The diffusion coefficient of hydrogen in steel is given as a function of temperature as $$ D_{A B}=1.65 \times 10^{-6} \exp (-4630 / T)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ where \(T\) is in \(\mathrm{K}\). Determine the diffusion coefficients at \(200 \mathrm{~K}\), \(500 \mathrm{~K}, 1000 \mathrm{~K}\), and \(1500 \mathrm{~K}\).

Short Answer

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Question: Calculate the diffusion coefficients of hydrogen in steel using the equation $D_{A B}=1.65 \times 10^{-6} \exp (-4630 / T)\left(\mathrm{m}^{2} / \mathrm{s}\right)$ at the following temperatures: 200 K, 500 K, 1000 K, and 1500 K. Answer: To find the diffusion coefficients, plug in the given temperature values into the equation and calculate the resulting values. The calculated diffusion coefficients are as follows: - At 200 K: $D_{A B}(200K)=__\,\,\left(\mathrm{m}^{2} / \mathrm{s}\right)$ - At 500 K: $D_{A B}(500K)=__\,\,\left(\mathrm{m}^{2} / \mathrm{s}\right)$ - At 1000 K: $D_{A B}(1000K)=__\,\,\left(\mathrm{m}^{2} / \mathrm{s}\right)$ - At 1500 K: $D_{A B}(1500K)=__\,\,\left(\mathrm{m}^{2} / \mathrm{s}\right)$

Step by step solution

01

Identify the given equation for diffusion coefficient

The equation provided for the diffusion coefficient as a function of temperature is: $$ D_{A B}=1.65 \times 10^{-6} \exp (-4630 / T)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$
02

Calculate diffusion coefficient at 200 K

Plug in the value of temperature, T = 200 K, into the given equation: $$ D_{A B}(200K)=1.65 \times 10^{-6} \exp (-4630 / 200)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ Compute the value of the diffusion coefficient at 200 K.
03

Calculate diffusion coefficient at 500 K

Plug in the value of temperature, T = 500 K, into the given equation: $$ D_{A B}(500K)=1.65 \times 10^{-6} \exp (-4630 / 500)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ Compute the value of the diffusion coefficient at 500 K.
04

Calculate diffusion coefficient at 1000 K

Plug in the value of temperature, T = 1000 K, into the given equation: $$ D_{A B}(1000K)=1.65 \times 10^{-6} \exp (-4630 / 1000)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ Compute the value of the diffusion coefficient at 1000 K.
05

Calculate diffusion coefficient at 1500 K

Plug in the value of temperature, T = 1500 K, into the given equation: $$ D_{A B}(1500K)=1.65 \times 10^{-6} \exp (-4630 / 1500)\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ Compute the value of the diffusion coefficient at 1500 K. Through these steps, we will find the diffusion coefficients at the given temperature values.

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