clear
clc
close all
%Use polyfit to solve for the phase lines
point11=[0,15];
point12=[0,300];
line1=polyfit(point11,point12,1);
m1=line1(1);
b1=line1(2);
xpf1=linspace(min(point11),max(point11),100);
ypf1=m1*xpf1+b1;
point21=[0,15];
point22=[700,300];
line2=polyfit(point21,point22,1);
m2=line2(1);
b2=line2(2);
xpf2=linspace(min(point21),max(point21),100);
ypf2=m2*xpf2+b2;
point31=[0,50];
point32=[700,300];
line3=polyfit(point31,point32,1);
m3=line3(1);
b3=line3(2);
xpf3=linspace(min(point31),max(point31),100);
ypf3=m3*xpf3+b3;
point41=[50,100];
point42=[300,800];
line4=polyfit(point41,point42,1);
m4=line4(1);
b4=line4(2);
xpf4=linspace(min(point41),max(point41),100);
ypf4=m4*xpf4+b4;
point51=[100,85];
point52=[800,300];
line5=polyfit(point51,point52,1);
m5=line5(1);
b5=line5(2);
xpf5=linspace(min(point51),max(point51),100);
ypf5=m5*xpf5+b5;
point61=[85,100];
point62=[300,0];
line6=polyfit(point61,point62,1);
m6=line6(1);
b6=line6(2);
xpf6=linspace(min(point61),max(point61),100);
ypf6=m6*xpf6+b6;
point71=[15,85];
point72=[300,300];
%Allow the user to set the percent of B
b=input(\'Enter the mass percent of B: \');
%Return an error if the percent of B is not a valid number
if b<0 || b>100
error(\'Please enter a value between 0 and 100.\')
end
%Allow the user to set the temperature
t=input(\'Enter the temperature [deg C]: \');
%Solve for percent composition of A
a=100-b;
%Determine phase based on temperature and percent composition of B using
%the phase lines
if t<300
if b<15 && t>m1*b+b1
phase=\'alpha\';
elseif b<15 && t=15 && b<=85
phase=\'alpha + beta\';
elseif b>85 && t>m6*b+b6
phase=\'beta\';
else phase=\'alpha + beta\';
end
elseif b<15
if t=15 && b<=50
if t50 && b<=85
if t=15 && b<=85 && t==300
fprintf(\'The provided conditions fall on the eutectic line.\ \')
end
if b==50 && t==300
fprintf(\'The provided conditions fall on the eutectic point.\ \')
end
%Output a formatted statement to display the phase
fprintf(\'For the composition of %0.2f%% A, %0.2f%% B and a temperature of %0.0f degrees
Celsius, the phase is %s.\ \',a,b,t,phase)
%Create a plot of the phase lines and the user\'s set point
figure(\'color\',\'white\')
%Set axes
axis([0 100 0 1000])
%Plot the phase lines, eutectic line, eutectic point, and the user\'s point
plot(xpf1,ypf1,\'-b\')
hold on
plot(xpf2,ypf2,\'-b\')
plot(xpf3,ypf3,\'-b\')
plot(xpf4,ypf4,\'-b\')
plot(xpf5,ypf5,\'-b\')
plot(xpf6,ypf6,\'-b\')
plot(point71,point72,\'-k\')
plot(b,t,\'ro\',\'MarkerFaceColor\',\'r\')
%Assign a title and axes labels
title(\'Phase Diagram of Elements A and B\')
xlabel(\'Percent Composition of B\')
ylabel(\'Temperature (T) [deg C]\')
%Set scaling for the axes
set(gca,\'XTick\',0:10:100,\'YTick\',0:100:1000)
%Place the phase names on the graph
text(40,200,\'alpha+beta\')
text(45,600,\'Liquid\')
text(90,300,\'beta\')
text(3,300,\'alpha\')
text(15,375,\'alpha + Liquid\')
text(62,375,\'beta + Liquid\')
Solution
clear
clc
close all
%Use polyfit to solve for the phase lines
point11=[0,15];
point.
3. elseif b<15
if t=15 && b<=50
if t50 && b<=85
if t=15 && b<=85 && t==300
fprintf('The provided conditions fall on the eutectic line. ')
end
if b==50 && t==300
fprintf('The provided conditions fall on the eutectic point. ')
end
%Output a formatted statement to display the phase
fprintf('For the composition of %0.2f%% A, %0.2f%% B and a temperature of %0.0f degrees
Celsius, the phase is %s. ',a,b,t,phase)
%Create a plot of the phase lines and the user's set point
figure('color','white')
%Set axes
axis([0 100 0 1000])
%Plot the phase lines, eutectic line, eutectic point, and the user's point
plot(xpf1,ypf1,'-b')
hold on
plot(xpf2,ypf2,'-b')
plot(xpf3,ypf3,'-b')
plot(xpf4,ypf4,'-b')
plot(xpf5,ypf5,'-b')
plot(xpf6,ypf6,'-b')
plot(point71,point72,'-k')
plot(b,t,'ro','MarkerFaceColor','r')
%Assign a title and axes labels
title('Phase Diagram of Elements A and B')
xlabel('Percent Composition of B')
ylabel('Temperature (T) [deg C]')
%Set scaling for the axes
set(gca,'XTick',0:10:100,'YTick',0:100:1000)
%Place the phase names on the graph
text(40,200,'alpha+beta')
text(45,600,'Liquid')
text(90,300,'beta')
4. text(3,300,'alpha')
text(15,375,'alpha + Liquid')
text(62,375,'beta + Liquid')
Solution
clear
clc
close all
%Use polyfit to solve for the phase lines
point11=[0,15];
point12=[0,300];
line1=polyfit(point11,point12,1);
m1=line1(1);
b1=line1(2);
xpf1=linspace(min(point11),max(point11),100);
ypf1=m1*xpf1+b1;
point21=[0,15];
point22=[700,300];
line2=polyfit(point21,point22,1);
m2=line2(1);
b2=line2(2);
xpf2=linspace(min(point21),max(point21),100);
ypf2=m2*xpf2+b2;
point31=[0,50];
point32=[700,300];
line3=polyfit(point31,point32,1);
m3=line3(1);
b3=line3(2);
xpf3=linspace(min(point31),max(point31),100);
ypf3=m3*xpf3+b3;
point41=[50,100];
point42=[300,800];
line4=polyfit(point41,point42,1);
6. phase='alpha + beta';
elseif b>85 && t>m6*b+b6
phase='beta';
else phase='alpha + beta';
end
elseif b<15
if t=15 && b<=50
if t50 && b<=85
if t=15 && b<=85 && t==300
fprintf('The provided conditions fall on the eutectic line. ')
end
if b==50 && t==300
fprintf('The provided conditions fall on the eutectic point. ')
end
%Output a formatted statement to display the phase
fprintf('For the composition of %0.2f%% A, %0.2f%% B and a temperature of %0.0f degrees
Celsius, the phase is %s. ',a,b,t,phase)
%Create a plot of the phase lines and the user's set point
figure('color','white')
%Set axes
axis([0 100 0 1000])
%Plot the phase lines, eutectic line, eutectic point, and the user's point
plot(xpf1,ypf1,'-b')
hold on
plot(xpf2,ypf2,'-b')
plot(xpf3,ypf3,'-b')
plot(xpf4,ypf4,'-b')
plot(xpf5,ypf5,'-b')
plot(xpf6,ypf6,'-b')
plot(point71,point72,'-k')
plot(b,t,'ro','MarkerFaceColor','r')
%Assign a title and axes labels
title('Phase Diagram of Elements A and B')
xlabel('Percent Composition of B')
ylabel('Temperature (T) [deg C]')
%Set scaling for the axes
![clear
clc
close all
%Use polyfit to solve for the phase lines
point11=[0,15];
point12=[0,300];
line1=polyfit(point11,point12,1);
m1=line1(1);
b1=line1(2);
xpf1=linspace(min(point11),max(point11),100);
ypf1=m1*xpf1+b1;
point21=[0,15];
point22=[700,300];
line2=polyfit(point21,point22,1);
m2=line2(1);
b2=line2(2);
xpf2=linspace(min(point21),max(point21),100);
ypf2=m2*xpf2+b2;
point31=[0,50];
point32=[700,300];
line3=polyfit(point31,point32,1);
m3=line3(1);
b3=line3(2);
xpf3=linspace(min(point31),max(point31),100);
ypf3=m3*xpf3+b3;
point41=[50,100];
point42=[300,800];
line4=polyfit(point41,point42,1);
m4=line4(1);
b4=line4(2);
xpf4=linspace(min(point41),max(point41),100);
ypf4=m4*xpf4+b4;
point51=[100,85];](https://image.slidesharecdn.com/clearclccloseallusepolyfittosolveforthephasel-230628084040-502e83bc/85/clear-clc-close-all-Use-polyfit-to-solve-for-the-phase-l-pdf-1-320.jpg)
![point52=[800,300];
line5=polyfit(point51,point52,1);
m5=line5(1);
b5=line5(2);
xpf5=linspace(min(point51),max(point51),100);
ypf5=m5*xpf5+b5;
point61=[85,100];
point62=[300,0];
line6=polyfit(point61,point62,1);
m6=line6(1);
b6=line6(2);
xpf6=linspace(min(point61),max(point61),100);
ypf6=m6*xpf6+b6;
point71=[15,85];
point72=[300,300];
%Allow the user to set the percent of B
b=input('Enter the mass percent of B: ');
%Return an error if the percent of B is not a valid number
if b<0 || b>100
error('Please enter a value between 0 and 100.')
end
%Allow the user to set the temperature
t=input('Enter the temperature [deg C]: ');
%Solve for percent composition of A
a=100-b;
%Determine phase based on temperature and percent composition of B using
%the phase lines
if t<300
if b<15 && t>m1*b+b1
phase='alpha';
elseif b<15 && t=15 && b<=85
phase='alpha + beta';
elseif b>85 && t>m6*b+b6
phase='beta';
else phase='alpha + beta';
end](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)