Asheet of steel 2.5-mm thick has nitrogen atmospheres on both sides at 900°c and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 1.85 × 10–10 m2/s, and the diffusion flux is found to be 1.0 × 10–7 kg/m2.s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 kg/m3. how far into the sheet from this high-pressure side will the concentration be 0.5 kg/m3

Explanation:

It is known that relation between diffusion flux () and the diffusion coefficient of () for the linear concentration profile at the steady state is as follows.

The negative sign shows that along the positive x-direction there occurs drop in concentration.

where,   and are the concentrations of at position 1 and 2 on steel sheet.

              and are the distances corresponding to distances on the sheet.

Now, putting the given values into the above formula as follows.

                        = 2.75 mm

Thus, we can conclude that 2.75 mm far into the sheet from given high-pressure side will the concentration be 0.5 .

in scientific notation, the value of the  speed of light in a vacuum

  will be written as 2.995 * 10^8. when this value is represented in the form of

  a * 10^b, then, a = 2.995 and b = 8.

the value of the speed of light in a vacuum given above can also be rounded up to approximately 300000000. in this case, the scientific notation will be written as 3 *10^8.