Adiffusion couple of two metals, a and b, was fashioned as shown in figure 5.1. after a 26 hour heat treatment at 1050°c (and subsequent cooling to room temperature) the concentration of a is 4.0 wt% at the 14-mm position within metal b. if another heat treatment is conducted on an identical diffusion couple, only at 711°c for 26 hours, at what position (in mm) will the composition be 4.0 wt% a? the preexponential and activation energy values for the diffusion of a in b are 2.4 × 10-4 m2/s and 154 kj/mol, respectively.

1.25 mm

Explanation:

Given:

Temperature = 1050°C = 1050 + 273 = 1323 K

concentration of A = 4.0 wt%

preexponential value for the diffusion, D₀ = 2.4 × 10⁻⁴ m²/s

activation energy value for the diffusion, = 154 kJ/mol = 154 × 10³ J/mol

Diffusion coefficient at 1050°C , D₁₀₅₀ =

here,

R is the ideal gas constant = 8.314 J/mol·K.

T is the temperature

Thus

D₁₀₅₀ =

or

D₁₀₅₀ = 1.98 × 10⁻¹⁰

and,

Diffusion coefficient at 711°C , D₇₁₁ =

D₇₁₁ =

or

D₇₁₁ = 1.58 × 10⁻¹²

also,

 = constant

here, x is the position

thus,

or

or

x₇₁₁ = 1.25 mm

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