week 2 problem 10

import numpy as np import matplotlib.pyplot as plt

def S_(N, V, U): """ Just a simple function to calculate entropy as defined in week 2 problem 10 """ return ((N*V*U)**(1/3))

Ntot = 50 #total amount - keep the same Vtot = 13 #total amount - keep the same Utot = 80 #total amount - keep the same NA = 30 #Can change in order to alter NA and NB VA = 9 #Can change in order to alter VA and VB NB = Ntot-NA VB = Vtot-VA UAlist = np.arange(0, Utot, 0.1) #creates UA to calculate S(UA) and then graph

#This cell calculates S(UA) for each UA SAlist = np.empty(len(UAlist)) for i in range(len(UAlist)): SAlist[i] = S_(NA, VA, UAlist[i])+S_(NB, VB, Utot-UAlist[i])

plt.plot(UAlist, SAlist) plt.xlabel(r"$U_A$ ( J )") plt.ylabel(r"S ( J K$^{-1} )$") plt.show() UAmax = UAlist[np.where(SAlist == np.max(SAlist))] print("The value of U_A that maximizes S(U_A) is ", UAmax) print("The maximum value of S(U_A) is ", np.max(SAlist))