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clear;
clc;
//To find Approx Value
function[A]=approx(V,n)
A=round(V*10^n)/10^n;//V-Value n-To what place
funcprot(0)
endfunction
function[Q]=MCPH(T0,T,A,B,C,D)
t=T/T0;
Q=(A+((B/2)*T0*(t+1))+((C/3)*T0*T0*((t^2)+t+1))+(D/(t*T0*T0)))
funcprot(0);
endfunction
function[Q]=IDCPH(T0,T,dA,dB,dC,dD)
t=T/T0;
Q=(dA+((dB/2)*T0*(t+1))+((dC/3)*T0*T0*((t^2)+t+1))+(dD/(t*T0*T0)))*(T-T0)
funcprot(0);
endfunction
function[Q]=IDCPS(T0,T,dA,dB,dC,dD)
t=T/T0;
Q=((dA)*log(t))+(((dB*T0)+(((dC*T0*T0)+(dD/(t*t*T0*T0)))*(t+1)/2))*(t-1))
funcprot(0);
endfunction
//Example 13.9
//Caption : Program to Determine Composition and Temperature of Product Steam
P=1;//[bar]
T0=298.15;//[K]
R=8.314;
//SO2 + 0.5O2 --> SO3
dHo_298=-98890;//[J/mol]
dGo_298=-70866;//[J/mol]
n_O2_i=0.5*1.2;// Moles O2 Entering
n_N2_i=n_O2_i*(79/21);//Moles N2 Entering
//n_SO2=1-e
//n_O2=0.6-(0.5*e)
//n_SO3=e
//n_N2=2.257
//By Energy Balance
//(dHo_298*e)+dHo_P = dH = 0 (A)
//dHo_P=Cp*(T-298.15) Cp=E nCp (B)
//Cp_SO2=R*MCPH(T0,T,5.699,0.801E-3,0,-1.015E+5)
//Cp_O2=R*MCPH(T0,T,3.639,0.506E-3,0,-0.227E+5)
//Cp_SO3=R*MCPH(T0,T,8.06,1.056E-3,0,-2.028E+5)
//Cp_N2=R*MCPH(T0,T,3.28,0.593E-3,0,0.04E+5)
//T=(-(dHo_298*e)/Cp)+T0 (C)
//K=(e/(1-e))*((3.857-(0.5*e))/(0.6-(0.5*e)))^0.5 (D)
//ln K = ((dHo_298-dGo_298)/(R*T0))-(dHo_298/(R*T))+I1-(I2/T) (E)
//I1=IDCPS(T0,T,0.5415,0.002E-3,0,-0.8995E+5)
//I2=IDCPH(T0,T,0.5415,0.002E-3,0,-0.8995E+5)
//Iteration
A1=300;//Initial
i=-1;
while(i==-1)
I1=IDCPS(T0,A1,0.5415,0.002E-3,0,-0.8995E+5);
I2=IDCPH(T0,A1,0.5415,0.002E-3,0,-0.8995E+5);
//Applying in Eqn (E)
K = exp(((dHo_298-dGo_298)/(R*T0))-(dHo_298/(R*A1))+I1-(I2/A1));
//Applying in Eqn (D)
if(isreal(K))
x=0;
// p=poly([-0.6*(K^2) 1.7*(K^2) 3.857-(1.6*(K^2)) 0.5*((K^2)-1)],'e','c')
// (0.5*((K^2)-1)*(x^3))+((3.857-(1.6*(K^2)))*(x^2))+(1.7*(K^2)*x)+(-0.6*(K^2))
F_x=(0.5*((K^2)-1)*(x^3))+((3.857-(1.6*(K^2)))*(x^2))+(1.7*(K^2)*x)+(-0.6*(K^2));
F_a=F_x;
x=1;
F_x=(0.5*((K^2)-1)*(x^3))+((3.857-(1.6*(K^2)))*(x^2))+(1.7*(K^2)*x)+(-0.6*(K^2));
//F_x=(x^3)-(4*x)+1;
F_b=F_x;
root=-100;
A=0;
B=1;
i=1;
while(i==1)
a=A;
F_a=(0.5*((K^2)-1)*(a^3))+((3.857-(1.6*(K^2)))*(a^2))+(1.7*(K^2)*a)+(-0.6*(K^2));
//F_a=(a^3)-(4*a)+1;
b=B;
F_b=(0.5*((K^2)-1)*(b^3))+((3.857-(1.6*(K^2)))*(b^2))+(1.7*(K^2)*b)+(-0.6*(K^2));
//F_b=(b^3)-(4*b)+1;
x1=((a*F_b)-(b*F_a))/(F_b-F_a);
F_x1=(0.5*((K^2)-1)*(x1^3))+((3.857-(1.6*(K^2)))*(x1^2))+(1.7*(K^2)*x1)+(-0.6*(K^2));
//F_x1=(x1^3)-(4*x1)+1;
if((F_a*F_x1)<0) then
flag=1;
A=a;
B=x1;
else((F_x1*F_b)<0)
flag=2;
A=x1;
B=b;
end
x1_a=approx(x1,4);
b_a=approx(b,4);
a_a=approx(a,4);
if(x1_a==b_a)
root=approx(x1,5);
i=0;
break;
elseif(x1_a==a_a)
root=approx(x1,5);
i=0;
break;
end
end
e=root;
Cp_SO2=R*MCPH(T0,A1,5.699,0.801E-3,0,-1.015E+5);
Cp_O2=R*MCPH(T0,A1,3.639,0.506E-3,0,-0.227E+5);
Cp_SO3=R*MCPH(T0,A1,8.06,1.056E-3,0,-2.028E+5);
Cp_N2=R*MCPH(T0,A1,3.28,0.593E-3,0,0.04E+5);
n_SO2=1-e;
n_O2=0.6-(0.5*e);
n_SO3=e;
n_N2=2.257;
if(n_SO2<0 | n_O2<0 | n_SO3<0)
e=0;
end
Cp=(n_SO2*Cp_SO2)+(n_O2*Cp_O2)+(n_SO3*Cp_SO3)+(n_N2*Cp_N2);
//Applying in Eqn (C)
B=(-(dHo_298*e)/Cp)+T0;
m=(A1+B)/2;
dT=approx(abs(m-A1),2);
if(dT<0.1)
i=0;
T=approx(A1,1);
e=approx(e,2);
break;
end
A1=m;
i=-1;
else
i=-1;
A1=A1+1;
end
end
disp(e,'Fraction')
n_SO2=1-e
n_O2=0.6-(0.5*e)
n_SO3=e
n_N2=2.257
nt=n_SO2+n_O2+n_SO3+n_N2;
y_SO2=approx(n_SO2/nt,4);
y_O2=approx(n_O2/nt,4);
y_SO3=approx(n_SO3/nt,4);
y_N2=approx(n_N2/nt,4);
disp(T,'Final Temperature')
disp(y_SO2,'Composition of SO2')
disp(y_O2,'Composition of O2')
disp(y_SO3,'Composition of SO3')
disp(y_N2,'Composition of N2')
//End
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