Ahypothetical metal alloy has a grain diameter of 1.7 ´ 10-2 mm. after a heat treatment at 450°c for 250 min the grain diameter has increased to 4.5 ´ 10-2 mm. compute the time required for a specimen of this same material (i. e., d0 = 1.7 ´ 10-2 mm) to achieve a grain diameter of 8.7 ´ 10-2 mm while being heated at 450°c. assume the n grain diameter exponent has a value of 2.1.

1103 minutes/66180 seconds

Explanation:

FIRST STEP: is to FIND the value of K using the formula below;

K= d^n - d^n(o)/t (1).

Parameters given from the question d^n = 4.5×10^-2 mm, d^n(o)= 1.7 × 10^-2 mm, t= 250 minutes(min) and n= 2.1.

Slotting in the parameters into the equation (1) above,then;

(4.5×10^-2)^2.1 - (1.7×10^-2)^2.1/ 250

= 5.2 × 10^-6 mm^2.1/min.

SECOND STEP: with the value of K from the second step, we can use it to calculate the required time based on the diameter. Therefore, equation (1) becomes;

t= d^2.1 - d^2.1(o)/ K

(8.7×10^-2)^2.1 - (1.7×10^-2)^2.1/ 5.2 × 10^-6

= 1,103 minutes.

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