import numpy as np import matplotlib.pyplot as plt

# Entropy equation def s(N, V, U): return (N * V *U) ** (1/3)

# Verify a) as sanity check s(50, 13, 80)

# Vary U_a from 0 to 80 in intervals of 0.1 U_a = np.linspace(0, 80, 801)

# PART B # Find S_a and S_b as functions of U_a and U - U_a respectively S_a = s(30, 9, U_a) S_b = s(20, 4, 80 - U_a) # Add them up to find total entropy of system S_tot = S_a + S_b S_tot

# Plot S_tot vs U_a plt.plot(U_a, S_tot) plt.xlabel("U_a") plt.ylabel("Total Entropy") plt.show()

# Find U_a for which total entropy was maximized U_a[np.argmax(S_tot)]

# Max value of S_tot S_tot[np.argmax(S_tot)]

# PART E # Change volumes # Find S_a and S_b as functions of U_a and U - U_a respectively S_a = s(30, 7.8, U_a) S_b = s(20, 5.2, 80 - U_a) # Add them up to find total entropy of system S_tot = S_a + S_b S_tot

# Max value of S_tot S_tot[np.argmax(S_tot)]

# Find U_a for which total entropy was maximized U_a[np.argmax(S_tot)]

def T(N, V, U): return 3 * U ** (2/3) / ( (N * V) ** (1/3))

# Temp in part a) T(50, 13, 80)

# Temp in part e) T_a = T(30, 7.8, 48.0) T_b = T(20, 5.2, 32.0) T_a, T_b