Predict Grain Diameter at 650°C After 199 min

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The discussion centers on predicting the grain diameter of a metal alloy at 650°C after 199 minutes, given that the growth follows a quadratic function with n=2. The measured grain diameters at 30 minutes and 90 minutes are 0.039 mm and 0.066 mm, respectively. Participants suggest using a quadratic growth equation to extrapolate the grain diameter for the specified time. The need for clarification on the variable 'n' and the relevant equations is emphasized to solve the problem accurately.

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The average grain diameter for a metal alloy was measured as a function of time at 650°C. The results are tabulated below:

Time Grain diameter
(min) (mm)
30 3.9 x 10-2
90 6.6 x 10-2

Predict what the grain diameter would be (in mm) after 199 min at the same temperature if n=2.

any ideA?
 
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Hi Sniperfx20, welcome to PF. Can you tell us what n is? It would also be helpful if you told us any equations that you've been given along with showing your attempt at the problem.
 
Sniperfx20 said:
The average grain diameter for a metal alloy was measured as a function of time at 650°C. The results are tabulated below:

Time Grain diameter
(min) (mm)
30 3.9 x 10-2
90 6.6 x 10-2

Predict what the grain diameter would be (in mm) after 199 min at the same temperature if n=2.

any ideA?
Looks like a grain growth problem. One has two sizes and two times, and one is trying to use a function. Is 'n' an exponent to a growth or diffusion equation? If so, then n=2 is a quadratic function.
 

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