6th_Sem_01 Plotting variation of Energy(E) & Specific heat at constant Volume(Cv) with Temperatue(T) for Maxwell-Boltzmann Statistics for 2 particles in 2 single state system using Python & Matplotlib

Plotting variation of Energy(E) & Specific heat at constant Volume(C_v) with Temperature(T) for Maxwell-Boltzmann Statics for 2 particles in 2 single state system using Python & Matplotlib 

Since the particles are distinguishable in MB statistics we can denote them as A & B

Configuration		Energy of the Configuration	No of states (gi)
0	ε
AB	-	0	1
-	AB	2ε	1
A	B	ε	2
B	A

The Partation function of the system is,

The mean energy of the system,

Now,

Now,

or,

for simplification let us assume,                      𝟄=1    &

So now,     Z(x)=1+exp(-2/x)+2exp(-1/x)

      〈E〉=(2exp(-2/x)+2exp(-1/x))/Z

      〈E²〉=(4exp(-2/x)+2exp(-1/x))/Z

Now it's time to write a program that can plot these functions, you can use this program or can modify it for more customisation.

import numpy as np import matplotlib.pyplot as plt x=np.linspace(0.01,2,1000) z=1+np.exp(-2/x)+2*np.exp(-1/x) E=(2*np.exp(-2/x)+2*np.exp(-1/x))/z Ep=E/2.0 Esq=E**2 E2=(4*np.exp(-2/x)+2*np.exp(-1/x))/z Cv1=(E2-Esq)/x**2 Cv1p=Cv1/2.0 Cv2=np.diff(E)/np.diff(x) Cv2p=Cv2/2.0 xx=0.5*(x[1:]+x[0:-1]) plt.plot(x,Ep,'b',x,Cv1p,'r',xx,Cv2p,'g--') plt.xlabel('Temperature(T)') plt.ylabel('E & Cv') plt.title('E & Cv Vs. Temp. plots') plt.legend(['E','Cv1','Cv2']) plt.grid() plt.show()

This is the output of the program

If you change the program, post your program in the comments. Believe me it is very interesting to modify and create your own program.

Thanks for finally reading. If you have any questions, comment below. I'll try to help it.

🙏Thank You🙏