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A process stream at temperature T₁ (°C) is fed to a tank as shown in Figure Q4. Heat, Q (kW), is added to the tank by means of an electric heater. The tank is well-mixed, and the temperature of the stream exiting the tank is T (°C). Under steady state operations, the flow rates into and out of the tank remain constant at G (m³ s-¹). (a) (b) (c) G, Ti Q G, T Figure Q4: A tank heating system Develop the sets of equations that describes the steady and unsteady states of the process. Obtain the Laplace transforms of the model in terms of deviation variables. Determine the transfer function relating the change in the inlet temperature, Ti, and the change in heat, Q, to the change in the outlet temperature, T.

A process stream at temperature T₁ (°C) is fed to a tank as shown in Figure Q4. Heat, Q (kW), is added to the tank by means of an electric heater. The tank is well-mixed, and the temperature of the stream exiting the tank is T (°C). Under steady state operations, the flow rates into and out of the tank remain constant at G (m³ s-¹). (a) (b) (c) G, Ti Q G, T Figure Q4: A tank heating system Develop the sets of equations that describes the steady and unsteady states of the process. Obtain the Laplace transforms of the model in terms of deviation variables. Determine the transfer function relating the change in the inlet temperature, Ti, and the change in heat, Q, to the change in the outlet temperature, T.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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4 A process stream at temperature Ti (°C) is fed to a tank as shown in Figure Q4. Heat, Q (kW), is added to the tank by means of an electric heater. The tank is well-mixed, and the temperature of the stream exiting the tank is T (°C). Under steady state operations, the flow rates into and out of the tank remain constant at G (m³ s-1). (a) (b) (c) (d) G, Ti Q G, T Figure Q4: A tank heating system Develop the sets of equations that describes the steady and unsteady states of the process. Obtain the Laplace transforms of the model in terms of deviation variables. Determine the transfer function relating the change in the inlet temperature, Ti, and the change in heat, Q, to the change in the outlet temperature, T. Draw the block diagram representing the transfer functions for this process.
Transcribed Image Text:4 A process stream at temperature Ti (°C) is fed to a tank as shown in Figure Q4. Heat, Q (kW), is added to the tank by means of an electric heater. The tank is well-mixed, and the temperature of the stream exiting the tank is T (°C). Under steady state operations, the flow rates into and out of the tank remain constant at G (m³ s-1). (a) (b) (c) (d) G, Ti Q G, T Figure Q4: A tank heating system Develop the sets of equations that describes the steady and unsteady states of the process. Obtain the Laplace transforms of the model in terms of deviation variables. Determine the transfer function relating the change in the inlet temperature, Ti, and the change in heat, Q, to the change in the outlet temperature, T. Draw the block diagram representing the transfer functions for this process.
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