# Exercise 3.23

from math import log, pi
def egg(M, T0=20, Ty=70):
    rho = 1.038
    K = 5.4e-3
    c = 3.7
    Tw = 100
    t = M**(2.0/3) * c * rho**(1.0/3) / (K * pi**2 * ((4*pi)/3)**(2.0/3)) * log(0.76*(T0-Tw)/(Ty-Tw))
    return t

# For a soft boiled egg, the yolk temperature (Ty) should not exceed 70, 
# while for a hard boiled egg, the yolk temperature should be allowed to
# reach 70. This is according to Exercise 1.12 on page 46. So how should 
# we set Ty? Here we use Ty=65 for soft boiled egg and Ty=80 for hard 
# boiled egg. 

# Soft boiled, small, from fridge:
print(egg(47, T0=4, Ty=65))/60

# Soft boiled, large, from fridge:
print(egg(67, T0=4, Ty=65))/60

# Soft boiled, small, from hot room:
print(egg(47, T0=25, Ty=65))/60

# Soft boiled, large, from hot room:
print(egg(67, T0=25, Ty=65))/60

# Hard boiled, small, from fridge:
print(egg(47, T0=4, Ty=80))/60

# Hard boiled, large, from fridge:
print(egg(67, T0=4, Ty=80))/60

# Hard boiled, small, from hot room:
print(egg(47, T0=25, Ty=80))/60

# Hard boiled, large, from hot room:
print(egg(67, T0=25, Ty=80))/60