A sheet 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 x 10^-10 m^2/s, and the diffusion flux is found to be 1.0 x 10^-7 kg/m^2 s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 kg/m^3. How far into the sheet from this high-pressure side will the concentration be 0.5 kg/m3? Assume a linear concentration profile.

x = 2.78x10⁻³ m

Explanation:

According to Fick's law of diffusion:

Where:

J: is the diffusion flux = 1.0x10⁻⁷ kg/(s*m²)    

D: is the diffusion coefficient = 1.85x10⁻¹⁰ m²/s              

: is the nitrogen concentration in the surface of steel = 2 kg/m³

: is the nitrogen concentration in the point x = 0.5 kg/m³

s: is the position at the steel's surface = 0

x: is the position into the sheet where the concentration is Cₓ

So, x is:

Therefore, the nitrogen concentration will be 0.5 kg/m³ at 2.78x10⁻³ m in the steel sheet.

I hope it helps you!

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explanation:

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.