This set of Distillation Design Multiple Choice Questions & Answers (MCQs) focuses on “2N Newton Method”.

1. The 2N Newton method is based on algorithm of?

a) N X N

b) 2 X N

c) N X M

d) 2 X M

View Answer

Explanation: The 2N Newton method is based on algorithm of 2 X N, while N X N is called as the Jacobin matrix.

2. X_{IJ} and Y_{ij} are the component balances of

a) Equilibrium relation

b) Constant relation

c) Final relation

d) Direct relation

View Answer

Explanation: X

_{IJ}and Y

_{ij}are the component balances of Equilibrium relation, Whereas X=Y represents the final relation of the system.

3. Which method uses the summation of the equations for vapor and liquid components?

a) NR Method

b) RF Method

c) Tomich Method

d) 2N Method

View Answer

Explanation: Tomich Method uses the summation of the equations for vapor and liquid components, while RF and NR are based on the initial conditions of column.

4. The independent variables of independent functions are used as, Fi =

a) [E_{1} E_{2} E_{3} …. E_{N-1} E_{N}, K_{1} K_{2} K_{3} …. K_{N-1} K_{N}].

b) [T_{1} T_{2} T_{3} …. T_{N-1} T_{N}, K_{1} K_{2} K_{3} …. K_{N-1} K_{N}].

c) [S_{1} S_{2} S_{3} …. S_{N-1} S_{N}, E_{1} E_{2} E_{3} …. E_{N-1} E_{N}].

d) [K_{1} K_{2} K_{3} …. K_{N-1} K_{N}, T_{1} T_{2} T_{3} …. T_{N-1} T_{N}].

View Answer

Explanation: As F

_{i}= [S

_{1}S

_{2}S

_{3}…. S

_{N-1}S

_{N}, E

_{1}E

_{2}E

_{3}…. E

_{N-1}E

_{N}]

^{T}, where S is the same factor as used in Fenske’s equation and E are the respective energy of the systems.

5. The stages flow rate and the vapor flow rates are expressed, as

a) [E_{1} E_{2} E_{3} …. E_{N-1} E_{N}, V_{1} V_{2} K_{3} …. V_{N-1} V_{N}].

b) [T_{1} T_{2} T_{3} …. T_{N-1} T_{N}, V_{1} V_{2} V_{3} …. V_{N-1} V_{N}].

c) [S_{1} S_{2} S_{3} …. S_{N-1} S_{N}, E_{1} E_{2} E_{3} …. E_{N-1} E_{N}].

d) [K_{}1 K_{2} K_{3} …. K_{N-1} K_{N}, T_{1} T_{2} T_{3} …. T_{N-1} T_{N}].

View Answer

Explanation: As X

_{i}= [T

_{1}T

_{2}T

_{3}…. T

_{N-1}T

_{N}, V

_{1}V

_{2}V

_{3}…. V

_{N-1}V

_{N}]

^{T}, where T is defined as respective temperature and the volume V corresponding to the same relation.

6. The initial assumption to Tomich method is

a) Set initial Temperature

b) Set total stages

c) Final Pressure

d) Initial Pressure

View Answer

Explanation: The initial assumption to Tomich method is to set initial Temperature for each stage, for any other method feed rates and total mole balance are assumed.

7. The θ_{j} factor is a

a) Subtracted

b) Additive

c) Multiplier

d) Divider

View Answer

Explanation: As |L/V| = θ

_{j}*|L

_{j}/V

_{j}|

_{CR}and θ

_{j}factor is a Multiplier, this is based on a correlation that acts as a correction factor of the calculation.

8. Newton’s method is a fixed point iteration method, As P_{n}

a) g(P_{n-1})

b) (P_{n-1})

c) g

d) P_{n}

View Answer

Explanation: Always Pn = g (P

_{n-1}) is fixed point as in newton method, while other method NR and RS stage iterations are made as the problem proceeds.

9) Newton’s method cannot continue, if for some P_{n-1}

a) f’(P_{n+1})

b) f’(P)

c) f’(P_{n-1})

d) P

View Answer

Explanation: Newton’s method cannot continue if for some f’ (P

_{n-1}), as the derivative at some point becomes zero then this is called as failure in the newton’s method.

10. Given ε>0. Then

a) f(a)f(b)>0

b) f(a)f(b)=0

c) f(a)f(b)=1

d) f(a)f(b)<0

View Answer

Explanation: Choose a and b so that f (a) f(b)< 0, if a and b are not given they are assumed to be as the average value of f(0) for two consecutive negative and positive outcomes.

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