(a) Interpretation: The transfer function which relates tank temperature to the inlet liquid temperature is to be determined. 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 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

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A pilot process is being planned to produce antibiotic P. Antibiotic P is a compound secreted by microorganism A during the stationary phase. To produce P, substrate S is required. The growth of microorganism A follows the Monod equation, with a maximum specific growth rate $\mu_m = 1 h^{-1}$ and a half-saturation constant $K_s = 700\ mg/L$.The pilot process uses a chemostat with a working volume of $1000\ L$. In this chemostat, the outflow is processed to separate microorganisms, which are then concentrated tenfold and recycled. A sterile medium containing $15\ g/L$ of substrate is supplied at a flow rate of $100\ L/h$, while the recycled flow (concentrated) contains $5\ g/L$ and is also fed into the chemostat.Microorganism A yields $0.5\ g$ of biomass per $1\ g$ of substrate consumed $(Y^M_{X/S} = 0.5\ g\ A/g\ S)$, and its death rate $(k_d)$ is negligible. Additionally, $1\ g$ of microorganism A produces $0.05\ g$ of antibiotic P per hour $(q_P = 0.05 g\ P/h\cdot g\ A)$, and $1\ g$…

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Answer 2

Question

Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

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Answer 3

Question

Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

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Answer 4

Question

Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

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Answer 5

Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Answer 6

Chapter 4, Problem 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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 4.9E

Interpretation Introduction

(a)

Interpretation:

The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The steady-state gain for the transfer function determined in part (a) is to be calculated.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Answer 10

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Answer 11

Interpretation Introduction

(c)

Interpretation:

It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.

Concept introduction:

In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by s→0.

Answer 12

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Answer 13

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Answer 14

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Answer 15

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 transfer function which relates tank temperature to the inlet liquid temperature is to be determined.

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