An undesirable consequence of welding steel by acetylene torch is the rise in hydrogen concentration in the metal. That hydrogen contamination embrittles the steel. The metal is typically subjected to a vacuum heat treatment to restore ductility. A steel part is placed in a vacuum furnace at 600∘C for one hour. The H concentration (initially uniform in the weld) falls to 1/2 its initial value at a depth of 500μm from the surface: It is known that the diffusivity of H in the steel at 600∘ C is 3.091×10−4 cm2/sec. An identical part is heat treated at 700∘ C. Under these conditions the H concentration falls to 1/2 its initial value at a depth of 500μm in 50 minutes. What is the diffusivity of H in steel at 700∘ C?
Give your answer in units of cm2/s, in scientific notation up to two decimal places
To find the diffusivity of hydrogen in steel at 700°C, we can use Fick's second law of diffusion:
D = (x^2)/(4t)
Where:
D is the diffusivity of hydrogen
x is the distance at which the concentration falls to 1/2 its initial value
t is the time it takes for the concentration to fall to 1/2 its initial value
We are given that x = 500 μm (or 0.5 cm) and t = 50 minutes. We need to convert the time to seconds:
t = 50 minutes * 60 seconds/minute = 3000 seconds
Now, we can plug the values into the formula:
D = (0.5^2)/(4 * 3000) = 0.000083 cm^2/s
Therefore, the diffusivity of hydrogen in steel at 700°C is approximately 8.3 × 10^-5 cm^2/s.