Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
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Chapter 5, Problem 5.26E
Interpretation Introduction

(a)

Interpretation:

The difference between the measured value of temperature (Tm) and the bath temperature (T) at t=0.1 min and t=1.0 min are to be calculated after the temperature change.

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

F(s)=[f(t)]=0f(f)estdt

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 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 the deviation variable (y). It is generally used while modeling a process. Mathematically it is defined as:

y=yy¯

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

Interpretation Introduction

(b)

Interpretation:

The value of the maximum deviation between Tm(t) and T(t) is to be calculated. Also, the time when this maximum deviation is reached 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=yy¯

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

Interpretation Introduction

(c)

Interpretation:

The graph of T(t) and Tm(t) for 3 min is to be plotted. Also, the time lag between Tm and T for large values of t 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=yy¯

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

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