A nonisothermal batch reactor can be described by the following equations: - (-10/(T+273)) dC dt dT...

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A nonisothermal batch reactor can be described by the following equations: - (-10/(T+273)) dC dt dT = 1000 el-10/(T+273) C –

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Answer 1

Answer #1

$\frac{dC}{dt} = f(t_i,C_i)= -e^{(-10/(T_i+273))}C_i$

Ci+1 = C; + slope * h

$Slope = f(t_{i + 1/2},C_{i+1/2})$

$t_{i+1/2}= t_i + *h/2$

$C_{i+1/2}= C_i + f(t_i,C_i)*h/2$

at t =0, Ci = 1.5 , ti=0 and Ti = 17.8 deg C

Now, sample calculation is shown for i = 1 ,

$t_{i+1/2}= t_i + *h/2 = 0+0.1/2 = 0.05$

$f(t_i,C_i)= -e^{(-10/(T_i+273))}C_i = -e^{(-10/(17.8+273))}*1.5 = -1.449$

$C_{i+1/2}= C_i + f(t_i,C_i)*h/2 = 1.5 +(-1.449)*0.1/2 = 1.428$

$Slope = f(t_{i + 1/2},C_{i+1/2}) = -e^{-10/(Ti+273)}*C_{i+1/2}=-e^{-10/(17.8+273)}*1.428=-1.379$

$C_{i+1}= C_i + slope*h = 1.5 +(-1.379)*(0.1)= 1.362$

$\frac{dT}{dt} = f(t,T)= 1000e^{(-10/(T+273))}C -7.89(T-20)$

$f(t_i,T_i)= 1000e^{(-10/(T_i+273))}C_i -7.89(T_i-20)= 1000e^{(-10/(17.8+273))}*1.5 -7.89(17.8-20) = 1446.6$

$T_{i+1/2}= T_i + f(t_i,T_i)*h/2 = 17.8 +(1446.6)*0.1/2 = 91.13$

$Slope = f(t_{i+1/2},T_{i+1/2})= 1000e^{(-10/(T_{i+1/2}+273))}C_i -7.89(T_{i+1/2}-20)= 1000e^{(-10/(91.13+273))}*1.5 -7.89(91.13-20) =898.1$

$T_{i+1}= T_i + slope*h = 17.8 +(898.1)*(0.1)= 107.6$

Similarly we can calculate for other value of i

time (t)	t _{i + 0.5}		C _{i + 0.5}	slope	Conc (Ci)		T _{i + 0.5}	slope	Temp (T)
min		f(t _{i ,}C _i )		f(t _{i + 1,}C _{i + 1})	gmol/L	f(t _{i ,}T _i )		f(t _{i + 1,}T _{i + 1})	T
0					1.5				17.8
0.1	0.05	1.449295	1.427535	-1.379279776	1.362072	1466.653	91.13265	898.1301	107.613
0.2	0.15	1.326752	1.295734	-1.262134404	1.235859	635.4851	139.3873	387.4748	146.3605
0.3	0.25	1.206737	1.175522	-1.147822007	1.121076	209.7528	156.8481	127.7076	159.1313
0.4	0.35	1.095431	1.066305	-1.041912651	1.016885	-2.31429	159.0155	-1.40809	158.9904
0.5	0.45	0.993616	0.967204	-0.94507199	0.922378	-103.019	153.8395	-62.6553	152.7249
0.6	0.55	0.900964	0.87733	-0.856961948	0.836682	-146.235	145.4132	-88.9152	143.8334
0.7	0.65	0.816848	0.795839	-0.776974004	0.758984	-160.197	135.8235	-97.3833	134.0951
0.8	0.75	0.740568	0.721956	-0.704437655	0.688541	-159.643	126.1129	-97.0273	124.3923
0.9	0.85	0.67143	0.654969	-0.638693014	0.624671	-152.225	116.7811	-92.5022	115.1421
1	0.95	0.608783	0.594232	-0.57911799	0.566759	-141.888	108.0477	-86.2053	106.5216
1.1	1.05	0.552021	0.539158	-0.52513767	0.514246	-130.634	99.98986	-79.3537	98.58621
1.2	1.15	0.500591	0.489216	-0.476226096	0.466623	-119.454	92.6135	-72.5495	91.33126
1.3	1.25	0.45399	0.443924	-0.431904684	0.423433	-108.814	85.89056	-66.0758	84.72368
1.4	1.35	0.41176	0.402845	-0.391739239	0.384259	-98.9102	79.77817	-60.0514	78.71854
1.5	1.45	0.373487	0.365584	-0.355336462	0.348725	-89.8019	74.22844	-54.5123	73.2673

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