Answered: The transfer function, which is the…

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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Question

The transfer function, which is the first-order dynamics of a heater of a semiconductor core, shows the relationship between the power level P at the heater input and the changes in temperature T is given below.

T'(s) / P'(s) = K / (τs+1)

Here the unit of K is 0C/Kw and the unit of τ is min.

When an engineer changed the power input in steps from 1 to 1.5 kW, the process was steady. The engineer notes the following;
(i) Process temperature is initially 80 0C.
(ii) 4 minutes after the change of power input, the temperature is 120 0C.
(iii) It is 280 0C after 30 minutes.

(a) What are K and τ in the process transfer function?
(b) Another time, what will be the maximum rate of change of process temperature if the engineer linearly changes the power input at a rate of 0.5 kW/min?

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