Question about plotting graph.

The code below is how I got T1.

Now, I'd like to plot T1 vs T0(it was a fixed value 450).

What code should I input here?

I tried

T0 = linspace (273, 500);

plot (T0, y)

but it doesn't work

Please, advise. Thank you in advance.

clc, clear all; close all;

syms T1
U = 8000;  % cal/(min*C)
Cp0 = 50;  % cal/(mol*C)
Fa0 = 80;  % 80mol/min
E = 40000; % cal/mol
H = -7500; % cal/mol
t = 100;    % min^-1 
T0 = 450;   % K
Ta = 300;   % K
T2 = 350;   % K
R = 1.987;   % cal/(mol*K)
k2 = 6.6*10^-3; % min^-1

%Heat removed

k = U/(Cp0*Fa0);
Tc = (k*Ta+T0)/(1+k);
Rt = Cp0*(1+k)*(T1-Tc);

%Heat generated


k1 = k2*exp((E/R)*((1/T2)-(1/T1)));
Gt = -H*t*k1/(1+(t*k1));

y = vpasolve (Rt == Gt, T1)

Answer 1

[Walter Roberson]

For some T values, there are two solutions; which one you get depends upon the starting point for your search.

t0 = linspace(273, 500, 350);
nt = length(t0);

syms T1 T0 real
U = 8000;  % cal/(min*C)
Cp0 = 50;  % cal/(mol*C)
Fa0 = 80;  % 80mol/min
E = 40000; % cal/mol
H = -7500; % cal/mol
t = 100;    % min^-1 
%T0 = 450;   % K
Ta = 300;   % K
T2 = 350;   % K
R = 1.987;   % cal/(mol*K)
k2 = 6.6*10^-3; % min^-1
%Heat removed
k = U/(Cp0*Fa0);
Tc = (k*Ta+T0)/(1+k);
Rt = Cp0*(1+k)*(T1-Tc);
%Heat generated
k1 = k2*exp((E/R)*((1/T2)-(1/T1)));
Gt = -H*t*k1/(1+(t*k1));
eqns = subs(Rt == Gt, T0, t0);
y = zeros(1, nt);
old = 200;
for K = 1 : nt
    sol = double(vpasolve(eqns(K), T1, old));
    if isempty(sol)
        y(K) = nan;
    else
        y(K) = sol;
        old = sol;
    end
end

plot(t0, y, 'b-')

y1 = zeros(1, nt);
old = 500;
for K = 1 : nt
    sol = double(vpasolve(eqns(K), T1, old));
    if isempty(sol)
        y1(K) = nan;
    else
        y1(K) = sol;
        %old = sol;
    end
end

plot(t0, y1, 'b-')

y2 = zeros(1, nt);
old = 350;
for K = 1 : nt
    sol = double(vpasolve(eqns(K), T1, old));
    if isempty(sol)
        y2(K) = nan;
    else
        y2(K) = sol;
        %old = sol;
    end
end

plot(t0, y2, 'b-')

Answer 2

[Mischa Kim]

Hi, how about

plot(T0,y,'ro')

Since this is only one single data point it is hard to see in the plot, hence I change the color and shape.

[Sun Wook Han]

How do I need to define T0?

I tried

T0 = linspace(273, 500) 
plot (T0, y, 'ro')

but it doesn't work.

the error message says..

Error using mupadengine/feval_internal

More equations than variables is only supported for

polynomial systems.

Error in sym/vpasolve (line 172)

sol =

eng.feval_internal('symobj::vpasolve',eqns,vars,X0);

Error in Untitled3 (line 28)

y = vpasolve (Rt == Gt, T1)

[Mischa Kim]

I misinterpreted your question. Thanks, @Walter Roberson for providing an excellent answer.