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//Engineering and Chemical Thermodynamics
//Example 2.13
//Page no :73
clear ; clc ;
//Given data :
del_h0_f_CO2 = -393.51 ; //[kJ/mol], From Appendix A.3
del_h0_f_CO = -110.53 ; //[kJ/mol], From Appendix A.3
del_h0_f_H2O = -241.82 ; //[kJ/mol], From Appendix A.3
del_h0_f_C3H8 = -103.85 ; //[kJ/mol], From Appendix A.3
del_h0_f_O2 = 0 ; //[kJ/mol], From Appendix A.3
A_CO2 = 5.457 ; // From table E2.13
B_CO2 = 1.05 * 10^-3 ;
D_CO2 = -1.16 * 10^5 ;
A_CO = 3.379 ;
B_CO = 5.57 * 10^-4;
D_CO = -3.1 * 10^3 ;
A_H2O = 3.470 ;
B_H2O = 1.45 * 10^-3;
D_H2O = 1.21 * 10^4 ;
A_N2 = 3.280 ;
B_N2 = 5.93 * 10^-4;
D_N2 = 4.00 * 10^3 ;
//Let
n_C3H8 = 10 ; //[mol]
n_N2 = (0.79/0.21) * (9.7/2) * n_C3H8 ; //[mol]
n_CO2 = 2.7 * n_C3H8 ; //[mol]
n_CO = 0.3 * n_C3H8 ; //[mol]
n_H2O = 4 * n_C3H8 ; //[mol]
n_O2 = (9.7 / 2)* n_C3H8 ; //[mol]
T_reff = 298 ; //[K]
del_H_rxn_298 = n_CO2 * del_h0_f_CO2 + n_CO * del_h0_f_CO + n_H2O * del_h0_f_H2O - n_C3H8 * del_h0_f_C3H8 - n_O2 * del_h0_f_O2 ; //[kJ]
//The co-efficients of T2 in the equation of degree 3 are
a = 8.314*(n_CO2 * (B_CO2/2) + n_CO * (B_CO/2) + n_H2O * (B_H2O/2) + n_N2 * (B_N2/2));
b = 8.314*(n_CO2 * A_CO2 + n_CO * A_CO + n_H2O * A_H2O + n_N2 * A_N2) ;
d =8.314*(- n_CO2 * D_CO2 - n_CO * D_CO - n_H2O * D_H2O -n_N2 * D_N2) ;
c = (del_H_rxn_298 *1000) + 8.314 * (n_CO2 * (- T_reff * A_CO2 - B_CO2/2 * T_reff^2 + D_CO2/T_reff) + n_CO * (- T_reff * A_CO - B_CO/2 * T_reff^2 + D_CO/T_reff) + n_H2O * (- T_reff * A_H2O - B_H2O/2 * T_reff^2 + D_H2O/T_reff) + n_N2 * (-T_reff * A_N2 - B_N2/2 * T_reff^2 + D_N2/T_reff));
T2=poly(0,'T2');
P = d + c*T2 + b*T2^2 + a*T2^3 ;
M = roots(P);
disp(" Example: 2.13 Page no : 73") ;
disp(" The roots of the equation containig T2 as variable are (K)-")
disp(M);
disp(" But T2 must be more than 298K . So we have to choose the most suitable solution .")
// The answer in the textbook does not statisfy the equation while it is counter-checked .
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