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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

When \(\alpha\)-iron is subjected to an atmosphere of hydrogen gas, the concentration of hydrogen in the iron, \(C_{\mathrm{H}}\) (in weight percent), is a function of hydrogen pressure, \(p_{\mathrm{H}_{2}}\) (in MPa), and absolute temperature \((T)\) according to $$ C_{\mathrm{H}}=1.34 \times 10^{-2} \sqrt{p_{\mathrm{H}}_{2}} \exp \left(-\frac{27.2 \mathrm{~kJ} / \mathrm{mol}}{R T}\right) $$ Furthermore, the values of \(D_{0}\) and \(Q_{d}\) for this diffusion system are \(1.4 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) and \(13,400 \mathrm{~J} / \mathrm{mol}\), respectively. Consider a thin iron membrane \(1 \mathrm{~mm}\) thick that is at \(250^{\circ} \mathrm{C}\). Compute the diffusion flux through this membrane if the hydrogen pressure on one side of the membrane is \(0.15 \mathrm{MPa}\) (1.48 atm), and on the other side \(7.5 \mathrm{MPa}\) (74 atm).

The steady-state diffusion flux through a metal plate is \(5.4 \times 10^{-10} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\) at a temperature of \(727^{\circ} \mathrm{C}(1000 \mathrm{~K})\) and when the concentration gradient is \(-350 \mathrm{~kg} / \mathrm{m}^{4} .\) Calculate the diffusion flux at \(1027^{\circ} \mathrm{C}(1300 \mathrm{~K})\) for the same concentration gradient and assuming an activation energy for diffusion of \(125,000 \mathrm{~J} / \mathrm{mol}\).

For a steel alloy it has been determined that a carburizing heat treatment of 10 -h duration will raise the carbon concentration to \(0.45 \mathrm{wt} \%\) at a point \(2.5 \mathrm{~mm}\) from the surface. Estimate the time necessary to achieve the same concentration at a 5.0-mm position for an identical steel and at the same carburizing temperature.

A sheet of BCC iron \(1 \mathrm{~mm}\) thick was exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other side at \(725^{\circ} \mathrm{C}\). After reaching steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were determined to be \(0.012\) and \(0.0075 \mathrm{wt} \%\). Compute the diffusion coefficient if the diffusion flux is \(1.4 \times 10^{-8} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\). Hint: Use Equation \(4.9\) to convert the concentrations from weight percent to kilograms of carbon per cubic meter of iron.

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 \(1.43 \times 10^{-9} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\).
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