Chapter 5: Problem 4
Briefly explain the concept of steady state as it applies to diffusion.
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Chapter 5: Problem 4
Briefly explain the concept of steady state as it applies to diffusion.
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Carbon is allowed to diffuse through a steel plate \(15 \mathrm{~mm}\) thick. The concentrations of carbon at the two faces are \(0.65\) and \(0.30 \mathrm{~kg} \mathrm{C} / \mathrm{m}^{3}\) Fe, which are maintained constant. If the preexponential and activation energy are \(6.2 \times\) \(10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) and \(80,000 \mathrm{~J} / \mathrm{mol}\), respectively, compute the temperature at which the diffusion flux is \(1.43 \times 10^{-9} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\).
An FCC iron-carbon alloy initially containing \(0.35 \mathrm{wt} \% \mathrm{C}\) is exposed to an oxygen-rich and virtually carbon-free atmosphere at \(1400 \mathrm{~K}\) (1127 \(\left.^{\circ} \mathrm{C}\right)\). Under these circumstances the carbon diffuses from the alloy and reacts at the surface, with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at \(0 \mathrm{wt} \%\) C. (This process of carbon depletion is termed decarburization.) At what position will the carbon concentration be \(0.15 \mathrm{wt} \%\) after a 10 -h treatment? The value of \(D\) at \(1400 \mathrm{~K}\) is \(6.9 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).
Nitrogen from a gaseous phase is to be dif? fused into pure iron at \(700^{\circ} \mathrm{C}\). If the surface concentration is maintained at \(0.1 \mathrm{wt} \% \mathrm{~N}\) what will be the concentration \(1 \mathrm{~mm}\) from the surface after \(10 \mathrm{~h}\) ? The diffusion coefficient for nitrogen in iron at \(700^{\circ} \mathrm{C}\) is \(2.5 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).
Self-diffusion involves the motion of atoms that are all of the same type; therefore, it is not subject to observation by compositional changes, as with interdiffusion. Suggest one way in which self-diffusion may be monitored.
(a) Briefly explain the concept of a driving force. (b) What is the driving force for steady-state diffusion?
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