TEMPERATURE Vs SPECIFIC HEAT - LINEAR CUBIC CURVE FITTING USING PYTHON

1. What does popt and pcov mean?
Answer: curve fit calculates coefficients and output as popt. popt contains coefficients a,b,c,d. 
pcov : 2d array. The estimated covariance of popt.

2. What does np.array(temperature) do?
numpy array for passing all temperature values as an array to function.

3. What does the * in *popt mean?
* refers to coefficients a,b,c,d contained in popt.

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CURVE FITTING PYTHON CODING 
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# CURVE FITTING FOR LINEAR EQUATION (Y=AX+B)

import numpy as np
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit

#curve fit function
def func_linear(t,a,b):
	return a*t+b

#reading thermodynamic data file
def read_file():
	temperature=[]
	cp=[]
	for line in open(\'data\',\'r\'):
		values=line.split(\',\')
		temperature.append(float(values[0]))
		cp.append(float(values[1]))

	return[temperature,cp]

# program linear
temperature,cp = read_file()
popt, pcov = curve_fit(func_linear,temperature,cp)
fit_cp = func_linear(np.array(temperature),*popt)

#GRAPH

plt.plot(temperature,cp,color=\"blue\",linewidth=3)
plt.plot(temperature,fit_cp,color=\"red\",linewidth=3)
plt.title(\'Specific Heat Vs Temperature\')
plt.legend([\'Actual data\',\'Curve fit\'])
plt.xlabel(\'Temperature[K]\')	
plt.ylabel(\'cp\')
plt.show()

# CURVE FIT FOR CUBIC EQUATION (Y=AX^3+BX^2+CX+D)

import numpy as np
import matplotlib.pyplot as plt 
from scipy.optimize import curve_fit

# Curve fit function - a*t^3+b*t^2+c*t+d
# a, b, c, d are coefficients / constants
def func_cubic(t,a,b,c,d):
	return a*pow(t,3)+b*pow(t,2)+c*t+d

# reading the data file (temperature and specific heat)
def read_file():
	temperature=[]
	cp=[]
	for line in open(\'data\',\'r\'):
		values=line.split(\',\')
		temperature.append(float(values[0]))
		cp.append(float(values[1]))

	return[temperature,cp]

# program cubic fit

temperature,cp=read_file()
popt,pcov=curve_fit(func_cubic,temperature,cp)
fit_cp=func_cubic(np.array(temperature),*popt)

#GRAPH

plt.plot(temperature,cp,color=\"blue\",linewidth=3)
plt.plot(temperature,fit_cp,color=\"red\",linewidth=3)
plt.title(\'Specific Heat Vs Temperature\')
plt.legend([\'Actual data\',\'Curve fit\'])
plt.xlabel(\'Temperature[K]\')	
plt.ylabel(\'cp\')
plt.show()

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GRAPH-LINEAR CURVE FIT

GRAPH - CUBIC CURVE FIT

SCREENSHOT1 (LINEAR PLOT)

SCREENSHOT2 (CUBIC PLOT)