Problem 1 (30 points) (a) Estimate the total length of the threads in a twin bed sheet

Problem 1 (30 points)

(a) Estimate the total length of the threads in a twin bed sheet. Provide your answer in units of

feet. Briefly explain why your estimate may be too low and why your estimate may be too

high. (Note: A twin bed is the smallest standard size and is similar to that in your dorm room.)

(b) Your bath tub has dimensions of 60 inches long, 32 in wide, and 16 in deep. It has a circular

drain of radius 0.90 cm. After some measurements, you determine that the bath tub fills at a

constant rate of 50 kg/min, but that the bath tub drains at a rate proportional to the height of

The water level (H) in the tub:

Vdrain = A(2gH) 1/2

Where A is the cross-sectional area of the drain and g is the gravitational constant.

If you start filling the bath tub with the drain unplugged, when would the water start to overflow the bathtub?

(c) The double factorial function n!! Indicates the product of all the even integers up to n if n is

Even or the product of all the odd integers up to n if n is odd. For example,

5!!=5x3x1=15 and 6!! =6x4x2 = 48

Using python, write a script to calculate the value of n!! And demonstrate the application of

your code to calculate 15!! And 20!!

(Note: You are not permitted to use Excel for this problem and your python code is more

Important than the numerical answers for the solution.)

Problem 2 (35 points)

A decomposition reaction (2A — B + C) is performed in a catalytic reactor with a single pass

Conversion of 20%. The stream entering the reactor is the combination of a fresh feed stream and a

recycle stream. The effluent stream from the reactor is moved to a separator where the products are

perfectly separated from the unreacted reactants and any inerts. The stream consisting of unreacted

reactants and inerts is split such that 10 mol % is purged and the remainder is recycled to the reactor.

Analyze this system on the basis of the feed to the reactor being 200 kmol/hr of A and 10 kmol/hr

inerts.

(a) Draw a process flow diagram and label every stream including key process variables.

(b) What is the purpose of the purge stream?

(c) Determine the reactor products. Provide the equations used in your analysis.

(d) Calculate the fresh feed flow rate and composition.

(e) If the fresh feed was processed at a total flow rate of 1000 kg/hr, what would be the

composition and flow rate of the product stream?

(f) What is the overall conversion for this reaction process?

(g) Suggest two improvements to the process that would increase the overall conversion.

Problem3 (35 points)

You are tasked with separating a stream of xylene isomers (ethyl benzene, p-xylene, m-xylene, and

o-xylene) via a series of distillation columns. A common calculation to determine the difficulty of

separating compounds in a vapor—liquid equilibrium is the relative volatility. For species m and n, the

relative volatility is defined as

a_m,n=Y_m/x_m/Y_n/X_n

Where Y_m is the mole fraction of species m in the vapor and X_m is the mole fraction of species m in

liquid. If a_m,n is close to 1, then the stream is more difficult to separate. If a_m,n >> 1 then species m

is more volatile than, n and conversely, if  a_m,n << 1 then species m is less volatile than n.

(a) For species 1 and 2, show the relative volatility a1,2 equals the vapor pressure ratio at the

System temperature, p1 /p2.

Assume the binary mixtures follow idealized thermodynamic behavior in the vapor and liquid

phases. Why can this assumption be justified for the xylene isomer mixture?

(b) Which are the most and least volatile species in the xylene isomer mixture?

(c) For the xylene isomer stream at 95°C, calculate the relative volatility for all combinations of

species in the stream (e.g., ethylbenzene to p-xylene, p-xylene to m-xylene, etc.). Which

combination would you classify as the most challenging to separate by distillation?

(d) For a binary mixture of species m and n, show that

Ym=am1xm1+am,n-1xm,

Like another format : Ym=(am,n Xm )/1+(am,n-1)xm

(e) Use the equation in part (d) for an ethyl benzene and o-xylene system at 95°C to estimate the

mole fractions of ethyl benzene in the vapor phases in equilibrium with liquids having

Ethyl benzene mole fractions of 0.3 and 0.7. Calculate the total pressure for each of these two

distinct situations.

(f) Rationalize your results in part (e) in terms of what you know about VLE.