Chapter 14

A thick wall made of natural rubber is exposed to pure oxygen gas on one side of its surface. Both the wall and oxygen gas are isothermal at \(25^{\circ} \mathrm{C}\), and the oxygen concentration at the wall surface is constant. Determine the time required for the oxygen concentration at \(x=5 \mathrm{~mm}\) to reach \(5 \%\) of its concentration at the wall surface.

Consider a piece of steel undergoing a decarburization process at \(925^{\circ} \mathrm{C}\). The mass diffusivity of carbon in steel at \(925^{\circ} \mathrm{C}\) is \(1 \times 10^{-7} \mathrm{~cm}^{2} / \mathrm{s}\). Determine the depth below the surface of the steel at which the concentration of carbon is reduced to \(40 \%\) from its initial value as a result of the decarburization process for \((a)\) an hour and \((b)\) ten hours. Assume the concentration of carbon at the surface is zero throughout the decarburization process.

A thick nickel wall is exposed to pure hydrogen gas at \(165^{\circ} \mathrm{C}\) on one side of its surface. The hydrogen concentration at the wall surface is constant. Determine the hydrogen concentration at the penetration depth in percentage of its concentration at the wall surface.

When handling corrosive and toxic substances, chemical resistant gloves should be worn. When selecting gloves to handle a substance, the suitability of the gloves should be considered. Depending on the material of the gloves, they could be easily permeable by some substances. An employee is handling tetrachloroethylene solution for a metal-cleaning process. Dermal exposure to tetrachloroethylene can cause skin irritation, and long-term exposure to it can have adverse neurological effects on humans. As a protective measure, the employee wears rubber-blend gloves while handling the tetrachloroethylene solution. The average thickness of the gloves is \(0.67 \mathrm{~mm}\), and the mass diffusivity of tetrachloroethylene in the gloves is \(3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}\). Estimate how long can the employee's hand be in contact with the tetrachloroethylene solution before the concentration of the solution at the inner glove surface reaches \(1 \%\) of the concentration at the outer surface. Is this type of glove suitable for handling tetrachloroethylene solution?

A steel part whose initial carbon content is \(0.12\) percent by mass is to be case-hardened in a furnace at \(1150 \mathrm{~K}\) by exposing it to a carburizing gas. The diffusion coefficient of carbon in steel is strongly temperature dependent, and at the furnace temperature it is given to be \(D_{A B}=7.2 \times 10^{-12} \mathrm{~m}^{2} / \mathrm{s}\). Also, the mass fraction of carbon at the exposed surface of the steel part is maintained at \(0.011\) by the carbon-rich environment in the furnace. If the hardening process is to continue until the mass fraction of carbon at a depth of \(0.7 \mathrm{~mm}\) is raised to \(0.32\) percent, determine how long the part should be held in the furnace.

A heated piece of steel, with a uniform initial carbon concentration of \(0.20 \%\) by mass, was exposed to a carburizing atmosphere for an hour. Throughout the entire process, the carbon concentration on the surface was \(0.70 \%\). If the mass diffusivity of carbon in steel in this process was uniform at \(1 \times\) \(10^{-11} \mathrm{~m}^{2} / \mathrm{s}\), determine the percentage of mass concentration of carbon at \(0.2 \mathrm{~mm}\) and \(0.4 \mathrm{~mm}\) below the surface after the process.

What is diffusion velocity? How does it affect the mass-average velocity? Can the velocity of a species in a moving medium relative to a fixed reference point be zero in a moving medium? Explain.

What is the difference between mass-average velocity and mole-average velocity during mass transfer in a moving medium? If one of these velocities is zero, will the other also necessarily be zero? Under what conditions will these two velocities be the same for a binary mixture?

Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium.

Consider one-dimensional mass transfer in a moving medium that consists of species \(A\) and \(B\) with \(\rho=\rho_{A}+\rho_{B}=\) constant. Mark these statements as being True or False. (a) The rates of mass diffusion of species \(A\) and \(B\) are equal in magnitude and opposite in direction. (b) \(D_{A B}=D_{B A}\). (c) During equimolar counterdiffusion through a tube, equal numbers of moles of \(A\) and \(B\) move in opposite directions, and thus a velocity measurement device placed in the tube will read zero. (d) The lid of a tank containing propane gas (which is heavier than air) is left open. If the surrounding air and the propane in the tank are at the same temperature and pressure, no propane will escape the tank and no air will enter.