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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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Transcribed Image Text:**Title: Analysis of a Second-Order Dynamical System in an Electrically Heated Process** **Introduction:** This study examines an electrically heated process showcasing second-order dynamics. The parameters are as follows: - Gain (K): 5°C/kW - Time Constant (τ): 1.2 minutes - Damping Ratio (ζ): 0.3 **Initial Condition:** The process begins at a steady-state temperature of 70°C with a heater input power of 20 kW. Subsequently, the heater input is increased to 25 kW and maintained at this level. **Problem Statement:** a) Derive an expression for the process temperature as a function of time. b) Calculate the maximum temperature reached and determine the time at which it occurs. **Approach:** The analysis involves solving the second-order differential equation characterizing the temperature response to a step change in heater input. The solution will yield the temperature profile as a function of time, allowing us to find both the maximum temperature and the time it occurs. **Conclusion:** By understanding the response of this system, key insights into the dynamics of electrically heated processes can be gained, aiding in the design and control of similar systems.

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