Question

Under the steady-state condition, Fick’s first law is given as

\(J = - D\frac{{dc}}{{dx}}\)

Where, J = Diffusion flux,

D = Diffusion coefficient,

dc / dx = Concentration gradient

The unit of diffusion coefficient will be:

1. m/s²
2. m/s
3.

m²/s

4. kg/m³

Answer 1

Correct Answer - Option 3 :

m²/s

Concept:

Fick’s Law of diffusion states that “the mass flux of a constituent per unit area is proportional to the concentration gradient”.

\(J = - D\frac{{dc}}{{dx}}\)

where

J = mass flux of constituent per unit area, \(\frac{{dc}}{{dx}}= concentration~ gradient\)

-ve sign indicates that the concentration gradient decreasing in the direction of mass transfer.

Calculation:

\(J = \frac{{\dot m}}{A} = kg/{m^2}s\)

\(\frac{{dc}}{{dx}} = \frac{{kg/{m^3}}}{m} = kg/{m^4}\)

∴ \(D = \frac{J}{{\frac{{dc}}{{dx}}}}\)

\( \Rightarrow D = \frac{{\frac{{kg}}{{{m^2}s}}}}{{\frac{{kg}}{{{m^4}}}}}\)

\( \Rightarrow D = \frac{{kg}}{{{m^2}s}} \times \frac{{{m^4}}}{{kg}}\)

∴ D = m²/s