Question

The saturation concentration of dissolved oxygen in freshwater can be calculated with the equation: In osf - -139.34411 +1.575701 x 10-6.642308 x 101.243800 x 1010 1-8.621949 x 10" 10101-8.621949 x 10 1 where, osf is the saturation concentration of dissolved oxygen in freshwater at I atm ( osf is in mg/liter); and Ta absolute temperature (K). According to this equation, saturation decreases with increasing temperature. For typical natural waters, the oxygen concentration ranges from 14.621 mg/liter at 0°C (273 K) to 6.949 mg/liter at 35°C (308 K). a) Plot oxygen concentration osfas a function of temperature T, in the range 273 sTs 308 K b) Given a target oxygen concentration of osf- 10 mg/liter, it is required to estimate the required temperature in K. e) Solve using the MATLAB function fzero, with an initial guess To-250 K. d) Redo part (c) with an initial guess of 150 K. Is the solution feasible, i.e. T is in the acceptable range (273 sT. s 308 K)? Is it possible to solve the equation as a polynomial? If yes, determine all the roots and decide on the feasible ones (Hint: use roots) e)

Answer 1

Below are the codes to your question

clc
clear all
close all
osf=@(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4));
fplot(osf,[273,308]);
nOsf=@(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4))-10;
pt=fzero(nOsf,280);
hold on;
plot(pt,10,'*k');
title('osf vs Ta');
xlabel('Ta');
ylabel('osf');

Figure 1 File Edit View nsert Iools Desktop Window Help osf vs Ta 15 14 13 12 10 275 280 285 290 295 300 305 та O Type here to search 41) ENG 3:28 PM ^

b)

clc
clear all
close all
f=@(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4))-10;
fplot(f,[273,308]);
pt=fzero(f,280);
hold on;
plot(pt,0,'*k');
title('f vs Ta');
xlabel('Ta');
ylabel('f(Ta)');

Figure 1 File Edit View nsert Iools Desktop Window Help fvs Ta 2 -2 275 280 285 290 295 300 305 Ta O Type here to search ^ 口痰41) ENG 3:30 PM

c)

clear all
clc
f = @(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4))-10;
a=280;
b=300;
iter = 0;
e=0.05;
if f(a)*f(b)>=0

                disp('No Root')

else

                prev = (a+b)/2;
                p=a;
                while (abs(p-fzero(f,280))>e)
                    prev=p;

                                 iter =iter+ 1;

                                p = (a+b)/2;

                                if f(p) == 0

                                                break;

                                end

                                if f(a)*f(p)<0

                                                b = p;

                                else

                                                a = p;

                                end

                end

end
    fprintf('Total Iterations %d, root=%2.8f\n',iter,p);

clear all 2 -cl 3- @ (T) +1.575701"(10^5) /T-6.642308*(10^7)/ (T"21+1.243800*(10^10) / (T^3)-8.621949" (10^11)/ (T-4))-10: f a 280 b-300; exp (-139.34411 = 7- e0.os: if f (a) f (b) 0 10 disp ('No Root') Command Window New to MATLAB? Watch this Video, see Examples or read GettingStarted. Total Iterations 8, root-288.51562500 fx >>

f)

=================================

Bisect method

==================================

clear all
clc
f = @(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4))-10;
a=280;
b=300;
iter = 0;
e=0.05;
if f(a)*f(b)>=0

                disp('No Root')

else

                prev = (a+b)/2;
                p=a;
               for iter=1:4
                    prev=p;

                              

                                p = (a+b)/2;

                                if f(p) == 0

                                                break;

                                end

                                if f(a)*f(p)<0

                                                b = p;

                                else

                                                a = p;

                                end

                end

end
    fprintf('Total Iterations %d, root=%2.8f\n',iter,p);

==============================

False position method

==============================

clc

f = @(T) exp(-139.34411 +1.575701*(10^5)/T-6.642308*(10^7)/(T^2)+1.243800*(10^10)/(T^3)-8.621949*(10^11)/(T^4))-10;
x0=280;
x1=300;
i=0;
imax=20;
x2=300;
for i=1:4
if(i~=1)
    x1=x2;
    end
    x2=x1-((f(x1)/(f(x1)-f(x0)))*(x1-x0));
    x0=x1;
end
    fprintf('Total Iteration %d, root=%2.8f\n',i,x2);

7 imax=20; x2-300; for i=1 : 4 10- 12- 13- 14- 15- 16 - Command Window x2-x1- ((f (xl)/ (f (xl)-f (x0))) x0=x1 ; (xl-x0)) fprint f("Total Iteration %d, root-%2.8f\n', i, x2); New to MATLAB? Watch this Video see Examples or read Getting Started. Total Iteration 4, root-288.53833365