Question

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

Answer 1

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 =
`d^(n) -do^(n) /t`

= 7.48 × 10⁻¹³ m/min

=
`\frac {(7.3 * 10^(-5) )^(2.2)* (2.4*10^(-5) )^(2.2)}{500}` = 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 =
`d^(n) -do^(n) /k` =
`\frac {(7.3 * 10^(-5) )^(2.2)* (2.4*10^(-5) )^(2.2)}{1.4*10^(-12) }` =503.08 = 504 min approximately.