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18 Dec 2019

Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1Â° and 47.9Â°, respectively, with the tensile axis. The critical resolved shear stress is 20.7 MPa, Calculate the minimum stress (in MPa) necessary to cause the single crystal to yield.

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Carbon dioxide can be separated from other gases by preferential absorption into an amine solution. The carbon dioxide can be recovered by heating at atmospheric pressure. Suppose pure CO_2 vapor is available from such a process at 80 degree C and 1 bar. Suppose the CO_2 is liquefied and marketed in 43-L laboratory gas cylinders that are filled with 90% (by mass) liquid at 295 K. Explore the options for liquefaction, storage, and marketing via the following questions. Use the Peng-Robinson for calculating fluid properties. Submit a copy of the H-U-S table for each state used in the solution.

c) Consider the liquefaction via compression of the CO_2 vapor from 80 degree C, 1 bar to 6.5 MPa in a two-stage compressor with interstage cooling. Each stage (n_c=0.8) operates adiabatically. The interstage pressure is 2.5 MPa, and the interstage cooler returns the CO_2 temperature to 295 K. The two-stage compressor is followed by cooling in a heat exchanger to 295 K and 6.5 MPa. Determine all process temperatures and pressures, the work and heat transfer requirement for each step, and the overall heat and work.

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1) LaNi₅ metal alloys are well known for their ability to reversibly store and desorb hydrogen at

temperatures just below atmospheric pressure and at room temperature.

A) (2 pts.) The hydrogen is an example of what kind of defect/dislocation: _________________________-

B) (6 pts.) Use greater than, less than, or equal signs to indicate whether LaNi₅ metal or LaNi₅H_x metal is

going to be superior for each of the following properties (Note the last one is different.):

Yield stress LaNi₅ LaNi₅H_x

Modulus of elasticity LaNi₅ LaNi₅H_x

Brittleness LaNi₅ LaNi₅H_x

Ultimate compressive strength LaNi₅ LaNi₅H_x

Electrical conductivity LaNi₅ LaNi₅H_x

Brittleness LaNi₅ LaNi₅H_x

C) (5 pts.) Assume the diffusivity of hydrogen atoms, D_H, through LaNi₅H_x obeys the relationship below,

that the LaNi₅H_x has a crystal diameter of 10^-6 m, absorbs hydrogen at 333 K,

and has an activation energy for diffusion of 10000 J/mole. First, estimate the

diffusivity of hydrogen in m²/sec at 333 K.

D_H = 1 x 10^-14 * exp (-E_diff/(8.314*T)), where D_H is in m²/sec and T is in K.

Then, using the dimensionless group relationship you learned with regard to diffusion, estimate

the amount of time that it would take the hydrogen to diffuse the length of the diameter of

the crystal, assuming that if the dimensionless group is approximately one, then the

hydrogen atom had sufficient time to diffuse across the entire diameter of the crystal. Read

part D before finishing this one. Your answer will be > 1 minute.

D) (3 pts.) When Dr. Brenner worked in industry, the civilian application for LaNi₅H_x was as a hydrogen storage medium for a hydrogen-driven bus. The biggest problem to overcome was the time necessary to fill the tank. In terms of particle or crystal diameters or other microstructural characteristics, explain how one might modify the LaNi₅H_x hydride materials to shorten the time necessary to fill the tank with hydrogen. Hint: There may be an alternate pathway for diffusion.

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