The saturation concentration of dissolved oxygen in freshwater can be calculated
ID: 2264113 • Letter: T
Question
The saturation concentration of dissolved oxygen in freshwater can be calculated with the equation
lnosf=139.34411+1.575701×105Ta6.642308×107T2a+1.243800×1010T3a8.621949×1011T4alnosf=-139.34411+1.575701×105Ta-6.642308×107Ta2+1.243800×1010Ta3-8.621949×1011Ta4
where osf = the saturation concentration of dissolved oxygen in freshwater at 1 atm (mg L1) and Ta = absolute temperature (K). Remember that Ta = T + 273.15, where T = temperature (°C). According to this equation, saturation decreases with increasing temperature. For typical natural waters in temperate climates, the equation can be used to determine that oxygen concentration ranges from 14.621 mg/L at 0 °C to 6.949 mg/L at 35 °C. Given a value of oxygen concentration, this formula and the bisection method can be used to solve for temperature in °C.
Test the M-file you developed for osf = 12, 14, and 14 mg/L. (Round the final answers to four decimal places.)
The temperature (°C) values obtained are as follows:
osf (mg/L) ans 12 14 14Explanation / Answer
The code I developed for this question is as follows:
clc;clear all;close all;
osf=12;
a=0;b=35;
f=@(T) (exp((-139.34411)+((1.575701*10^5)./(T+273.15))-((6.642308*10^7)./((T+273.15).^2))+((1.243800*10^10)./((T+273.15).^3))-((8.621949*10^11)./((T+273.15).^4)))-osf);
x(1)=a;y(1)=b;
z(1)=(a+b)/2;
if (f(x(1))*f(z(1)))<0
x(2)=x(1);y(2)=z(1);
else
x(2)=z(1);y(2)=y(1);
end
sol=zeros(1,100);
for i=2:100
z(i)=(x(i)+y(i))./2;
if (f(x(i))*f(z(i)))<0
x(i+1)=x(i);y(i+1)=z(i);
else
x(i+1)=z(i);y(i+1)=y(i);
end
if (z(i)-z(i-1))<=0.05
sol(i)=z(i);
end
end
display(sol(100));
Thus, by changing the value of osf in line-2 of code, we can get corresponding Temperature(in 0C),
Results:
For osf=12, Temperature(0C)= 7.465188974647191 = 7.4652 ( Accurate upto 4 decimal places)
For osf=13, Temperature(0C)= 4.316387743963247 = 4.3164 ( Accurate upto 4 decimal places)
For osf=14, Temperature(0C)= 1.554671588568937 = 1.5547( Accurate upto 4 decimal places)
Final result,
The temperature (°C) values obtained are as follows: osf (mg/L) Temperature(°C) 12 7.4652 13 4.3164 14 1.5547Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.