A heater for a semiconductor wafer has first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is T′(s)/P′(s)=K/(?s+1 ) where K has units [∘C/Kw] and ? has units [min].The process is at steady state when an engineer changes the power input stepwise from 1 to 2 kW. She notes the following:(i)The process temperature initially is 100∘C.(ii)Four minutes after changing the power input, the temperature is 400∘C.(iii)Thirty minutes later the temperature is 500∘C.(a)What are K and ? in the process transfer function?(b)If at another time the engineer changes the power input linearly at a rate of 0.5 kW/min, what can you say about the maximum rate of change of process temperature: When will itoccur? How large will it be?
A heater for a semiconductor wafer has first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is T′(s)/P′(s)=K/(?s+1 ) where K has units [∘C/Kw] and ? has units [min].The process is at steady state when an engineer changes the power input stepwise from 1 to 2 kW. She notes the following:(i)The process temperature initially is 100∘C.(ii)Four minutes after changing the power input, the temperature is 400∘C.(iii)Thirty minutes later the temperature is 500∘C.(a)What are K and ? in the process transfer function?(b)If at another time the engineer changes the power input linearly at a rate of 0.5 kW/min, what can you say about the maximum rate of change of process temperature: When will itoccur? How large will it be?
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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A heater for a semiconductor wafer has first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is T′(s)/P′(s)=K/(?s+1 ) where K has units [∘C/Kw] and ? has units [min].The process is at steady state when an engineer changes the power input stepwise from 1 to 2 kW. She notes the following:(i)The process temperature initially is 100∘C.(ii)Four minutes after changing the power input, the temperature is 400∘C.(iii)Thirty minutes later the temperature is 500∘C.(a)What are K and ? in the process transfer function?(b)If at another time the engineer changes the power input linearly at a rate of 0.5 kW/min, what can you say about the maximum rate of change of process temperature: When will itoccur? How large will it be?
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