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[]
[null,"問題4.5　発熱反応による温度変化を伴う反応 [VBA：数値積分、オイラー法]"]
[null,"　反応A → Bを回分操作の完全混合断熱リアクター（熱の出入りがない：q=0）で反応させる。反応物Aの物質収支と熱収支はそれぞれ次のように表せられる。\n\n　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　(4.19)\n\n　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　(4.20)\n\n反応速度式は次式で表わされる。\n\n　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　(4.21)\n\n　この反応は発熱反応である。なお，=1000 kg m-3，Cp=4180 J kg-1 K-1,　Hrxn=－88244 J mol-1，k0=6.2×104 m3 mol-1 min-1, 　Ea=77330 J mol-1である。気体定数はR=8.314 J mol-1 K-1。初期の反応物濃度はCA0=8020 mol m-3，温度はT0=366 Kである。以下の問に答えなさい。\n\n1) CA=3,200 mol m-3になるまでの時間t [min]を数値積分（シート計算によるSimpson則）で求めなさい。なお，式(4.19)と式(4.20)から，\n\n　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　(4.22)\n\nの関係が得られる。この式を反応速度式（式(4.21)）の温度Tに代入してCAについて積分を行う。分割数は40としなさい。\n\n2) 反応物濃度と温度の時間変化をオイラー法（VBAでマクロを作成。解くべき微分方程式2本はFunction文を使って呼び出して計算すること。式(4.22)は使わない）で解いて，グラフを作成しなさい。時間刻みtは1 minで，t=40 minまで計算する。\n"]

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[]
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["MOD(数値、除数)：",null,"は割算でわりきれなかった余りを返す"]
[]
[]
[]
["分割数n","  i","CA","f(CA)","even","odd"]
[null,0]
["積分下限a",1]
[null,2,null,null,null,null,"①A12に分割数（例えば40）を入力"]
["積分上限b",3,null,null,null,null,"②A14とA16に積分区間aとbを入力"]
[null,4,null,null,null,null,"③A18で刻み幅を計算する"]
["刻み幅h",5,null,null,null,null,"④A12-A32にオートフィルで番号0-40を入力"]
[null,6,null,null,null,null,"⑤CA,i+1=CA,i+hによりCA(i)の値をC12-C32に入力"]
[null,7,null,null,null,null,"⑥CA,iに対応したf(CA,i)を計算しD12-D32に入力"]
[null,8,null,null,null,null,"⑦Sf(CA,i)（偶数部分）とSf(CA,i)（奇数部分）に分ける"]
[null,9,null,null,null,null,"⑧Sf(CA,i)（偶数部分）の和とSf(CA,i)（奇数部分）の和を計算する（E33, F33）"]
[null,10,null,null,null,null,"⑨面積を求める（B54）"]
[null,11]
[null,12]
[null,13,null,null,null,null,null,null,"k0",62000,"[m3 mol-1 min-1]"]
[null,14,null,null,null,null,null,null,"Ea",77330,"[J mol-1]"]
[null,15,null,null,null,null,null,null,"DHrxn",-88244,"[J mol-1]"]
[null,16,null,null,null,null,null,null,"Cp",4180,"[J kg-1 K-1]"]
[null,17,null,null,null,null,null,null,"r",1000,"[kg m-3]"]
[null,18,null,null,null,null,null,null,"CA0",8020," [mol m-3]"]
[null,19,null,null,null,null,null,null,"T",366,"[K]"]
[null,20]
[null,21]
[null,22]
[null,23]
[null,24]
[null,25]
[null,26]
[null,27]
[null,28]
[null,29]
[null,30]
[null,31]
[null,32]
[null,33]
[null,34]
[null,35]
[null,36]
[null,37]
[null,38]
[null,39]
[null,40]
[]
["積分値"]

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[]
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["MOD(数値、除数)：",null,"は割算でわりきれなかった余りを返す"]
[]
[]
[]
["分割数n","  i","CA","f(CA)","even","odd"]
[40,0,{"$f":"$A$14+$A$18*B12","v":8020},{"$f":"-1/$J$25*1/(C12^2*EXP(-$J$26/(8.314*($J$31-(-$J$27)/($J$29*$J$28)*(C12-$J$30)))))","v":-2.7290396543013018E-2},{"$f":"IF(MOD(B12,2)=0,D12,0)","v":-2.7290396543013018E-2},{"$f":"IF(MOD(B12,2)=1,D12,0)","v":0}]
["積分下限a",1,{"$f":"$A$14+$A$18*B13","v":7899.5},{"$f":"-1/$J$25*1/(C13^2*EXP(-$J$26/(8.314*($J$31-(-$J$27)/($J$29*$J$28)*(C13-$J$30)))))","v":-2.3603594668658009E-2},{"$f":"IF(MOD(B13,2)=0,D13,0)","v":0},{"$f":"IF(MOD(B13,2)=1,D13,0)","v":-2.3603594668658009E-2}]
[{"$f":"J30","v":8020},2,{"$f":"$A$14+$A$18*B14","v":7779},{"$f":"-1/$J$25*1/(C14^2*EXP(-$J$26/(8.314*($J$31-(-$J$27)/($J$29*$J$28)*(C14-$J$30)))))","v":-2.0473545471627188E-2},-2.0473545471627188E-2,0,"①A12に分割数（例えば40）を入力"]
["積分上限b",3,7658.5,{"$f":"-1/$J$25*1/(C15^2*EXP(-$J$26/(8.314*($J$31-(-$J$27)/($J$29*$J$28)*(C15-$J$30)))))","v":-1.7809000725675799E-2},0,-1.7809000725675799E-2,"②A14とA16に積分区間aとbを入力"]
[3200,4,7538,-1.5534722000398342E-2,-1.5534722000398342E-2,0,"③A18で刻み幅を計算する"]
["刻み幅h",5,7417.5,-1.3588502303505072E-2,0,-1.3588502303505072E-2,"④A12-A32にオートフィルで番号0-40を入力"]
[{"$f":"(A16-A14)/A12","v":-120.5},6,7297,-1.1918771211377162E-2,-1.1918771211377162E-2,0,"⑤CA,i+1=CA,i+hによりCA(i)の値をC12-C32に入力"]
[null,7,7176.5,-1.0482663750203446E-2,0,-1.0482663750203446E-2,"⑥CA,iに対応したf(CA,i)を計算しD12-D32に入力"]
[null,8,7056,-9.2444589188880859E-3,-9.2444589188880859E-3,0,"⑦Sf(CA,i)（偶数部分）とSf(CA,i)（奇数部分）に分ける"]
[null,9,6935.5,-8.1743136721680078E-3,0,-8.1743136721680078E-3,"⑧Sf(CA,i)（偶数部分）の和とSf(CA,i)（奇数部分）の和を計算する（E33, F33）"]
[null,10,6815,-7.2472337224874636E-3,-7.2472337224874636E-3,0,"⑨面積を求める（B54）"]
[null,11,6694.5,-6.4422346733836854E-3,0,-6.4422346733836854E-3]
[null,12,6574,-5.7416565304143179E-3,-5.7416565304143179E-3,0]
[null,13,6453.5,-5.1306021342260571E-3,0,-5.1306021342260571E-3,null,null,"k0",62000,"[m3 mol-1 min-1]"]
[null,14,6333,-4.5964759748110878E-3,-4.5964759748110878E-3,0,null,null,"Ea",77330,"[J mol-1]"]
[null,15,6212.5,-4.12860452365025E-3,0,-4.12860452365025E-3,null,null,"DHrxn",-88244,"[J mol-1]"]
[null,16,6092,-3.7179229298114199E-3,-3.7179229298114199E-3,0,null,null,"Cp",4180,"[J kg-1 K-1]"]
[null,17,5971.5,-3.3567158753133831E-3,0,-3.3567158753133831E-3,null,null,"r",1000,"[kg m-3]"]
[null,18,5851,-3.0384027360024356E-3,-3.0384027360024356E-3,0,null,null,"CA0",8020," [mol m-3]"]
[null,19,5730.5,-2.7573590729565566E-3,0,-2.7573590729565566E-3,null,null,"T",366,"[K]"]
[null,20,5610,-2.5087679846206054E-3,-2.5087679846206054E-3,0]
[null,21,5489.5,-2.2884960587443871E-3,0,-2.2884960587443871E-3]
[null,22,5369,-2.0929896364471168E-3,-2.0929896364471168E-3,0]
[null,23,5248.5,-1.9191878861823102E-3,0,-1.9191878861823102E-3]
[null,24,5128,-1.7644498207901754E-3,-1.7644498207901754E-3,0]
[null,25,5007.5,-1.626492906098409E-3,0,-1.626492906098409E-3]
[null,26,4887,-1.5033413284013765E-3,-1.5033413284013765E-3,0]
[null,27,4766.5,-1.3932823295015983E-3,0,-1.3932823295015983E-3]
[null,28,4646,-1.294829296913937E-3,-1.294829296913937E-3,0]
[null,29,4525.5,-1.206690525382284E-3,0,-1.206690525382284E-3]
[null,30,4405,-1.1277427537400677E-3,-1.1277427537400677E-3,0]
[null,31,4284.5,-1.0570087361850501E-3,0,-1.0570087361850501E-3]
[null,32,4164,-9.9363823559052867E-4,-9.9363823559052867E-4,0]
[null,33,4043.5,-9.3689193373778503E-4,0,-9.3689193373778503E-4]
[null,34,3923,-8.861278436392778E-4,-8.861278436392778E-4,0]
[null,35,3802.5,-8.4078988606651149E-4,0,-8.4078988606651149E-4]
[null,36,3682,-8.0039835916608925E-4,-8.0039835916608925E-4,0]
[null,37,3561.5,-7.6454208951376467E-4,0,-7.6454208951376467E-4]
[null,38,3441,-7.3287210789074742E-4,-7.3287210789074742E-4,0]
[null,39,3320.5,-7.05096746356466E-4,0,-7.05096746356466E-4]
[null,40,{"$f":"$A$14+$A$18*B52","v":3200},-6.8097810811851506E-4,-6.8097810811851506E-4,0]
[null,null,null,null,{"$f":"SUM(E13:E51)","v":-9.5218346863017431E-2},{"$f":"SUM(F12:F52)","v":-0.10821207049750886}]
["積分値",{"$f":"A18*(D12+D52+4*F53+2*E53)/3","v":26.158796739749274}]

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[null,null,"DHrxn",-88244,"[J mol-1]"]
[null,null,"Cp",4180,"[J kg-1 K-1]"]
[null,null,"r",1000,"[kg m-3]"]
[null,null,"CA0",8020,"[mol m-3]"]
[null,null,"T",366,"[K]"]
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[null,null,"t [min]","CA [mol m-3]","T [K]"]
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