(a) Interpretation: The given model is to be linearized and deviation variables are to be introduced. Concept introduction: For chemical processes, dynamic models consisting 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 deviation variable ( y ′ ) . It is generally used while modelling a process. Mathematically it is defined as: y ′ = y − y ¯ In steady-state process, the accumulation in the process is taken as zero.

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Answer 1

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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 2

Question

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Answer 7

Chapter 4, Problem 4.7E

Interpretation Introduction

(a)

Interpretation:

The given model is to be linearized and deviation variables are to be introduced.

Concept introduction:

For chemical processes, dynamic models consisting 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 deviation variable (y′). It is generally used while modelling a process. Mathematically it is defined as:

y′=y−y¯

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

Answer 8

Interpretation Introduction

(b)

Interpretation:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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:

Four transfer functions relating outputs x1 and y1 to inputs x0 and y2 are to be derived and placed in standard form.

Concept introduction:

For chemical processes, dynamic models consisting 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

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Answer 11

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Answer 12

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Answer 13

Ch. 4 - Prob. 4.1E Ch. 4 - Prob. 4.2E Ch. 4 - Prob. 4.3E Ch. 4 - Prob. 4.4E Ch. 4 - Prob. 4.5E Ch. 4 - A stirred-tank blending system can be described by...Ch. 4 - Prob. 4.7E Ch. 4 - Prob. 4.8E Ch. 4 - Prob. 4.9E Ch. 4 - Prob. 4.10E

Solution Summary: The author explains the linearization of a given model and the introduction of deviation variables for chemical processes.

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Chapter 4 Solutions