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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
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.
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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