education.wiley.com/was/U//v2/asseSSHIOぐ→e Homework - Chapter 107 of 10三View PoliciesCurrent Attempt in ProgressThe kinetics of some phase transformations obey the Avramirelationship. Using the fraction transformed-time data given below,determine the total time required for the transformation to go to93% completion.Fraction transformed Time (s)0.212.10.826.3Type here to search

FRACTION TRANSFORMED TIME (s) 0.2 12.1 0.8 26.3 TO DETERMINE: (a) The total time required for the transformation to go to 93% completion, t.The Avrami relationship is given as, 1-y=e-ktn -------------------- (1) Taking natural logarithms ln on both sides, we get, ln1-y=-ktn (or) -ln1-y=ktn Rearranging above equation, we have, ln11-y=ktn ------------------- (2) Now taking natural logarithms again, we have, lnln11-y=lnk+nlnt --------------------- (3) Using above equation, we can calculate the time taken for transformation.The total time required for the transformation to go to 93% completion, t: FOR DATA-1: Substituting for equation (3), we have, lnln11-0.2=lnk+nln12.1 ------------------- (4) FOR DATA-2: Substituting for equation (3), we have, lnln11-0.8=lnk+nln26.3 ------------------- (5) Solving equation (4) and (5), we get, n=1.725 and k=0.0167. For y=93%=0.93, the time taken is calculated using the equation, ln1-y=-ktn (or) t=-ln1-yk1/n ------------------ (6) Substituting for equation (6), we have, t=-ln1-0.930.01671/1.725 t=-ln0.070.01670.58 t=--2.660.01670.58 t=159.280.58 The time taken for 93% of transformation is calculated as, t=18.934 s.The total time required for the transformation to go to 93% completion, t is calculated as, t=18.934 s,

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