Curve Fitting of temperature and specific heat variation

%curve fitting of temperature vs specific heat
clear all
close all
clc
%load the data which contains variation of specific heat with temperature
temp_cp=load(\'data\');

temperature=temp_cp(:,1);
cp=temp_cp(:,2);




%%curve fit
%%cp=a*t^2+b*t+c

coeff=polyfit(temperature,cp,2);
predicted_cp=polyval(coeff,temperature);

%plotting the data
figure(1)
title(\'Second Order Fit\')
hold on
xlabel(\'Temperature [K]\',\'color\',\'r\')
ylabel(\'Specific Heat [KJ/Kg-K]\',\'color\',\'r\')
plot(temperature,cp,\'linewidth\',1,\'color\',\'g\')
plot(temperature,predicted_cp,\'linewidth\',1,\'color\',\'r\')
legend(\'Original data set\',\'curve fit\')
grid on


%using third order polynomial
coeff_3=polyfit(temperature,cp,3)
predicted_cp1=polyval(coeff_3,temperature)
figure(2)
title(\'Third Order Fit\')
hold on
plot(temperature,cp,\'linewidth\',1,\'color\',\'g\')
plot(temperature,predicted_cp1,\'linewidth\',1,\'color\',\'r\')
xlabel(\'Temperature [K]\',\'color\',\'r\')
ylabel(\'Specific Heat [KJ/Kg-K]\',\'color\',\'r\')
legend(\'Original data set\',\'curve fit\')


 

To get more smooth curve fit we can use higher order polynomials or splitwise polynomials which means using differents polynomials for different range of temperatures.