take home

 
clc;
clear;
%Initializing variables to be used later
answer = 500;
error = 100;
 
%Opens File named VLEdata.txt and stores data from the file
fid = fopen('VLEdata.txt','r');
headers = textscan(fid,'%s',3,'delimiter', '\n');
headers{1,1}(1);
headers{1,1}(2);
headers{1,1}(3);
data = textscan(fid,'%f %f %f','delimiter','\n');
X=data{1,1}(:,1);
Y=data{1,2}(:,1);
T=data{1,3}(:,1);
 
%Makes a matrix Z with the deminsions of X
sizeXYT=size(X);
rowsXYT=sizeXYT(1,1);
columnsXYT=sizeXYT(1,2);
Z=zeros(rowsXYT,columnsXYT);
 
%Divides matrix X and Y by 100 to get them in Mole Fractions
X=X./100;
Y=Y./100;
 
 
%for loop from 1 to rowsXYT that makes each index in Z equal to its
%corresponding indexes in Y and X to Y - X
for k=1:1:rowsXYT
    Z(k,1)=Y(k,1)-X(k,1);
end
 
%for loop from 1 to rowsXYT that takes the inverse of all Z indexes which
%are not equal to 0. Done to avoid divison by 0
for i.html">i=1:1:rowsXYT
    %If the Z index is not equal to 0 then proceed
    if Z(i.html">i,1)~=0
        %take the inverse of the Z index
Z(i.html">i,1)=Z(i.html">i,1).^(-1);
    end
end
%Makes a matrix A which shows the indexes in Z which are nonzero
    A=find(Z);
%Finds the size of Matrix A
    D=size(A);
%Sets variable l equal to the number of columns in Matrix A
    l=D(1,1);
%Creates a zero matrix of the same size as Matrix A
M = zeros(l,1);
N = zeros(l,1);
 
%for loop from 1 to the number of columns of matrix A
for k=1:1:l
    %Assigns num to the number contained in the given index in Matrix A
    num=A(k,1);
    %Uses num to assign matrix M the non-zero numbers from Z
    M(k,1)=Z(num,1);
    %Uses num to assign corresponding X values to N
    N(k,1)=X(num,1);
 
end
 
%Uses polyfit create a polynomial regression of N and M (non-zero Z values
%and their corresponding X values
p=polyfit(N,M,10);
 
%Plots the given data and the polynomial regression
t2=0:.01:1;
y2=polyval(p,t2);
plot(N,M,'o',t2,y2)
hold on;
title(headers{1,1}(1))
xlabel('x')
ylabel('1/Y-X')
grid()
 
%Sets the variable r equal to Xo
r=.8;
%Sets the function F equal to the polynomial regression found above
F=p(1,1)*r^10+p(1,2)*r^9+p(1,3)*r^8+p(1,4)*r^7+p(1,5)*r^6+p(1,6)*r^5+p(1,7)*r^4+p(1,8)*r^3+p(1,9)*r^2+p(1,10)*r+p(1,11);
%Sets the variable Finitial equal to the value of F at Xo
Finitial=F;
%Sets the variable LHS equal to the left hand side of the equation 
%log(n/n0)
LHS = log(25/50);
 
%While loop that will excecute so long as error is greater than or equal to .0001
while error >= .0001   
 
%Decreases the value of r by .0001 per iteration from its starting value of
%Xo
        r=r-.0001;
%Sets F equal to the value of the polynomial regression function at the new
%r value
F=p(1,1)*r^10+p(1,2)*r^9+p(1,3)*r^8+p(1,4)*r^7+p(1,5)*r^6+p(1,6)*r^5+p(1,7)*r^4+p(1,8)*r^3+p(1,9)*r^2+p(1,10)*r+p(1,11);
%Uses trapezodial approximation to find the area under the curve
RHS = ((r-.8)*((Finitial)+(F)))/2;
%Calculates and error between the area under the curve and the Left Hand Side of the
%equation
error = abs(RHS - LHS);
end
 
%Caluclates the Y value at the found X value using 1/(Y-X) = F(X)
Yvalue = (1/F)+r;
%fprintf to print out the compositions of liquid and vapor phases in the
%still when the remaining quanitity in the still is 25 moles
fprintf('LHS: %.4f\nRHS: %.4f\nError: %.4f\nLiquid Phase Quantity:%.4f\nVapor Phase Quantity: %.4f\n\n',LHS,RHS,error,r,Yvalue);