Question

using python

6. Solve the following non-linear equations using fsolve. 1.5 Al B1 Al 1.5 o= 42 G.-20 ,nol / liter, k-0.12 min. τ-5 min

Answer 1

Code:

from numpy import *
from scipy.optimize import * #importing all packages from scipy and numpy

def fun(z):
Ca1 = z[0]
Ca2 = z[1]
Cb1 = z[2]
Cb2 = z[3]
  
tau = 5 # in min
Ca0 = 20 # in mol / liter
k = 0.12 # in min^-1
  
F = empty((4)) # intialize F to store 4 equations
  
F[0] = (Ca0 - Ca1)/tau - k*pow(Ca1 , 1.5)
F[1] = -Cb1/tau + k*pow(Ca1 , 1.5)
F[2] = (Ca1 - Ca2)/tau - k*pow(Ca2 , 1.5)
F[3] = (Cb1 - Cb2)/tau - k*pow(Ca2 , 1.5)
return F
  
  
zguess = array([1, 1, 1, 1])
z = fsolve(fun, zguess)
print(z)

Output:

Ca1 = 7.55 , Ca2 = 3.55 , Cb1 = 12.45 , Cb2 = 8..45