Answer:
The time to achieve a grain diameter of 7.3× 10⁻² mm is 477 minutes
Explanation:
We need to first solve for K
Given that:
grain diameter exponent (n) = 2.2
grain diameter (d) = 7.3 × 10⁻² mm = 7.3× 10⁻⁵ m
d₀ = 2.4 × 10⁻² mm = 2.4 × 10⁻⁵ m
t = 500 min
then from k = [tex]d^{n} -do^{n} /t[/tex]
= 7.48 × 10⁻¹³ m/min
= [tex]\frac {(7.3 * 10^{-5} )^{2.2}* (2.4*10^{-5} )^{2.2}}{500}[/tex] = 1.44×10⁻¹²
From K we can determine the time required based on the desired diameter
grain diameter (d) = 7.3 × 10⁻² mm = 7.3× 10⁻⁵ m
so t =[tex]d^{n} -do^{n} /k[/tex] = [tex]\frac {(7.3 * 10^{-5} )^{2.2}* (2.4*10^{-5} )^{2.2}}{1.4*10^{-12} }[/tex] =503.08 = 504 min approximately.
