Chapter 5, Problem 5.49P

Interpretation Introduction

Interpretation:

The time required to obtain $10\text{wt\%}\text{Zn}$ at the depth of $\text{0}\text{.5}\text{mm}$ below the surface of copper should be calculated. The feasibility of process with respect to given conditions should be determined. Also, the practical problems arise by increasing the temperature to ${\text{1000}}^{°}\text{C}$ should be explained.

Concept introduction:

Fick's Law of diffusion: This law states that molar flux is directly proportional to concentration gradient. The law is stated as:

  $\text{J}\text{=}-\text{D}\frac{{\text{dC}}_{\text{A}}}{\text{dx}}$

Where,

J is the molar flux defined as the number of atoms passing per unit area per unit time.

D is the diffusion coefficient in ${\text{cm}}^{\text{2}}\text{/sec}$.

  $\frac{{\text{dC}}_{\text{A}}}{\text{dx}}$ is the concentration gradient in $\frac{\text{atoms}}{{\text{cm}}^{\text{3}}\text{.cm}}$.

Factors affection diffusion are as follows:

1. Temperature
2. Diffusion coefficient

The following equation is stated as:

  $\text{D}={\text{D}}_{\text{0}}\exp \left(\frac{\text{-Q}}{\text{RT}}\right)$

Where,

Q is the activation energy in calorie/ mole.

R is universal gas constant in $\frac{\text{cal}}{\text{mole}\text{K}}$.

T is the absolute temperature in kelvin.

  ${\text{D}}_{\text{0}}$ is constant for given diffusion system and its value is defined as $\frac{\text{1}}{\text{T}}=0$ or $\text{T}\text{=}\infty$.