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ser-zykov [4K]
3 years ago
5

For some transformation having kinetics that obey the Avrami equation, the parameter n is known to have a value of 1.7. If, afte

r 100 s, the reaction is 50% complete, how long (total time) will it take the transformation to go to 99% completion?

Engineering
2 answers:
luda_lava [24]3 years ago
8 0

Answer:

It would take approximately 305 s to go to 99% completion

Explanation:

Given that:

y = 50% = 0.5

n = 1.7

t = 100 s

We need to first find the parameter k from the equation below.

exp(-kt^n)=1-y

taking the natural logarithm of both sides:

-kt^n=ln(1-y)\\kt^n=-ln(1-y)\\k=-\frac{ln(1-y)}{t^n}

Substituting values:

k=-\frac{ln(1-y)}{t^n}= -\frac{ln(1-0.5)}{100^1.7} = 2.76*10^{-4}

Also

t^n=-\frac{ln(1-y)}{k}\\t=\sqrt[n]{-\frac{ln(1-y)}{k}}

Substituting values and y = 99% = 0.99

t=\sqrt[n]{-\frac{ln(1-y)}{k}}=\sqrt[1.7]{-\frac{ln(1-0.99)}{2.76*10^{-4}}}=304.6s

∴ t ≅ 305 s

It would take approximately 305 s to go to 99% completion

V125BC [204]3 years ago
6 0

Answer: Time = 304.6 seconds

Explanation: please find the attached file for the solution

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