Question

Use a computer to make two plots of the Boltzmann, Fermi-Dirac, and Bose-Einstein distributions functions versus x=(LaTeX: \epsilon-\mu ϵ − μ )/kT. For one make both axes linear. For the other make the y-axis logarithmic, and indicate the x- and y- ranges where the distribution functions agree to better than one percent.

Answer 1

Please find the attached plots. I wrote a code in python to generate this graph. I am attaching the code for your convenience.

Python code

from math import *
import numpy as np
import matplotlib.pyplot as plt
X=np.linspace(0.0001,10, 5000)
fdd=[1/(exp(x)+1) for x in X ]
bee=[1/(exp(x)-1) for x in X]
btt=[exp(-x) for x in X]
plt.plot(X,fdd, label='Fermi Dirac distribution')
plt.plot(X,bee, label='Bose einstein distribution' )
plt.plot(X,btt, label='Boltzmann distribution')
plt.legend()
plt.yscale('log')
plt.ylabel('f(x)')
plt.ylim(0,5)
plt.xlabel('x=(e-\u03bc)/kbT')
plt.title('logarithmic plot')
plt.savefig('distribution_logarithmic.png')
plt.yscale('linear')
plt.title('linear plot')
plt.savefig('distribution_linear.png')