Question

A hypothetical metal alloy has a grain diameter of 2. 4 × 10−2 mm. After a heat treatment at 575°C for 500 min, the grain diameter has increased to 4. 1 × 10−2 mm. Compute the time required for a specimen of this same material (i. E. , d0 = 2. 4 × 10−2 mm) to achieve a grain diameter of 5. 5 × 10−2 mm while being heated at 575°C. Assume the n grain diameter exponent has a value of 2. 2

Answer 1

Step-by-step explanation: To compute the time required for the specimen to reap a grain diameter of five.Five × 10^(-2) mm at the same time as being heated at 575°C, we are able to use the grain increase equation:

(d2/d1) = exp(k*t)

where d2 is the very last grain diameter (5. Five × 10^(-2) mm), d1 is the initial grain diameter (2.4 × 10^(-2) mm), ok is the fee consistent, and t is the time.

First, we want to discover the charge constant, k? We can use the given information approximately the warmth treatment to calculate it:

(d2/d1) = (four.1 × 10^(-2) mm) / (2.4 × 10^(-2) mm) = 1.708

exp(k*t) = 1.708

Using the exponent property of logarithms, we can rewrite this equation as:

okay*t = ln(1.708)

Now, we can calculate the cost of k*t:

k*t = ln(1.708)

t = ln(1.708) / k

To find the time required for the specimen to gain a grain diameter of 5.5 × 10^(-2) mm, we want to replacement the fee of k from the given facts:

k = n * (d1^(-n))

ok = 2.2 * (2.Four × 10^(-2) mm)^(-2.2)

Now, we can replace the price of ok into the equation to find t:

t = ln(1.708) / k

Calculate the fee of ok and then alternative it into the equation to decide the time required for the specimen to gain the favored grain diameter of five.Five × 10^(-2) mm.