A sheet of steel 5.0-mm thick has nitrogen atmospheres on both sides at 1000°C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 1.95 × 10-10 m2 /s, and the diffusion flux is found to be 1.2 × 10-7 kg/m2.s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 3 kg/m3 . How far into the sheet from this high-pressure side will the concentration be 0.5 kg/m3 ? Assume a linear concentration profile

The distance from the higher concentration side is

Explanation:

From the question we are told that

    The thickness of the steel is

    The temperature is  

     The diffusion coefficient of nitrogen in steel  is

     The diffusion flux is

      The concentration of nitrogen in steel is

       The concentration at distance d is

Generally Fick's first law show the relationship between diffusion flux and concentration under an assumption of steady state and this can be represented mathematically as

  Where D is the diffusion coefficient and   is the concentration gradient

    and  J is the diffusion flux

  Now if we are considering two concentration the equation for concentration gradient  becomes

Where   is the concentraion at high pressure while is concentration at low pressure

   is the position at the high concentration  side

     is the position at the low concentration side

Now sustituting values into the formula for  concentration gradient

Now substituting values into equation for Fick's law

Since  the position the higer concentration side from origin is the from the equation  we see that the distance of the sheet  from the higher concentration side is  

if they have a finite resultant