In the game of craps, people bet on the outcome of the throw of two, six-sided dice. Specifically, wagers are placed on the sum of the outcome on the upward facing number on each of the two dice. We are going to discuss relative likelihoods by counting the number of ways (the number of microstates) associated with specific sums (the macrostate).

A. How many microstates are associated with a throw summing to 4?

B. How many microstates are associated with a throw summing to 5?

C. How many microstates are associated with a throw summing to 10?

D. Which is more likely, rolling 2 dice that sum up to 4 or rolling 2 dice that sum up to 5?

E. Which is more likely, rolling 2 dice that sum up to 4 or rolling 2 dice that sum up to 10?

The following module data are those for the DuPont B-10 permeator

Membrane recovery ratio: 35%

Salt rejection: 99.2%

Maximum applied pressure: 6895 kPa

Minimum brine flow rate: 1.584 m³/d

Maximum brine flow rate: 14.256 m³/d

Permeate flow rate: 2.46 m³/d

Design Data

Feed salinity is 42,000 ppm

Permeate flow rate: 5000 m³/d

Permeate pressure: 101 kPa

Design a single stage system by calculating the number of modules, osmotic pressure, permeation pressure difference, flow rates, and stream salinity.

Problem 1

Rectification. McCabe-Thiele Method. A mixture of benzene-toluene is to be distilled in a fractionating tower at 101.3 kPa. The column is fed 120 kg mol /h of a saturated liquid at the boiling point with 60 mol % benzene and 40 mol % toluene. The content of the distillate is 92 mol % benzene, and of the bottoms 5 mol % benzene. The reflux ratio is 3:1.

(a) Calculate the kg mol/h distillate: D=_______

(b) Calculate the kg mol/h bottoms: W=__________

(c) Attach the plot with the equilibrium line, 45? degree line, q-line, enriching and stripping operating lines, and stepping off the trays. Show with the dashed lines the stepping off assuming the Murphree tray efficiency is 0.5.

(d) Identify the position of the feed (the tray number) and inidicate the relative position of the feed to the tray: feed from bottom, from top, or both from top and from bottom.

Feed on tray ______from__________

(e) Determine graphically the theoretical number of trays:

N= _________plus a reboiler

(f) Determine graphically the actual number of trays for the case of Murphree efficiency

0.5:
N= ______plus a reboiler

(g) Calculate the overall tray efficiency in case of 0.5 Murphree tray efficiency: E0 =

(h) Attach the plot with the equilibrium line, 45? degree line, q-line, and enriching and

stripping operating lines for the case of minimum reflux ratio.

(i) Identify the point of intersection of the enriching operating line and q-line for the case of minimum reflux ratio:

x= _______y=_______

(j) Find minimum reflux ratio:

Rm=________

Estimating random-packed tower height. Consider random-packed tower in which distillation is performed under the same conditions as in Problem 1. Using 2-in Metal Intalox rings, calculate the HETP and the height of the tower.

(a) HETP=____
(b) The tower height par H= ______

Compare and contrast the key characteristics of anionic polymerization and conventional free-radical polymerization

What is the difference between HIPS and ABS in terms of chemical compositions? Explain the toughening mechanism associated with those two types of plastics.

Agricultural irrigation uses a significant amount of water, and in some regions it has overwhelmed other water needs. Suppose water is drawn from a reservoir and delivered into an irrigation ditch. For most of the length of the ditch, the delivery is through a 10-cm ID pipe, and in the last few meters the pipe diameter is 7 cm. The exit from the pipe is 300 m lower than the pipe inlet.

(a) Assume that the pipe is smooth (i.e., ignore friction) and that the delivery rate is 4000 kg/h. Estimate the required pressure difference between pipe inlet and outlet. How far below the surface of the reservoir is the pipe inlet?

(b) How would your answer be different if the pipe were not smooth? Explain.

(c) What are possible environmental impacts of diverting significant quantities of river water for use in irrigation? Cite at least two sources for your response.

a. Draw a process diagram to produce AlN powders by carbothermic reduction process. Include all possible steps, and briefly explain each step if needed.

b. In this process, what would be the keys to obtain high quality sinterable AlN powders?

In an air-conditioning system, dry air flows over tubes carrying refrigerant R134a. The air is cooled by transferring heat to the R134a; the air enters with a volume flow rate of 0.75 m3 s–1 at 305 K and 100 kPa, and it exits at 290 K and 95 kPa. The R134a enters at 4 bar in a vapor-liquid coexistence state with a quality of 20%; it exits at 4 bar and 30 °C. Ignoring heat transfer at the outer surface of the air conditioner, neglecting kinetic and potential energy changes, and assuming a steady state, determine a) the mass flow rate of R134a and b) the rate of heat transfer between the air and the R134a. Use the available tables, diagrams, and other reliable sources to obtain required thermodynamic data.

a.Why the Carnot cycle is not a realistic model for steam power plant? Justify your answer. [3 marks]

b. A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 9 MPa and 15 kPa. The mass flow rate of the steam through the cycle is 35 kg/s. The moisture content of the steam at the turbine is not to exceed 10 %.

i. Generate the T - s (Temperature – specific entropy) diagram of the cycle. [4 marks]

ii. Determine the minimum turbine inlet temperature in °C. [6 marks]

iii. Calculate the thermal efficiency of the cycle. [4 marks]

iv. Does the performance of the given Rankine cycle improve if the steam leaves the turbine as saturated vapor? Explain your answer. [

A bubble-point feed mixture of 5 mol% A and 95 mol% B is to be distilled to obtain a distillate containing 35 mol% A and a bottoms containing 0.2 mol% A. The column has a partial reboiler and a partial condenser. If the constant relative volatility is given to be ?A,B = 6. Using graphical method, find out:

a) The minimum number of equilibrium stages.

b) The minimum boilup ratio: ??? /??

c) The actual number of stages if the boilup ratio is 1.2 times the minimum.

Methanol (also known as wood alcohol and methyl alcohol) is used as a raw material in the manufacture of formaldehyde, acetic acid, and a number of other chemicals. One way it can be synthesized is by reacting carbon dioxide and hydrogen:

CO₂ + 3H₂?CH₃OH + H₂O

The fresh feed to a methanol synthesis process contains hydrogen, carbon dioxide and 0.4 mole% inerts. The reactor effluent passes to a condenser that removes essentially all of the methanol and water formed and none of the reactants or products. The latter substances are recycled to the reactor. To avoid buildup of the inerts in the system, a purge stream is withdrawn from the recycle. The feed to the reactor (not fresh feed to the process) contains 28 mole% CO₂, 70 mole% H₂, and 2 mole% inerts. The single pass conversion of hydrogen is 60%. Calculate the molar flow rates and molar compositions of the fresh feed, the total feed to the reactor, the recycle stream and the purge stream for a methanol production rate of 110 kmol/h.

Please show how the solution was arrived at I'm trying to understand how to do the problem.

4.(2) The fern is defined as the unit of force required to accelerate a unit of mass, called the bung, with the gravitational acceleration on the surface of the moon, which is one-sixth the normal gravitational acceleration on earth. a) What is the conversion factor that would be used to convert a force from the natural unit to the derived unit in this system (“gc”)? b) What is the weight in ferns of a 5.6 bung object on the moon? What does the same object weigh in Seattle?

What are the factors that affect the different fouling behaviours of thin film composite (TFC) and cellulose triacetate (CTA) forward osmosis (FO) membranes when treating wastewater.

9.10. A completely mixed bioreactor is used for ethanol fermentation of hydrolyzed starch solution containing 30 g/l total sugar. The following data are available: ?_m = 0.15 h^–1, K_S = 0.5 g/l, F = 10 l/h, Y_X/S = 0.1 g X/g S, Y_P/S = 0.5 gP/gS, k_S = 0.1 d^–1.

a. For 95% conversion of substrate to product, determine the required reactor volume and ethanol productivity when the system was operated without cell recycle.

b. For the same degree of conversion, determine the required reactor volume and ethanol productivity when the system was operated with cell recycle. r = 0.4, C = X_r/X = 3, ? = 0.1.