C₁=C₂₁ (929) [1-a (25)] + The schematic diffusion profile in Figure 5.13 shows these concentration parameters as well as concentration profiles at times t = 0 and t> 0. Please note that at t = 0, the x = 0 position is taken as the initial diffusion couple interface, whereas C1 is the impurity concentration for x <0, and C2 is the impurity content for x > 0. Consider a diffusion couple composed of pure nickel and a 55 wt% Ni-45 wt% Cu alloy. Determine the time this diffusion couple must be heated at 1000°C in order to achieve a composition of 56.5 wt% Ni at distance of 15 um into the Ni-Cu alloy referenced to the original interface. Values for the pre-exponential and activation energy for this diffusion system are 2.3x104 m²/s and 252,000 J/mol respectively. C₁ Concentration t> 0 1101 4x10 C₂- x=0 C₁-C₂ x>0 Position

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Consider a diffusion couple composed of two semi-infinite solids of the same 
metal and that each side of the diffusion couple has a different concentration of the same elemental 
impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion 
couple. For this situation, the solution to Fick’s second law) is as follows

Cx=C₂ +
C₂ + ( 9₁-²₂) [₁-cα (25)]
2
The schematic diffusion profile in Figure 5.13 shows these concentration parameters as well as
concentration profiles at times t = 0 and t> 0. Please note that at t = 0, the x = 0 position is taken
as the initial diffusion couple interface, whereas C1 is the impurity concentration for x<0, and
C2 is the impurity content for x > 0. Consider a diffusion couple composed of pure nickel and a
55 wt% Ni-45 wt% Cu alloy. Determine the time this diffusion couple must be heated at 1000°C
in order to achieve a composition of 56.5 wt% Ni at distance of 15 µm into the Ni-Cu alloy
referenced to the original interface. Values for the pre-exponential and activation energy for this
diffusion system are 2.3x104 m²/s and 252,000 J/mol respectively.
Concentration
t> 07
t=01
<<<x<0
C₂-
x=0
C₁-C₂
2
x>0
Position
Transcribed Image Text:Cx=C₂ + C₂ + ( 9₁-²₂) [₁-cα (25)] 2 The schematic diffusion profile in Figure 5.13 shows these concentration parameters as well as concentration profiles at times t = 0 and t> 0. Please note that at t = 0, the x = 0 position is taken as the initial diffusion couple interface, whereas C1 is the impurity concentration for x<0, and C2 is the impurity content for x > 0. Consider a diffusion couple composed of pure nickel and a 55 wt% Ni-45 wt% Cu alloy. Determine the time this diffusion couple must be heated at 1000°C in order to achieve a composition of 56.5 wt% Ni at distance of 15 µm into the Ni-Cu alloy referenced to the original interface. Values for the pre-exponential and activation energy for this diffusion system are 2.3x104 m²/s and 252,000 J/mol respectively. Concentration t> 07 t=01 <<<x<0 C₂- x=0 C₁-C₂ 2 x>0 Position
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