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A thermocouple is initially at temperature of T, and it is used to measure the temperature of air (Tair). It would take a while for the temperature of the thermocouple junction to approach Tair. The thermocouple junction can be approximated by a copper sphere of 0.5 mm in diameter. Using the lumped system analysis (chapter 5, undergraduate heat transfer textbook), derive an expression for T(1) (it should look like: (T(t)-Tair)/(Tr-Tair) = e, where T, is the initial temperature of the thermocouple, and Tair is the air temperature). Calculate the time constant (assuming the convection heat transfer coefficient h=5 W/m²K). Use the thermal properties of copper from your undergraduate textbook or any other books. Usually t=3r is used as the response time of the thermocouple with 5% measuring error. Explain why? If the thermocouple size is increased to 5 mm in diameter, what is the response time?

A thermocouple is initially at temperature of T, and it is used to measure the temperature of air (Tair). It would take a while for the temperature of the thermocouple junction to approach Tair. The thermocouple junction can be approximated by a copper sphere of 0.5 mm in diameter. Using the lumped system analysis (chapter 5, undergraduate heat transfer textbook), derive an expression for T(1) (it should look like: (T(t)-Tair)/(Tr-Tair) = e, where T, is the initial temperature of the thermocouple, and Tair is the air temperature). Calculate the time constant (assuming the convection heat transfer coefficient h=5 W/m²K). Use the thermal properties of copper from your undergraduate textbook or any other books. Usually t=3r is used as the response time of the thermocouple with 5% measuring error. Explain why? If the thermocouple size is increased to 5 mm in diameter, what is the response time?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A thermocouple is initially at temperature of T; and it is used to measure the temperature of air (Tair). It would take a while for the temperature of the thermocouple junction to approach Tair. The thermocouple junction can be approximated by a copper sphere of 0.5 mm in diameter. Using the lumped system analysis (chapter 5, undergraduate heat transfer textbook), derive an expression for T(t) (it should look like: (T(t)-Tair )/(Ti-Tair) = e, where T; is the initial temperature of the thermocouple, and Tair is the air temperature). Calculate the time constant 7 (assuming the convection heat transfer coefficient h=5 W/m²K). Use the thermal properties of copper from your undergraduate textbook or any other books. Usually t=3t is used as the response time of the thermocouple with 5% measuring error. Explain why? If the thermocouple size is increased to 5 mm in diameter, what is the response time?
Transcribed Image Text:A thermocouple is initially at temperature of T; and it is used to measure the temperature of air (Tair). It would take a while for the temperature of the thermocouple junction to approach Tair. The thermocouple junction can be approximated by a copper sphere of 0.5 mm in diameter. Using the lumped system analysis (chapter 5, undergraduate heat transfer textbook), derive an expression for T(t) (it should look like: (T(t)-Tair )/(Ti-Tair) = e, where T; is the initial temperature of the thermocouple, and Tair is the air temperature). Calculate the time constant 7 (assuming the convection heat transfer coefficient h=5 W/m²K). Use the thermal properties of copper from your undergraduate textbook or any other books. Usually t=3t is used as the response time of the thermocouple with 5% measuring error. Explain why? If the thermocouple size is increased to 5 mm in diameter, what is the response time?
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