Find the diffusivity through slab if N flux of A 4 mol/sq.m sec, concentration difference is 2mol/cu.m and distance is 3 m.a)2 sq.m/sb)4 sq.m/sc)6 sq.m/sd)8 sq.m/sCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

To find the diffusivity through a slab, we can use Fick's first law of diffusion, which states that the flux of a species A through a medium is proportional to the concentration gradient of A. Mathematically, it is represented as:

J = -D * (∂C/∂x)

where J is the flux of A, D is the diffusivity of A, C is the concentration of A, and x is the distance.

Given:
Flux of A (J) = 4 mol/sq.m sec
Concentration difference (∂C/∂x) = 2 mol/cu.m
Distance (x) = 3 m

We need to find the diffusivity (D).

Let's rearrange Fick's law to solve for D:

D = -J / (∂C/∂x)

Now substitute the given values:

D = -4 mol/sq.m sec / 2 mol/cu.m

Simplifying the expression:

D = -2 sq.m/s

Since diffusivity is a positive value, we can drop the negative sign:

D = 2 sq.m/s

Therefore, the diffusivity through the slab is 2 sq.m/s, which matches option C.

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