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function [v,err,count] = Clapeyrons(P)

% Calculate molar volume as predicted by the Ideal Gas Law equation

% using the Newton-Raphson algorithm with initial estimate

% determined by ideal gas law.

% Inputs:

R = 0.082057; % Ideal gas constant in L atm / K mol

T = 293; % Temperature in K

Tc = 416.90; % Critical temperature of Cl2 in K

Pc = 78.72918; % Critical Pressure of Cl2 in atm

a = ((R^2)*(Tc^(5/2)))/(9*Pc*(2^(1/3)-1));

b = (R*Tc*(2^(1/3)-1))/(3*Pc);

% P = 1; % Pressure in atm

% Outputs:

% v equals molar volume in L/mol as predicted by

% equation for gas considered at temperature T and pressure P.

% err equals modulus of function evaluated at approximate root.

% count is number of iterations taken by Newton-Raphson algorithm.

% Version 1: created 24/04/19. Author: Paul Curran

% Version 2: created 06/02/20. Author: Savana Stewart

if (~isscalar(P)) || (~isreal(P)) || P <= 0

error('Input argument P must be positive real scalar.')

end

Iteration_limit = 20; % maximum number of iterations permitted

Tolerance=10^-7; % maximum acceptable value for modulus of

A = (a*P)/((R^2)*(T^(5/2)));

B = (b*P)/(R*T);

v = R * T / P;

Z = (P*v)/(R*T);

C = A-B-B^2;

f1 = [1 -1 C -A*B]; % f = (Z^3) - (Z^2) + (A-B-(B^2))*Z - (A*B)

f = polyval(f1,Z);

v = Z*R*T/P;

for count = 1:Iteration_limit + 1

% Terminate with error message if iteration limit exceeded:

if count == Iteration_limit + 1

error('Iteration limit reached. Iteration did not converge.')

end

% Terminate iteration if function is sufficiently small at current

% estimate

if abs(f)<Tolerance

break

end

%f_dash = 3*Z^2 - 2*Z + (A - B - (B^2)); % Evaluate derivative of f

f_dash = [0 3 -2 C];

Z = Z - (f1./f_dash); % Newton-Raphson iteration

end

err = abs(f); % Error is magnitude of f(v) at final root estimate

end

%%

% COPY THE FOLLOWING INTO THE COMMAND WINDOW

% P = [1 1.5 2 2.5 3 5 10 15 25 50 100];

% v = zeros(1,length(P));

% for i=1:length(P)

% [u,err,count]=Clapeyrons(P(i));

% v(i)=u;

% end

%

% P1=[1:0.1:100];

% V1=R*T./P1;

% plot(P1,V1)

% hold on

% plot(P,v,'or')

I says iteration limit reached but I only changed the format a little. How do I fix it?

KALYAN ACHARJYA
on 13 Feb 2020

Edited: KALYAN ACHARJYA
on 13 Feb 2020

Its doing as defined in the code, when the iteration reached more than iteration limit, it reflects the message as mentioned within the code

if count == Iteration_limit + 1

error('Iteration limit reached. Iteration did not converge.')

end

Before getting the break statement, your code reached the limit, please check, there may be abs(f) never less than Tolerance

if abs(f)<Tolerance

break

end

Its simple code, debug it step by step, ensure that it reached the break statement before reched the iteration limit, ensure that f is changing in right direction during each iteration. The loop execute the iteration as number of times=iteration limit.

Choose the right parameters values or codition to reached the break before reached to operation limit, see the tolerance value also.

KALYAN ACHARJYA
on 13 Feb 2020

Change the variables value or tolerance value, when I change the tolerance value, it converging

Tolerance=10^7; % I know this is the correct value as required

# Do the Basic Maths, you get the appropriape typical values, so that it converge

>> [v,err,count]=Clapeyrons(5)

v =

4.8085

err =

0.0572

count =

1

>>

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