(a) Interpretation: The transfer function which relates the changes in q 0 to changes in q 2 is to be derived for the given process under given conditions. 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. For a function f ( t ) , the Laplace transform is given by, F ( s ) = L [ f ( t ) ] = ∫ 0 ∞ f ( f ) e − s t d t Here, F ( s ) represents the Laplace transform, s is a variable which is complex and independent, f ( t ) is any function of time which is being transformed, and L is the operator which is defined by an integral. f ( t ) is calculated by taking inverse Laplace transform of the function F ( s ) . 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 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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.

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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.

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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A biodiesel mixture consisting of 60 mol% methyl oleate (MO), 25 mol% methyl linoleate (ML), and 15 mol% methyl palmitate (MP) is held at 373.15 K and 200 MPa. Given PC-SAFT parameters: segment number \( m_i = [5.7, 6.3, 4.8] \), segment diameter \( \sigma_i = [3.95, 3.98, 3.91] \) Å, dispersion energy \( \epsilon_i/k = [260, 270, 250] \) K, and binary interaction parameters \( k_{ij} = 0.01 \), determine the isentropic speed of sound (m/s) using the PC-SAFT Helmholtz energy formulation and the thermodynamic identity\[c^2 = \left( \frac{\partial P}{\partial \rho} \right)_T + \frac{T \left( \frac{\partial P}{\partial T} \right)_\rho^2 }{ \rho^2 c_v },\]assuming the density is precomputed at 200 MPa and \( c_v \) is obtained from ideal mixing of pure-component values.

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Answer 2

Question

Chapter 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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.

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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.

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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Answer 3

Question

Chapter 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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.

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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.

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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.

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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.

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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.

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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.

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

Answer 6

Chapter 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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 6, Problem 6.16E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates the changes in q0 to changes in q2 is to be derived for the given process under given conditions.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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:

The differential equation model for the given system when valve 1 is left partially open is to be derived.

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

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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 11

Interpretation Introduction

(c)

Interpretation:

The form of the transfer function Q′2(s)Q′0(s) is to be discussed when valve 1 is left partially open without deriving the transfer function.

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 12

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

Answer 13

Interpretation Introduction

(d)

Interpretation:

It is to be discussed if the response of q2 for changes in q0 is fast or slow for case (b) as compared with case (a). Also, it is to be explained that the derivation of the response expression is not necessary.

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.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=∫0∞f(f)e−stdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

Answer 14

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Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 6 - Prob. 6.1E Ch. 6 - Prob. 6.2E Ch. 6 - Prob. 6.3E Ch. 6 - Prob. 6.4E Ch. 6 - Prob. 6.5E Ch. 6 - Prob. 6.6E Ch. 6 - Prob. 6.7E Ch. 6 - Prob. 6.8E Ch. 6 - Prob. 6.9E Ch. 6 - Prob. 6.10E

Solution Summary: The author explains the transfer function which relates the changes in q_0 to changes

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Chapter 6 Solutions