000000000001},{"$f":"D22/E22","v":0.13636363636363638},{"$f":"B22","v":0.05}]
[2,0.1,{"$f":"1-B23","v":0.9},{"$f":"$B$19*B23","v":0.30000000000000004},{"$f":"D23+C23","v":1.2000000000000002},{"$f":"D23/E23","v":0.25},0.1]
[3,0.15,{"$f":"1-B24","v":0.85},{"$f":"$B$19*B24","v":0.44999999999999996},{"$f":"D24+C24","v":1.2999999999999998},{"$f":"D24/E24","v":0.34615384615384615},0.15]
[4,0.2,0.8,0.60000000000000009,1.4000000000000001,0.4285714285714286,0.2]
[5,0.25,0.75,0.75,1.5,0.5,0.25]
[6,0.3,0.7,0.89999999999999991,1.5999999999999999,0.5625,0.3]
[7,0.35,0.65,1.0499999999999998,1.6999999999999997,0.61764705882352944,0.35]
[8,0.4,0.6,1.2000000000000002,1.8000000000000003,0.66666666666666663,0.4]
[9,0.45,0.55000000000000004,1.35,1.9000000000000001,0.71052631578947367,0.45]
[10,0.5,0.5,1.5,2,0.75,0.5]
[11,0.55000000000000004,0.44999999999999996,1.6500000000000001,2.1,0.7857142857142857,0.55000000000000004]
[12,0.6,0.4,1.7999999999999998,2.1999999999999997,0.81818181818181823,0.6]
[13,0.65,0.35,1.9500000000000002,2.3000000000000003,0.84782608695652173,0.65]
[14,0.7,0.30000000000000004,2.0999999999999996,2.3999999999999995,0.875,0.7]
[15,0.75,0.25,2.25,2.5,0.9,0.75]
[16,0.8,0.19999999999999996,2.4000000000000004,2.6000000000000005,0.92307692307692302,0.8]
[17,0.85,0.15000000000000002,2.5499999999999998,2.6999999999999997,0.94444444444444442,0.85]
[18,0.9,9.9999999999999978E-2,2.7,2.8000000000000003,0.9642857142857143,0.9]
[19,0.95,5.0000000000000044E-2,2.8499999999999996,2.8999999999999995,0.98275862068965525,0.95]
[20,1,0,3,3,1,1]

{"sheet":"WatStoff","index":41,"n_rows":85,"n_cols":14,"rows_kept":85,"cut":false,"hidden":false,"merged":[]}
["Wärme und Stoffaustausch"]
[]
["Wärmeaustauscher",null,null," "]
["k [W/m²K]",1000]
["A [m²]",250]
["A Anzahl",20]
["ΔA [m²]",{"$f":"B5/B6","v":12.5}]
["Strom 1",null,null,"Strom2"]
["m1 [kg/s]",100,null,"m2 [kg/s]",100]
["T1 [°C]",20,null,"T2  [°C]",90]
["Cp1 [J/kg/K]",4100,null,"Cp2 [J/kg/K]",2500]
[]
[]
["Lfd Nr.","A Summe %","T1 [°C]","Q1* [W]","T2 [°C]","Q2* [W]"," Δϑ [°C]","ΔQw*=k*ΔA*Δϑ [W]","ΔT1 [°C]","ΔT2 [°C]","Summe Q"]
[1,0,{"$f":"E10","v":90},0,20,0,{"$f":"C15-E15","v":70},{"$f":"$B$4*$B$7*G15","v":875000},{"$f":"-H15/($B$9*$B$11)","v":-2.1341463414634148},{"$f":"H15/($E$9*$E$11)","v":3.5},{"$f":"D15","v":0}]
[2,5,{"$f":"C15+I15","v":87.865853658536579},{"$f":"$B$9*$B$11*(C15-C16)","v":875000.00000000244},{"$f":"E15+J15","v":23.5},{"$f":"$E$9*$E$11*(E15-E16)","v":-875000},64.365853658536579,{"$f":"$B$4*$B$7*G16","v":804573.17073170724},{"$f":"-H16/($B$9*$B$11)","v":-1.9623735871505055},{"$f":"H16/($E$9*$E$11)","v":3.2182926829268288},{"$f":"D16","v":875000.00000000244}]
[3,10,85.90348007138607,{"$f":"$B$9*$B$11*(C16-C17)","v":804573.17073170876},{"$f":"E16+J16","v":26.71829268292683},{"$f":"$E$9*$E$11*(E16-E17)","v":-804573.17073170748},59.185187388459241,{"$f":"$B$4*$B$7*G17","v":739814.84235574049},{"$f":"-H17/($B$9*$B$11)","v":-1.8044264447700988},{"$f":"H17/($E$9*$E$11)","v":2.9592593694229619},{"$f":"K16+D17","v":1679573.1707317112}]
[4,15,84.099053626615969,739814.84235574142,29.677552052349792,-739814.84235574072,54.421501574266173,{"$f":"$B$4*$B$7*G18","v":680268.76967832714},{"$f":"-H18/($B$9*$B$11)","v":-1.6591921211666516},{"$f":"H18/($E$9*$E$11)","v":2.7210750787133087},{"$f":"K17+D18","v":2419388.0130874524}]
[5,20,82.439861505449315,680268.7696783283,32.398627131063101,-680268.76967832714,50.041234374386214,625515.42967982765,-1.5256473894629943,2.5020617187193106,3099656.7827657806]
[6,25,80.914214115986326,625515.42967982555,34.900688849782412,-625515.42967982776,46.013525266203914,575169.06582754897,-1.4028513800671927,2.300676263310196,3725172.212445606]
[7,30,79.511362735919136,575169.06582754804,37.201365113092606,-575169.06582754862,42.309997622826529,528874.9702853316,-1.2899389519154429,2.1154998811413264,4300341.2782731541]
[8,35,78.22142378400369,528874.97028533265,39.316864994233931,-528874.97028533125,38.904558789769759,486306.984872122,-1.1861145972490781,1.9452279394884879,4829216.2485584868]
[9,40,77.035309186754617,486306.98487212003,41.262092933722421,-486306.98487212241,35.773216253032196,447165.20316290244,-1.0906468369826889,1.7886608126516097,5315523.2334306072]
[10,45,75.944662349771932,447165.20316290099,43.050753746374028,-447165.20316290163,32.893908603397904,411173.85754247382,-1.0028630671767653,1.6446954301698953,5762688.4365935083]
[11,50,74.94179928259517,411173.85754247225,44.695449176543924,-411173.85754247417,30.246350106051246,378079.37632564059,-0.92214482030644052,1.5123175053025624,6173862.2941359803]
[12,55,74.019654462288727,378079.37632564147,46.207766681846486,-378079.37632564048,27.811887780442241,347648.59725552803,-0.84792340794031229,1.3905943890221122,6551941.6704616221]
[13,60,73.171731054348413,347648.59725552879,47.598361070868599,-347648.59725552809,25.573369983479814,319667.12479349767,-0.7796759141304821,1.2786684991739907,6899590.267717151]
[14,65,72.392055140217934,319667.12479349639,48.877029570042588,-319667.12479349726,23.515025570175347,293937.81962719181,-0.7169215112858337,1.1757512785087672,7219257.392510647]
[15,70,71.675133628932102,293937.81962719129,50.052780848551357,-293937.81962719245,21.622352780380744,270279.40975475928,-0.65921807257258358,1.0811176390190371,7513195.2121378379]
[16,75,71.015915556359516,270279.40975475998,51.133898487570391,-270279.40975475853,19.882017068789125,248525.21335986405,-0.60615905697527817,0.9941008534394562,7783474.6218925975]
[17,80,70.409756499384244,248525.21335986169,52.127999341009847,-248525.21335986388,18.281757158374397,228521.96447967997,-0.5573706450723902,0.91408785791871983,8031999.8352524592]
[18,85,69.852385854311848,228521.96447968238,53.04208719892857,-228521.96447968076,16.810298655383278,210128.73319229097,-0.51250910534705119,0.84051493276916389,8260521.7997321412]
[19,90,69.339876748964798,210128.73319229044,53.882602131697737,-210128.73319229187,15.457274617267061,193215.93271583825,-0.47125837247765429,0.77286373086335303,8470650.5329244323]
[20,95,68.868618376487149,193215.93271583624,54.655465862561087,-193215.93271583738,14.213152513926062,177664.40642407577,-0.4333278205465263,0.71065762569630309,8663866.4656402692]
[21,100,68.435290555940625,177664.40642407461,55.366123488257386,-177664.40642407487,13.069167067683239,0,0,0,8841530.8720643446]
[null,null,null,{"$f":"SUM(D15:D35)","v":8841530.8720643446},{"$f":"E35+J35","v":55.366123488257386},{"$f":"SUM(F15:F35)","v":-8841530.8720643464},null,{"$f":"SUM(H15:H35)","v":8841530.8720643502}," "," "]
["Mittlere Temperaturdifferenz "]
[" Δϑm[°C]",{"$f":"D36/(B4*B5)","v":35.366123488257379},null,null," "," "," "]
["LMTD",{"$f":"((C35-E35)-(C15-E15))/(LN((C35-E35)/(C15-E15)))","v":33.922950090166829}]
[]
["Stoffaustausch"]
["Mengen"]
["Feststoff [g]",null,1]
["Wassermenge [g]",null,5]
["Dichte [g/cm³]",null,1]
["Wasservolumen[cm³]",null,{"$f":"C44/1","v":5}]
["Zeitabschnitt Δt [s]",null,0.5]
[]
["Feststoffdaten"]
["Dichte [g/cm³]",null,2.16]
["V0 [cm³]",null,{"$f":"C43/C50","v":0.46296296296296291}]
["C0  [g/cm³]",null,0.26400000000000001]
["k [cm/s]",null,0.4]
[]
["Würfel"]
["d0 [cm]",null,{"$f":"C51^(1/3)","v":0.77359813893546314}]
["A0 [cm²]",null,{"$f":"6*C56*C56","v":3.5907244833864733}]
[]
["Kugel"]
["d0 [cm³]",null,{"$f":"(C51*6/PI())^(1/3)","v":0.9598039704949537}]
["A0 [cm²]",null,{"$f":"C60*C60*PI()","v":2.8941094881544696}]
[]
[]
["Lfd Nr.","t [s]","m_fest [g]","m_Lösung [g]","V_Lösung=Vw+Vf [cm³]","C Lösung [g_Feststoff/cm³_Lösung]","ΔC [g_Feststoff/cm³_Lösung]","dm*_fest [g/s]","dm_fest [g]","dV_fest [cm³]","V_fest [cm³]","d_Würfel [cm]","A_Würfel [cm²]","Konz. Lösung [g/cm³]"]
[1,0,{"$f":"C43","v":1},0,{"$f":"C46","v":5},0,{"$f":"$C$52-F65","v":0.26400000000000001},{"$f":"$C$53*C57*G65","v":0.37918050544561166},{"$f":"H65*$C$47","v":0.18959025272280583},{"$f":"I65/$C$50","v":8.7773265149447138E-2},{"$f":"C51-J65","v":0.37518969781351574},{"$f":"K65^(1/3)","v":0.72124636091810501},{"$f":"6*L65^2","v":3.1211778788256561},{"$f":"F65*100","v":0}]
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["nicht benötigt"]
[]
[]
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