Determine which element violates the second law of thermodynamics

Given a set of known and unknown mass balances, the problem wanted me to solve for mass, and temperature. It also wants me to solve based on it the second law of thermodynamics is violated at any point in the code or if a temperature cross over is reached that is not possible. I coded a series of if statements, but it keeps returning the same value. Here is my code:

%MASTERY PROBLEM 1.1
clc
close all
clear variables
%---------------------------------------------------------------%
% Part 1
%---------------------------------------------------------------%
%form matrix of mass balances 
A_F = zeros(20);
A_F(1,1) = 1;A_F(1,2) = -1;
A_F(2,2) = 1;A_F(2,3) = -1;
A_F(3,3) = 1;A_F(3,4) = -1;
A_F(4,3) = 1;A_F(4,4) = -1;
A_F(5,5) = 1;A_F(5,6) = -1;
A_F(6,6) = 1;A_F(6,7) = -1;
A_F(7,6) = 1;A_F(7,7) = -1;
A_F(8,8) = 1;A_F(8,9) = -1;
A_F(9,9) = 1;A_F(9,10) = -1;
A_F(10,9) = 1;A_F(10,10) = -1;
A_F(11,11) = 1;A_F(11,12) = -1;
A_F(12,12) = 1;A_F(12,13) = -1;
A_F(13,12) = 1;A_F(13,13) = -1;
A_F(14,14) = 1;A_F(14,15) = -1;
A_F(15,15) = 1;A_F(15,16) = -1;
A_F(16,16) = 1;A_F(16,17) = -1;
A_F(17,16) = 1;A_F(17,17) = -1;
A_F(18,18) = 1;A_F(18,19) = -1;
A_F(19,19) = 1;A_F(19,20) = -1;
A_F(20,19) = 1;A_F(20,20) =1;
b_F = zeros(20,1);
%given values of F in matrix
FR = zeros(20,1);
FR(1) = 3.3;FR(2) = 3.3;FR(3) = 3.3;FR(4) = 3.3;
FR(5) = 2.4;FR(6) = 2.4;FR(7) = 2.4;
FR(8) = 1.8;FR(9) = 1.8;FR(10) = 1.8;
FR(11) = 6.9;FR(12) = 6.9;FR(13) = 6.9;
FR(14) = 3.4;FR(15) = 3.4;FR(16) = 3.4;FR(17) = 3.4;
FR(18) = 4.1;FR(19) = 4.1;FR(20) = 4.1;
%presents F in a table
% Heat capacities corresponding to flow rates
Cp = zeros(20,1);
Cp(1) = 2.4;Cp(2) = 2.4;Cp(3) = 2.4;Cp(4) = 2.4;
Cp(5) = 2.6;Cp(6) = 2.6;Cp(7) = 2.6;
Cp(8) = 0.8;Cp(9) = 0.8; Cp(10) = 0.8;
Cp(11) = 0.95;Cp(12) = 0.95;Cp(13) = 0.95;
Cp(14) = 1.35;Cp(15) = 1.35;Cp(16) = 1.35;Cp(17) = 1.35;
Cp(18) = 1.1;Cp(19) = 1.1;Cp(20) = 1.1;
%-------------------------------------------------------------------%
% Part 2: Display Temperatures in command line
%-------------------------------------------------------------------%
A_T = zeros(20);
b_T = zeros(20,1);
%input known temperature values into b_T
b_T(2) = 60;b_T(3) = 51;b_T(4) = 50;b_T(5) = 102;
b_T(6) = 81;b_T(9) = 121;b_T(10) = 70;b_T(11) = 55;
b_T(12) = 62;b_T(13) = 71;b_T(14) = 14;b_T(19) = 42; b_T(20) = 65;
%first row
A_T(1,1) = FR(1)*Cp(1);
A_T(1,2) = -FR(2)*Cp(2);
A_T(1,11) = FR(11)*Cp(11);
A_T(1,12) = -FR(12)*Cp(12);
A_T(2,2) = 1;
A_T(3,3) = 1;
A_T(4,4) = 1;
A_T(5,5) = 1;
A_T(6,6) = 1;
%seventh row
A_T(7,6) = FR(6)*Cp(6);
A_T(7,7) = -FR(7)*Cp(7);
A_T(7,19)  = FR(19)*Cp(19);
A_T(7,20) = -FR(20)*Cp(20);
%eighth row
A_T(8,8) = FR(8)*Cp(8);
A_T(8,9) = -FR(9)*Cp(9);
A_T(8,12) = FR(12)*Cp(12);
A_T(8,13) = -FR(13)*Cp(13);
A_T(9,9) = 1;
A_T(10,10) = 1;
A_T(11,11) = 1;
A_T(12,12) = 1;
A_T(13,13) =1;
A_T(14,14) = 1;
%row fifteen 
A_T(15,2) = FR(2)*Cp(2);
A_T(15,3) = -FR(3)*Cp(3);
A_T(15,14) = FR(14)*Cp(14);
A_T(15,15) = -FR(15)*Cp(15);
%row sixteen
A_T(16,5) = FR(5)*Cp(5);
A_T(16,6) = -FR(6)*Cp(6);
A_T(16,15) = -FR(15)*Cp(15);
A_T(16,16) = -FR(16)*Cp(16);
%row seventeen
A_T(17,9) = FR(9)*Cp(9);
A_T(17,10) = -FR(10)*Cp(10);
A_T(17,16) = FR(16)*Cp(16);
A_T(17,17) = FR(17)*Cp(17);
%row eighteen
A_T(18,3) = FR(3)*Cp(3);
A_T(18,4) = -FR(4)*Cp(4);
A_T(18,18) = FR(18)*Cp(18);
A_T(18,19) = -FR(19)*Cp(19);
A_T(19,19) = 1;
A_T(20,20) = 1;
% Create a system of equations to solve
N = length(A_T);             % Size of system
% Perform Forward Elimination
for i = 1:(N-1)
    for k = (i+1):N
        rki = A_T(k,i)/A_T(i,i);
        for j = i:N
            A_T(k,j) = A_T(k,j) - rki*A_T(i,j);
        end
        b_T(k) = b_T(k) - rki*b_T(i);
    end
end
% Perform Back Substitution
T = zeros(N,1);
T(N) = b_T(N)/A_T(N,N);
for i = N-1 : -1 : 1
    summ = b_T(i);
    for j = i+1:N
        summ = summ - A_T(i,j)*T(j);
    end
    T(i) = summ/A_T(i,i);
end
t = renamevars(table(FR,T),["FR","T"],["Flowrates (kg/sec)","Temperatures (C)"])

t = 20×2 table
    Flowrates (kg/sec)    Temperatures (C)
    __________________    ________________

           3.3                  65.794    
           3.3                      60    
           3.3                      51    
           3.3                      50    
           2.4                     102    
           2.4                      81    
           2.4                  64.377    
           1.8                  161.97    
           1.8                     121    
           1.8                      70    
           6.9                      55    
           6.9                      62    
           6.9                      71    
           3.4                      14    
           3.4                  29.529    
           3.4                -0.98039    

%-------------------------------------------------------------%
% Part 3: Determine if any streams violate the second law
%-------------------------------------------------------------%
%The hot streams must get colder, cold streams must get hotter
law_violation = false;
% Exchanger A
if T(1) < T(2)
    fprintf('Second Law Violated with temperatures %g\n', T(1),T(2), 'Hot streams cannot get hotter %g\n');
end
if T(11) > T(12)
    fprintf('Second Law Violated with temperatures %g\n', T(11),T(12), 'Cold streams cannot get colder %g\n');
end
if (T(2) <= T(11))||T(1) >= T(12)
    law_violation = true;
    fprintf('Temperature crossover reached: %g\n', T(i));
end

Temperature crossover reached: 65.7936

%Exchanger B
if T(8) < T(9)
    fprintf('Second Law Violated with temperatures %g\n', T(8),T(9), 'Hot streams cannot get hotter %g\n');
end
if T(12) > T(13)
    fprintf('Second Law Violated with temperatures %g\n', T(12),T(13), 'Cold streams cannot get colder %g\n');
end
if T(9)<=T(12)||T(8)>=T(13)
    law_violation = true;
    fprintf('Temperature crossover reached: %g\n',T(i));
end

Temperature crossover reached: 65.7936

%Exchanger C
if T(2) < T(3)
    fprintf('Second Law Violated with temperatures %g\n', T(2),T(3), 'Hot streams cannot get hotter %g\n');
end
if T(14) > T(15)
    fprintf('Second Law Violated with temperatures %g\n', T(14),T(15), 'Cold streams cannot get colder %g\n');
end
if T(3)<T(14)
    fprintf('Temperature crossover reached: %g\n', T(3),'<%g\n',T(14));
end
if T(2)>T(15)
    fprintf('Temperature crossover reached: %g\n', T(2),'>%g\n',T(15));
end

Temperature crossover reached: 60
Temperature crossover reached: 62
Temperature crossover reached: 37
Temperature crossover reached: 103
Temperature crossover reached: 92
Temperature crossover reached: 110
Temperature crossover reached: 29.5294

%Exchanger D
if T(5) < T(6)
    fprintf('Second Law Violated with temperatures %g\n', T(5),T(6), 'Hot streams cannot get hotter %g\n');
end
if T(15) > T(16)
    fprintf('Second Law Violated with temperatures %g\n', T(15),T(16), 'Cold streams cannot get colder %g\n');
end

Second Law Violated with temperatures 29.5294
Second Law Violated with temperatures -0.980392
Second Law Violated with temperatures 67
Second Law Violated with temperatures 111
Second Law Violated with temperatures 108
Second Law Violated with temperatures 100
Second Law Violated with temperatures 32
Second Law Violated with temperatures 115
Second Law Violated with temperatures 116
Second Law Violated with temperatures 114
Second Law Violated with temperatures 101
Second Law Violated with temperatures 97
Second Law Violated with temperatures 109
Second Law Violated with temperatures 115
Second Law Violated with temperatures 32
Second Law Violated with temperatures 99
Second Law Violated with temperatures 97
Second Law Violated with temperatures 110
Second Law Violated with temperatures 110
Second Law Violated with temperatures 111
Second Law Violated with temperatures 116
Second Law Violated with temperatures 32
Second Law Violated with temperatures 103
Second Law Violated with temperatures 101
Second Law Violated with temperatures 116
Second Law Violated with temperatures 32
Second Law Violated with temperatures 99
Second Law Violated with temperatures 111
Second Law Violated with temperatures 108
Second Law Violated with temperatures 100
Second Law Violated with temperatures 101
Second Law Violated with temperatures 114
Second Law Violated with temperatures 32
Second Law Violated with temperatures 37
Second Law Violated with temperatures 103
Second Law Violated with temperatures 92
Second Law Violated with temperatures 110

if T(6)<T(15)
    fprintf('Temperature crossover reached: %g\n', T(6),'<%g\n',T(15));
end
if T(5)>T(16)
    fprintf('Temperature crossover reached: %g\n', T(5),'>%g\n',T(16));
end

Temperature crossover reached: 102
Temperature crossover reached: 62
Temperature crossover reached: 37
Temperature crossover reached: 103
Temperature crossover reached: 92
Temperature crossover reached: 110
Temperature crossover reached: -0.980392

%Exchanger E
if T(9) < T(10)
    fprintf('Second Law Violated with temperatures %g\n', T(9),T(10), 'Hot streams cannot get hotter %g\n');
end
if T(16) > T(17)
    fprintf('Second Law Violated with temperatures %g\n', T(16),T(17), 'Cold streams cannot get colder %g\n');
end

Second Law Violated with temperatures -0.980392
Second Law Violated with temperatures -15.0196
Second Law Violated with temperatures 67
Second Law Violated with temperatures 111
Second Law Violated with temperatures 108
Second Law Violated with temperatures 100
Second Law Violated with temperatures 32
Second Law Violated with temperatures 115
Second Law Violated with temperatures 116
Second Law Violated with temperatures 114
Second Law Violated with temperatures 101
Second Law Violated with temperatures 97
Second Law Violated with temperatures 109
Second Law Violated with temperatures 115
Second Law Violated with temperatures 32
Second Law Violated with temperatures 99
Second Law Violated with temperatures 97
Second Law Violated with temperatures 110
Second Law Violated with temperatures 110
Second Law Violated with temperatures 111
Second Law Violated with temperatures 116
Second Law Violated with temperatures 32
Second Law Violated with temperatures 103
Second Law Violated with temperatures 101
Second Law Violated with temperatures 116
Second Law Violated with temperatures 32
Second Law Violated with temperatures 99
Second Law Violated with temperatures 111
Second Law Violated with temperatures 108
Second Law Violated with temperatures 100
Second Law Violated with temperatures 101
Second Law Violated with temperatures 114
Second Law Violated with temperatures 32
Second Law Violated with temperatures 37
Second Law Violated with temperatures 103
Second Law Violated with temperatures 92
Second Law Violated with temperatures 110

if T(10)<T(16)
    fprintf('Temperature crossover reached: %g\n', T(10),'<%g\n',T(16));
end
if T(9)>T(17)
    fprintf('Temperature crossover reached: %g\n', T(9),'>%g\n',T(17));
end

Temperature crossover reached: 121
Temperature crossover reached: 62
Temperature crossover reached: 37
Temperature crossover reached: 103
Temperature crossover reached: 92
Temperature crossover reached: 110
Temperature crossover reached: -15.0196

%Exchanger F
if T(3) < T(4)
    fprintf('Second Law Violated with temperatures %g\n', T(3),T(4), 'Hot streams cannot get hotter %g\n');
end
if T(18) > T(19)
    fprintf('Second Law Violated with temperatures %g\n', T(18),T(19), 'Cold streams cannot get colder %g\n');
end
if T(4)<T(18)
    fprintf('Temperature crossover reached: %g\n', T(4),'<%g\n',T(18));
end
if T(3)>T(19)
    fprintf('Temperature crossover reached: %g\n', T(3),'>%g\n',T(19));
end

Temperature crossover reached: 51
Temperature crossover reached: 62
Temperature crossover reached: 37
Temperature crossover reached: 103
Temperature crossover reached: 92
Temperature crossover reached: 110
Temperature crossover reached: 42

%Exchanger G
if T(6) < T(7)
    fprintf('Second Law Violated with temperatures %g\n', T(6),T(7), 'Hot streams cannot get hotter %g\n');
end
if T(19) > T(20)
    fprintf('Second Law Violated with temperatures %g\n', T(19),T(20), 'Cold streams cannot get colder %g\n');
end
if T(7)<T(19)
    fprintf('Temperature crossover reached: %g\n', T(7),'<%g\n',T(19));
end
if T(6)>T(20)
    fprintf('Temperature crossover reached: %g\n', T(6),'>%g\n',T(20));
end

Temperature crossover reached: 81
Temperature crossover reached: 62
Temperature crossover reached: 37
Temperature crossover reached: 103
Temperature crossover reached: 92
Temperature crossover reached: 110
Temperature crossover reached: 65

Answer 1

[Walter Roberson]

    fprintf('Temperature crossover reached: %g\n', T(6),'<%g\n',T(15));

That is not the syntax for outputing multiple variables. fprintf() does not take pairs of formats and values to output: it takes a single format followed by zero or more values to output.

You would instead use something similar to

    fprintf('Temperature crossover reached: %g\n<%g\n', T(6),T(15));