A distillation column is being used to separate methanol and water at atmospheric pressure. The column temperature varies from approximately $65^{\circ} \mathrm{C}$ at the top to $100^{\circ} \mathrm{C}$ at the bottom. Liquid enters the top of the column and flows down to the bottom; vapor is generated in a reboiler at the bottom of the column, flows upward, and leaves at the top. The molar flow rate of vapor up the column may be assumed to be constant from top to bottom. The vapor velocity is kept below 5.0 ft/s to keep the vapor from entraining liquid (suspending and carrying away liquid droplets). a) Where in the column is the greatest risk of liquid entrainment? Explain your answer. b) Assuming that the liquid flowing down the column and the column internals (equipment inside the column) occupy a negligible fraction of the column cross-sectional area, estimate the minimum column diameter if the vapor flow rate is 25.0 lb-mole/min. c) Suppose the column is constructed with a diameter 10% greater than that determined in Part (b). What are the vapor velocities at the top and bottom of the column if the vapor molar flow rate in both locations is 25.0 lb-mole/min? How much can the vapor molar flow rate be increased without causing liquid entrainment? d) There is a need to increase process throughput, which would require the vapor molar flow rate to be doubled. It has been suggested that increasing the pressure in the column would allow that to be done without risking excessive liquid entrainment. Again applying a vapor velocity limit of 5 ft/s, what would the new pressure be?

Write the explicit formula for each sequence. Then generate the first five terms. $a_{1}=4, r=0.1$

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. I don't need to evince my value at this company because...

Use the method of reduction of order to find a solution of the given nonhomogeneous equation. The indicated function $y_{1}(x)$ is a solution of the associated homogeneous equation. Determine a second solution of the homogeneous equation and a particular solution of the nonhomogeneous equation. $y^{\prime \prime}-4 y^{\prime}+3 y=x; y_{1}=e^{x}$

A point source S of light is on the central axis of a thin positive lens. It is at a distance $l_{1}$ in front of the lens, and a real image of S appears at P, a distance $l_{2}$ from the lens. Is it possible to move the lens along the axis to a new location and not finally change the positions of S and P? If so, to where must the lens be relocated? Draw a diagram.

Air in industrial plants is subject to contamination by many different chemicals, and companies must monitor ambient levels of hazardous species to be sure they are below limits specified by the National Institute for Occupational Safety and Health (NIOSH). In personal breathing-zone sampling (as opposed to area sampling), workers wear devices that periodically collect air samples less than 10 inches away from their noses. Breathing-zone sampling and analysis methods for hundreds of species are set forth in the NIOSH Manual of Analytical Methods. For benzene, NIOSH specifies a recommended exposure limit (REL) of 0.1 ppm time-weighted average exposure (TWA), and the Occupational Safety and Health Administration (OSHA) permissible exposure limit (PEL) is 1.0 ppm TWA. A worker in a petroleum refinery has a personal breathing-zone sampler for benzene clipped to her shirt collar. Following the NIOSH prescription, air is pumped through the sampler at a rate of 0.200 L/min by a small battery-operated pump attached to the worker’s belt. The sampler contains an adsorbent that removes essentially all of the benzene from the air passing through it. After several hours, the sampler is removed and sent to a lab for analysis, and the worker puts on a fresh sampler. On a particular day when the temperature is $21^{\circ} \mathrm{C}$ and barometric pressure is 730 mm Hg, samples are collected during a 4-h period before lunch and a 3.5-h period after lunch. The analytical laboratory reports 0.17 mg of benzene in the first sample and 0.23 mg in the second. a) Calculate the average benzene concentration, $C_{\mathrm{B}}(\mathrm{ppm})$, in the worker's breathing zone during each sampling period, where $1 \mathrm{ppm}=1 \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{6} / 10^{6} \mathrm{mol}$ air. b) The worker’s TWA is the average concentration of benzene in her breathing zone during the eight hours of her shift. It is calculated by multiplying $C_{\mathrm{B}}$ in each sampling period by the time of that period, summing the products over all periods during the shift, and dividing by the total time of the shift. Assume that the worker’s exposure during the unsampled 30 minutes was zero, and calculate her TWA. c) If the worker’s exposure is above the recommended limits, what actions might the company take?

Escribe un párrafo de al menos seis oraciones describiendo cómo es la comunidad ideal donde te gustaría (you would like) vivir en el futuro y compárala con la comunidad donde vives ahora.

Strawberries contain about 15 wt% solids and 85 wt% water. To make strawberry jam, crushed strawberries and sugar are mixed in a 45:55 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. (a) Draw and label a flowchart of this process. (b) Do the degree-of-freedom analysis and show that the system has zero degrees of freedom (i.e., the number of unknown process variables equals the number of equations relating them). If you have too many unknowns, think about what you might have forgotten to do. ( c) Calculate how many pounds of strawberries are needed to make a pound of jam.

A stream of air (21 mole% $\mathrm{O}_{2}$, the rest $\mathrm{N}_{2}$) flowing at a rate of 10.0 kg/h is mixed with a stream of $\mathrm{CO}_{2}$. The $\mathrm{CO}_{2}$ enters the mixer at a rate of $20.0 \mathrm{m}^{3} / \mathrm{h} \text { at } 150^{\circ} \mathrm{C}$ and 1.5 bar. What is the mole percent of $\mathrm{CO}_{2}$ in the product stream?

A stream of air enters a 7.50-cm ID pipe with a velocity of 60.0 m/s at $27^{\circ} \mathrm{C}$ and 1.80 bar (gauge). At a point downstream, the air flows through a 5.00 cm ID pipe at $60^{\circ} \mathrm{C}$ and 1.53 bar (gauge). What is the average velocity of the gas at this point.

After being purged with nitrogen, a low-pressure tank used to store flammable liquids is at a total pressure of 0.03 psig. a) If the purging process is done in the morning when the tank and its contents are at $55^{\circ} \mathrm{F}$, what will be the pressure in the tank when it is at $85^{\circ} \mathrm{F}$ in the afternoon? b) If the maximum design gauge pressure of the tank is 8 inches of water, has the design pressure been exceeded? c) Speculate on the purpose of purging the tank with nitrogen.

Show that $A_{\mathrm{NFA}}$ is NL-complete.

How did Allied forces gain control of Europe's airspace prior to the ground invasion? How did this benefit Allied troops once they landed in Europe?

Escoge la forma correcta del verbo para completar las oraciones. Toni va a usar su bicicleta hasta que los coches híbridos (cuesten/cuestan) menos dinero.