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Chapter 14: Problem 12

At a given temperature and pressure, do you think the mass diffusivity of copper in aluminum will be equal to the mass diffusivity of aluminum in copper? Explain.

Short Answer

Expert verified
Answer: No, the mass diffusivities of copper in aluminum and aluminum in copper are not equal under the same temperature and pressure conditions due to the differences in atomic radii and lattice structures. The mass diffusivity of copper in aluminum will most likely be lower than the mass diffusivity of aluminum in copper.

Step by step solution

01

Understanding Mass Diffusivity

Mass diffusivity, also known as diffusion coefficient, is a measure of how easily one substance can diffuse into another. It depends on factors like temperature, pressure, and the nature of the substances involved.
02

Comparing Diffusivities

In this case, we are looking at the diffusivities of copper in aluminum and aluminum in copper. These two processes involve the same two elements, so their diffusivities will depend on the arrangements of the elements and the specific conditions of temperature and pressure.
03

Considering Interdiffusion

In a system where two elements can freely diffuse into each other, the diffusion process is called interdiffusion. The mass diffusivity in this case depends on the structure of the metal lattice and the relative sizes of the atoms.
04

Factors Affecting Diffusivities

Both copper and aluminum have a face-centered cubic lattice structure, which makes it easier for the atoms to diffuse into each other. However, the atomic radius of copper (128 pm) is slightly larger than that of aluminum (125 pm), which means that the copper atoms will have to squeeze into smaller spaces in the aluminum lattice during diffusion. Similarly, aluminum atoms will have more room in the copper lattice during diffusion.
05

Conclusion

Based on the differences in atomic radii and lattice structures, we can conclude that the mass diffusivities of copper in aluminum and aluminum in copper are not equal, even under the same temperature and pressure conditions. The mass diffusivity of copper in aluminum will most likely be lower than the mass diffusivity of aluminum in copper due to the size difference between the copper and aluminum atoms.

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Most popular questions from this chapter

A gas mixture in a tank at \(600 \mathrm{R}\) and 20 psia consists of \(1 \mathrm{lbm}\) of \(\mathrm{CO}_{2}\) and \(3 \mathrm{lbm}\) of \(\mathrm{CH}_{4}\). Determine the volume of the tank and the partial pressure of each gas.

Express the mass flow rate of water vapor through a wall of thickness \(L\) in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor.

Benzene \((M=78.11 \mathrm{~kg} / \mathrm{kmol})\) is a carcinogen, and exposure to benzene increases the risk of cancer and other illnesses in humans. A truck transporting liquid benzene was involved in an accident that spilled the liquid on a flat highway. The liquid benzene forms a pool of approximately \(10 \mathrm{~m}\) in diameter on the highway. In this particular windy day at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with an average wind velocity of \(10 \mathrm{~m} / \mathrm{s}\), the liquid benzene surface is experiencing mass transfer to air by convection. Nearby at the downstream of the wind is a residential area that could be affected by the benzene vapor. Local health officials have assessed that if the benzene level in the air reaches \(500 \mathrm{~kg}\) within the hour of the spillage, residents should be evacuated from the area. If the benzene vapor pressure is \(10 \mathrm{kPa}\), estimate the mass transfer rate of benzene being convected to the air, and determine whether the residents should be evacuated or not.

For the absorption of a gas (like carbon dioxide) into a liquid (like water) Henry's law states that partial pressure of the gas is proportional to the mole fraction of the gas in the liquid-gas solution with the constant of proportionality being Henry's constant. A bottle of soda pop \(\left(\mathrm{CO}_{2}-\mathrm{H}_{2} \mathrm{O}\right)\) at room temperature has a Henry's constant of \(17,100 \mathrm{kPa}\). If the pressure in this bottle is \(120 \mathrm{kPa}\) and the partial pressure of the water vapor in the gas volume at the top of the bottle is neglected, the concentration of the \(\mathrm{CO}_{2}\) in the liquid \(\mathrm{H}_{2} \mathrm{O}\) is (a) \(0.003 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (b) \(0.007 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (c) \(0.013 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (d) \(0.022 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (e) \(0.047 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\)

The diffusion coefficient of carbon in steel is given as $$ D_{A B}=2.67 \times 10^{-5} \exp (-17,400 / T) \quad\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ where \(T\) is in \(\mathrm{K}\). Determine the diffusion coefficient from \(300 \mathrm{~K}\) to \(1500 \mathrm{~K}\) in \(100 \mathrm{~K}\) increments and plot the results.
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