A hypothetical metal alloy has a grain diameter of 2.4 10-2 mm. After a heat treatment at 575C for 500 min, the grain diameter has increased to 7.3 10-2 mm. Compute the time required for a specimen of this same material (i. e., d0

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 =

= 7.48 × 10⁻¹³ m/min

= = 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 =  = =503.08 = 504 min approximately.

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