A 1mm sheet of FCC iron is used to contaion nitrogen in a heat exchanger at 1200 C. The concentration of N at one surface is 0.04 atomic percent and the concentration at the second surface is 0.005 atomic percent. Determine the flux of nitrogen through the foil in N atoms/cm^2xs. Look up any required parameters.
To determine the flux of nitrogen through the iron foil in N atoms/cm^2s, we can use Fick's First Law of Diffusion. The equation is given by:
J = -D * (dc/dx)
Where:
J is the diffusion flux in atoms/cm^2s
D is the diffusion coefficient in cm^2s^-1
dc/dx is the concentration gradient in atoms/cm^4
First, we need to calculate the concentration gradient (dc/dx). The concentration gradient is the difference in concentration between the two surfaces divided by the thickness of the foil.
dc/dx = (C2 - C1) / x
Where:
C2 is the concentration at the second surface (0.005 atomic percent)
C1 is the concentration at the first surface (0.04 atomic percent)
x is the thickness of the foil in cm (1 mm = 0.1 cm)
dc/dx = (0.005 - 0.04) / 0.1
dc/dx = -0.035 / 0.1
dc/dx = -0.35 atomic percent/cm
Next, we need to find the diffusion coefficient (D) for nitrogen in iron at 1200°C. It is advisable to consult a relevant reference or look up a diffusion database to obtain this value. The diffusion coefficient may vary depending on the temperature, composition, and other factors.
Once you have obtained the diffusion coefficient, you can multiply it by the concentration gradient to find the diffusion flux (J). The unit of J will be in atoms/cm^2s.
Please note that the diffusion coefficient for nitrogen in iron at 1200°C may not be readily available in this step-by-step AI model.
To determine the flux of nitrogen through the iron foil, we need to use Fick's first law of diffusion, which states that the flux of a species across a unit area is proportional to the concentration gradient.
The formula for Fick's first law of diffusion is:
J = -D * dc/dx
where J is the flux of the species (in atoms/cm^2·s), D is the diffusion coefficient (in cm^2/s), dc/dx is the concentration gradient (in atomic percent/cm).
Given:
- Thickness of the iron foil (t) = 1 mm = 0.1 cm
- Temperature (T) = 1200 °C = 1473 K
- Concentration at the first surface (C1) = 0.04 atomic percent
- Concentration at the second surface (C2) = 0.005 atomic percent
To calculate the diffusion coefficient (D) of nitrogen in iron at this temperature, we need to refer to experimental data or references. Let's assume the diffusivity (D) of nitrogen in iron at 1200 °C is 1 x 10^-7 cm^2/s.
Now, we can calculate the concentration gradient (dc/dx) and then the flux (J).
First, calculate the concentration gradient:
dc/dx = (C2 - C1) / t
= (0.005 - 0.04) / 0.1
= -0.35 atomic percent/cm
Next, substitute the values into Fick's first law of diffusion:
J = -D * dc/dx
= - (1 x 10^-7 cm^2/s) * (-0.35 atomic percent/cm)
= 3.5 x 10^-8 atomic percent·cm/s
Therefore, the flux of nitrogen through the 1mm FCC iron foil is 3.5 x 10^-8 atomic percent·cm/s.
Please note that the diffusion coefficient value assumed here is just for the purpose of calculation. Actual diffusivity values can vary and should be determined by referencing appropriate sources or experimental data.