Plot two lines on different graphs from integral

To=27+273.15;  %%k
cao=0.1;    %%mol/dm^3
k1=.01;  %%dm^3/mol*s
tha=1;thb=1;
ha=-20000; hb=-15000; hc=-41000; %%cal/mol
cpc=30;cpa=15;cpb=15; %%cal/mol*k
sumtcp=tha*cpa+thb*cpb;
delcp=cpc-cpb-cpa;
dhrx=hc-hb-ha;
E=10000;                       %%cal/mol
R=1.987;        %%cal/mol*k
vo=2;
fao=cao*vo;
cbo=cao;
ca=@(x) cao*(1-x);
cb=@(x) cbo*(1-x);

T=@(x) To+(-dhrx)*x/(sumtcp+delcp.*x) ;
k=@(x) k1*exp(E/R*(1/To-1/T(x)));
ra=@(x) -(k(x).*ca(x).*cb(x));
vpfr1=@(x) fao./(-ra(x));
vpfr=integral(vpfr1,0,.85);

>> xspan=0:.1:1;
>> plot(vpfr,xspan)
>> 

I would like to plot x vs vpfr and T vs Vpfr on different graphs. With Vpfr being the x-axis

This gives me ablank graph

[Rik]

Since vpfr is a scalar you are only plottin a single value. Is that what you mean?

[Rodrigo Blas]

Yes. I dont want to just plot a single point. How do i make it plot the line ?

[Ankit]

You have to convert your problem to as shown below. otherwise you will get only one value.

% Integrate the vector-valued function sin((1:5)*x) from 0 to 1:
Q = integral(@(x)sin((1:5)*x),0,1,'ArrayValued',true)

for plotting temp, just use the for loop:

T=@(x) To+(-dhrx)*x/(sumtcp+delcp.*x) ;
for i = 1:length(xspan)
    Temp(i) = T(xspan(i)) ;
end
figure;plot(Temp,xspan);grid on;

[Rik]

vpfr=integral(vpfr1,0,0.85,'ArrayValued',true);

That still returns a scalar.

@Rodrigo: you don't explain what you want to achieve, so it is difficult to give you good advice. How would you calculate the value of vpfr for a single value of xspan? Once that is clear we can help you extend it to an array.

[Rodrigo Blas]

I want to plot x from 0 to 1 on the y axis and plot its corresponding vpfr value on the x axis.

ca=@(x) cao*(1-x);
cb=@(x) cbo*(1-x);
T=@(x) To+(-dhrx)*x/(sumtcp+delcp.*x) ;
k=@(x) k1*exp(E/R*(1/To-1/T(x)));
ra=@(x) -(k(x).*ca(x).*cb(x));
vpfr1=@(x) fao./(-ra(x));
vpfr=integral(vpfr1,0,.85);

Using the integral of the vpfr function.

Answer 1

[Ameer Hamza]

I guess you are trying to do something like this. Note that I have varied x from 0 to 0.9, because at x=1, the integral diverges.

To=27+273.15;  %%k
cao=0.1;    %%mol/dm^3
k1=.01;  %%dm^3/mol*s
tha=1;thb=1;
ha=-20000; hb=-15000; hc=-41000; %%cal/mol
cpc=30;cpa=15;cpb=15; %%cal/mol*k
sumtcp=tha*cpa+thb*cpb;
delcp=cpc-cpb-cpa;
dhrx=hc-hb-ha;
E=10000;                       %%cal/mol
R=1.987;        %%cal/mol*k
vo=2;
fao=cao*vo;
cbo=cao;
ca=@(x) cao*(1-x);
cb=@(x) cbo*(1-x);
T=@(x) To+(-dhrx)*x./(sumtcp+delcp.*x); % <----- element-wise division should be used
k=@(x) k1*exp(E/R.*(1/To-1./T(x))); % <----- element-wise operators should be used
ra=@(x) -(k(x).*ca(x).*cb(x));
vpfr1=@(x) fao./(-ra(x));

x = 0:0.1:0.9;
vpfr = zeros(size(x));
for i=1:numel(x)
    vpfr(i) = integral(vpfr1,0,x(i));
end

plot(x, vpfr);
figure;
plot(T(x), vpfr);

[Rodrigo Blas]

Great! Thank You!

How would I do the same for vpfr vs T?

[Ameer Hamza]

Rodrigo, check the updated code. Which trying to plot T(x) vas vpfr, I found some other issues in your code. I have also corrected those. Please see my comment pointed out with "<-----"

[Rodrigo Blas]

Thank you

[Rodrigo Blas]

How would I do Vpfr vs T(x) in the same manner?

[Rodrigo Blas]

Nevermind. I figured it out. THank you so much

[Ameer Hamza]

I am glad to be of help.