Answer:
The time to achieve a grain diameter of 5.5 × 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) = 5.6 × 10⁻² mm = 5.6 × 10⁻⁵ m
d₀ = 2.4 × 10⁻² mm = 5.6 × 10⁻⁵ m
t = 500 min
[tex]K=\frac{d^{n} -d_{o}^{n}}{t} = \frac{(5.6*10^{-5})^{2.2}-(2.4*10^{-5})^{2.2} }{500}[/tex] = 7.48 × 10⁻¹³ m/min
From K we can determine the time required based on the desired diameter
grain diameter (d) = 5.5 × 10⁻² mm = 5.5 × 10⁻⁵ m
[tex]t=\frac{d^{n} -d_{o}^{n}}{K} = \frac{(5.5*10^{-5})^{2.2}-(2.4*10^{-5})^{2.2} }{7.48*10^{-13} }[/tex] = 477 min
