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Chapter 5: Problem 5

(a) Briefly explain the concept of a driving force. (b) What is the driving force for steady-state diffusion?

Short Answer

Expert verified
Answer: The driving force for steady-state diffusion is the concentration gradient, which represents the difference in concentration levels between two points in the medium. This gradient motivates particles to migrate from regions of higher concentration to lower concentration, leading to a constant diffusion rate until equilibrium is reached.

Step by step solution

01

(Step 1: Defining Driving Force)

A driving force can be defined as an external factor or influence that is responsible for causing a change in a given system. It provides the necessary energy to initiate a certain process or reaction, and establishes a gradient between the initial and final states of the system, thus driving the process toward its completion. In general, driving forces can include thermal, electrical, or concentration gradients.
02

(Step 2: Understanding Steady-State Diffusion)

Steady-state diffusion refers to the process where the rate of diffusion remains constant and does not change with time. In this type of diffusion, particles (such as atoms, ions, or molecules) move through a medium (solid or liquid) under the influence of a driving force. The movement of particles occurs from high-concentration regions to low-concentration regions, resulting in a smoother distribution of particles in the medium.
03

(Step 3: Identifying the Driving Force for Steady-State Diffusion)

The driving force for steady-state diffusion is the concentration gradient. This gradient represents the difference in concentration levels between two points in the medium. The concentration gradient acts as the motivating force for the particles to migrate from a region of higher concentration to a region of lower concentration. As long as the concentration gradient is maintained, the diffusion process will continue, with particles moving through the medium at a constant rate, until they reach an equilibrium state where the concentration becomes uniform throughout the medium.

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Most popular questions from this chapter

The diffusion coefficients for silver in copper are given at two temperatures: $$ \begin{array}{cc} \hline T\left({ }^{\circ} \mathrm{C}\right) & D\left(\mathrm{~m}^{2} / \mathrm{s}\right) \\ \hline 650 & 5.5 \times 10^{-16} \\ 900 & 1.3 \times 10^{-13} \\ \hline \end{array} $$ (a) Determine the values of \(D_{0}\) and \(Q_{d}\). (b) What is the magnitude of \(D\) at \(875^{\circ} \mathrm{C}\) ?

A sheet of steel \(1.5 \mathrm{~mm}\) thick has nitrogen atmospheres on both sides at \(1200^{\circ} \mathrm{C}\) and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is \(6 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\), and the diffusion flux is found to be \(1.2 \times\) \(10^{-7} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\). Also, it is known that the concentration of nitrogen in the steel at the highpressure surface is \(4 \mathrm{~kg} / \mathrm{m}^{3} .\) How far into the sheet from this high-pressure side will the concentration be \(2.0 \mathrm{~kg} / \mathrm{m}^{3}\) ? Assume a linear concentration profile.

Briefly explain the difference between selfdiffusion and interdiffusion.

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 \(6.9 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\).

Briefly explain the concept of steady state as it applies to diffusion.
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