(a) Interpretation: The response Y ( s ) and the quantitative value of y ( t ) are to be derived. 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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus, Y ( s ) = Y 1 ( s ) + Y 2 ( s ) + ⋯ + Y n ( s ) Here, n is the number of internal processes taking place in the system. 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 that 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 ) .

Question

Want to see the full answer?

Answer 1

Question

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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).

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Solve this question

Homework 8 View Policies Show Attempt History Current Attempt in Progress Question 3 of 5 Entering Steam > > Check table lookups for correct values. Check significant figures. Check unit conversions. Calculate the required flow rate of the entering steam in m³/min. 0.00132 m³/min eTextbook and Media Hint 0/1 Assistance Used Determine the specific enthalpy change of each stream first. Then use the known flow rate of the methanol to calculate the steam flow rate. Save for Later Heat Transferred × Check units and significant figures. Calculate the rate of heat transfer from the water to the methanol (kW). i 44.5 kW Hint Don't forget to convert minutes to seconds. Save for Later Attempts: 3 of 5 used Submit Answer Assistance Used Attempts: 2 of 5 used Submit Answer

← Homework 8 View Policies Show Attempt History Current Attempt in Progress A liquid mixture of benzene and toluene containing 52.0 wt% benzene at 100.0 °C and pressure Po atm is fed at a rate of 32.5 m³/h into a heated flash tank maintained at a pressure Ptank Material Balances Correct. 0.67/1 === Attempts: 1 of 5 used Calculate Ptank (atm), the mole fraction of benzene in the vapor, and the molar flow rates of the liquid and vapor products. Ptank .544 atm Ybz .657 mol benzene/mol vapor product nvapor 55.8 mol/s nliquid 37.6 mol/s Hint GO Tutorial Energy Balance Check heat capacities. Calculate the required heat input rate in kilowatts. i 0.447 kW Hint GO Tutorial Save for Later Assistance Used Attempts: 2 of 5 used Assistance Used Attempts: 1 of 5 used Submit Answer

Answer 2

Question

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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).

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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).

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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).

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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).

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Answer 6

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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 7

Chapter 5, Problem 5.24E

Interpretation Introduction

(a)

Interpretation:

The response Y(s) and the quantitative value of y(t) are to be derived.

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 an additive process model, the output of the entire process is the sum of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)+Y2(s)+⋯+Yn(s)

Here, n is the number of internal processes taking place in the system.

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 that 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 8

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Answer 9

Interpretation Introduction

(b)

Interpretation:

The response in part (a) is to be simulated and its major characteristics are to be identified.

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)] ..........(1)

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

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 13

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

Solution Summary: The author explains how the response and quantitative value of y(t) are to be derived.

Want to see the full answer?

Chapter 5 Solutions