(a) Interpretation: The transfer function H ′ ( s ) Q ′ i ( s ) for both the tanks is to be determined. Concept introduction: For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances. The process models generally include algebraic relationships which commence from thermodynamics , transport phenomena , chemical kinetics, and physical properties of the processes. The difference in the actual variable ( y ) and the original variable ( y ¯ ) is known as the deviation variable ( y ′ ) .It is generally used while modeling a process. Mathematically it is defined as: y ′ = y − y ¯ In the steady-state process, the accumulation in the process is taken as zero.

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Answer 1

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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2. A moving bed adsorption column needs to be designed to separate hydrophobic proteins from a fermentation broth. The following adsorption equilibrium data was observed in preliminary isotherm studies. The resin used was activated carbon with a porosity of 0.2. The overall mass transfer coefficient was determined to be 10 h¹, and the ratio of volumetric flow rate of broth to resin is 10. Determine the diameter of the column if the column height is limited to 2.5 m (indoor operation) with a flow rate of 20 m³/h, influent concentration of 7 g/L, and effluent concentration of 0.1 g/L. qi (mg/kg) Ci (g/L) 0.1 4.7 7.5 0.25 10.6 0.5 15.0 1.0 23.7 2.5 33.5 5.0 41.1 7.5

3. You are given a mixture of four proteins, whose properties are listed in the table below. Propose a process to purify each protein so that you end up with four solutions of pure protein. What resin would you use to bind the protein(s)? What changes to the buffer would you make to desorb the protein(s)? Contains an N-terminal His6-tag. Two 50 kDa subunits contain a non-heme Fe2+ in the active site. Protein Size (kDa) pl Specific Properties A 100 6.0 B 40 7.7 C 240 8.3 Ꭰ 225 5.5 Contains FAD redox center and an NADH binding domain. Composed of six 40-kDa subunits, each of which contains a [2Fe-2S] cluster. Composed of three subunits: 100 kDa structural subunit, 75 kDa subunit with a molybdopterin center, and 50 kDa subunit with FAD and an NADH binding domain.

Answer 2

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 3

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 4

Question

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

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Answer 5

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 6

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Answer 7

Chapter 5, Problem 5.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function H′(s)Q′i(s) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable (y) and the original variable (y¯) is known as the deviation variable (y′) .It is generally used while modeling a process. Mathematically it is defined as:

y′=y−y¯

In the steady-state process, the accumulation in the process is taken as zero.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The transient response of h(t) for both the tanks is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)]

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 12

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 13

Interpretation Introduction

(d)

Interpretation:

The tank that will overflow first and the time of overflow is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 14

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 15

Interpretation Introduction

(e)

Interpretation:

The new steady-state levels for both the systems are to be determined.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

Answer 16

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Answer 17

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Answer 18

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Answer 19

Ch. 5 - Prob. 5.1E Ch. 5 - Prob. 5.2E Ch. 5 - Prob. 5.3E Ch. 5 - Prob. 5.4E Ch. 5 - Prob. 5.5E Ch. 5 - Prob. 5.6E Ch. 5 - Appelpolscher has just left a meeting with Stella...Ch. 5 - Prob. 5.8E Ch. 5 - Prob. 5.9E Ch. 5 - Prob. 5.10E

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Chapter 5 Solutions