A thermocouple is known to have first-order dynamics represented by the following transfer function. Tm' (s) 1.00 T'(s) 4s +1 where Tm = thermocouple temperature measurement (C). Tis the actual temperature (C), and the time constant is given in seconds. he thermocouple is initially sitting in a pot of boiling water when it is picked up by a student and placed in a bucket full f ice and water at equilibrium. a) What is the thermocouple temperature measurement 4 seconds after being placed into the bucket of ice and water? b) How long will it take for the temperature measurement to reach steady-state? c) What is its final steady-state measurement? d) Your instrumentation vendor is proposing you replace this thermocouple with one that has the transfer function: Tm'(s) 1.10 T'(s) 0.4s + 1 Should you consider buying this new thermocouple to replace the old one above? Give your reasons for your decision.
A thermocouple is known to have first-order dynamics represented by the following transfer function. Tm' (s) 1.00 T'(s) 4s +1 where Tm = thermocouple temperature measurement (C). Tis the actual temperature (C), and the time constant is given in seconds. he thermocouple is initially sitting in a pot of boiling water when it is picked up by a student and placed in a bucket full f ice and water at equilibrium. a) What is the thermocouple temperature measurement 4 seconds after being placed into the bucket of ice and water? b) How long will it take for the temperature measurement to reach steady-state? c) What is its final steady-state measurement? d) Your instrumentation vendor is proposing you replace this thermocouple with one that has the transfer function: Tm'(s) 1.10 T'(s) 0.4s + 1 Should you consider buying this new thermocouple to replace the old one above? Give your reasons for your decision.
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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![**Transcription for Educational Website**
A thermocouple is known to have first-order dynamics represented by the following transfer function:
\[
\frac{T_m'(s)}{T'(s)} = \frac{1.00}{4s + 1}
\]
where \( T_m \) = thermocouple temperature measurement (°C), \( T \) is the actual temperature (°C), and the time constant is given in seconds.
The thermocouple is initially sitting in a pot of boiling water when it is picked up by a student and placed in a bucket full of ice and water at equilibrium.
a) What is the thermocouple temperature measurement 4 seconds after being placed into the bucket of ice and water?
b) How long will it take for the temperature measurement to reach steady-state?
c) What is its final steady-state measurement?
d) Your instrumentation vendor is proposing you replace this thermocouple with one that has the transfer function:
\[
\frac{T_m'(s)}{T'(s)} = \frac{1.10}{0.4s + 1}
\]
Should you consider buying this new thermocouple to replace the old one above? Give your reasons for your decision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02152486-4b3e-4971-933f-7bbbd61f61b8%2Fa71f4636-6df3-4fef-8b81-3c4b43066f57%2F7n538s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
A thermocouple is known to have first-order dynamics represented by the following transfer function:
\[
\frac{T_m'(s)}{T'(s)} = \frac{1.00}{4s + 1}
\]
where \( T_m \) = thermocouple temperature measurement (°C), \( T \) is the actual temperature (°C), and the time constant is given in seconds.
The thermocouple is initially sitting in a pot of boiling water when it is picked up by a student and placed in a bucket full of ice and water at equilibrium.
a) What is the thermocouple temperature measurement 4 seconds after being placed into the bucket of ice and water?
b) How long will it take for the temperature measurement to reach steady-state?
c) What is its final steady-state measurement?
d) Your instrumentation vendor is proposing you replace this thermocouple with one that has the transfer function:
\[
\frac{T_m'(s)}{T'(s)} = \frac{1.10}{0.4s + 1}
\]
Should you consider buying this new thermocouple to replace the old one above? Give your reasons for your decision.
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