from math import *

La=44000
Ta=353
Lb=42800
Tb=373
R=8.314

def dicho(xmin,xmax,x,p,f):


    while xmax-xmin>p:
        m=(xmin+xmax)/2
        if x>f(m):
            xmin=m
        if x<f(m):
            xmax=m
        if x==f(m):
            return(m)
    return(m)

def f(x,t,m):
    return(x/(1-(R*x*log(m))/t))
def g(x):
    return(f(Ta,La,x)-f(Tb,Lb,1-x))
def heteroazeotrope():
    a=dicho(0,1,0,0.00001,g)
    return(dicho(0,1,0,0.00001,g),(f(Ta,La,a)+f(Tb,Lb,1-a))/2)