04 Thermocouples Problem Set
THERMOCOUPLES | PRACTICE PROBLEMS
Complete the following to reinforce your understanding of the concept covered in this module.
PROBLEM 1: A thermocouple with a sensitivity of 3 ππ/Β°πΆ is used to measure the temperature of a steam duct in a power plant. Given an output of 0.082 π and using the standard reference temperature for the cold junction, what is the temperature of the hot junction closest too? A. 0 B. 21.7 C. 24.5 D. 27.3
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SOLUTION 1:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 0Β°πΆ
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Plugging in the given values for the voltage output, cold junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
3 Γ 10ST
π 0.082 π = Β°πΆ π β 0Β°πΆ
Solving for the temperature of the hot junction, we find: π = 27.3 Β°πΆ
Therefore, the correct answer choice is D. ππ. π
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PROBLEM 2: A thermocouple is placed in a moist environment with an ambient temperature of β100Β°πΆ. Which is the ANSI code of the thermocouple being used? A. π½ B. πΎ C. π D. πΈ
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SOLUTION 2:
The table for the PROPERTIES OF THERMOCOUPLES can be referenced under the topic of MEASUREMENT on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. As we are told the thermocouple will be used in an environment with an ambient temperature of β100Β°πΆ, we should evaluate the temperature range of each thermocouple. As this temperature is valid for multiple thermocouples, we need to look for an additional characteristic of the environment to guide us on which one to use. As we are told the environment is also moist, we notice that the thermocouple with ANSI Code T is said to be good for environments where moist is present.
Therefore, the correct answer choice is C. π
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PROBLEM 3: Given a class B resistance temperature detector with a reference temperature of 0 Β° πΆ, what is the tolerance value in units of ohms for a given temperature of 500Β°πΆ. A. 0.0 B. 0.5 C. 1.0 D. 1.5
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SOLUTION 3: The graph for the TOLERANCE VALUES OF THERMOCOUPLES can be referenced under the topic of MEASUREMENT on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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A RTD relies on the predictable behavior of the electrical resistance of materials changing with temperature as defined the temperature coefficient, πΌ. As we are told we have a class B resistance temperature detector, we can use the graph for the tolerance values of thermocouples to determine the tolerance value at the given temperature of 500Β°πΆ.
Drawing a vertical line from the stated temperature of 500Β°πΆ to where the class B line intersects, we find the tolerance value is Β±1.0, represented in units of ohms.
Therefore, the correct answer choice is C. π. π
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PROBLEM 4: A thermocouple composed of Chromel and another unknown metal with a total resistance of 810 πΊ is used to measure a thermodynamic system with a hot junction temperature of 740Β°πΆ. Given that the standard reference temperature is used, what is the sensitivity in units of ππ/Β°πΆ of the thermocouple if an ammeter measures an output of 0.75 ππ΄. A. 2 B. 8 C. 10 D. 25
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SOLUTION 4:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are not given the output in voltage, we can use Ohmβs Law to calculate the voltage output as a product of the given resistance (810 πΊ) and current output (0.75 ππ΄).
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The formula for the OHMβS LAW can be referenced under the topic of RESITIVITY on page 201 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
Plugging in the given values for current and resistance, we can calculate the voltage as:
π = πΌπ
π = 0.75 Γ 10ST π΄ 810 πΊ
π = 0.6075 π
As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 0Β°πΆ Plugging in the given value for the hot junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
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0.6075 π 740Β°πΆ β 0Β°πΆ
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Solving for the sensitivity of the thermocouple, we find:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: = 0.0008
π ππ =8 Β°πΆ Β°πΆ
Therefore, the correct answer choice is B. π
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PROBLEM 5: A thermocouple composed of two unknown metals is used to measure a thermodynamic system with a hot junction temperature of 120Β°πΉ. It is assumed the resistance of wire 1 is π g = 80 πΊ and the resistance of wire 2 is π h = 130 πΊ. Given that the standard reference temperature is used, what is the sensitivity in units of ππ/Β°πΉ of the thermocouple if an ammeter measures an output of 10.75 ππ΄. A. 2.5 B. 10 C. 26 D. 41
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SOLUTION 5:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are not given the output in voltage, we can use Ohmβs Law to calculate the voltage output as a product of the equivalent resistance (not given), and the current output (10.75 ππ΄).
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However, we are not given the equivalent resistance of the circuit, so we will need to calculate the equivalent resistance of circuits as two resistors in series. The formula for RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing. When resistors are in SERIES, the resistors act like a single resistor whose value is the sum of the resistors: π i = π g + π h Plugging in the given values for the resistance in each wire, we calculate the equivalent resistance as: π i = 80 πΊ + 130 πΊ = 210 πΊ The formula for the OHMβS LAW can be referenced under the topic of RESITIVITY on page 201 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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Plugging in the given values for current and calculated equivalent resistance, we can calculate the voltage as: π = πΌπ k
π = 10.75 Γ 10ST π΄ 210 πΊ
π = 2.258 π
As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 32Β°πΉ Plugging in the given value for the hot junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
2.258 π 120Β°πΉ β 32Β°πΉ
Solving for the sensitivity of the thermocouple, we find:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: = 0.0257
π ππ = 25.7 Β°πΉ Β°πΉ
Therefore, the correct answer choice is C.ππ
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Complete the following to reinforce your understanding of the concept covered in this module.
PROBLEM 1: A thermocouple with a sensitivity of 3 ππ/Β°πΆ is used to measure the temperature of a steam duct in a power plant. Given an output of 0.082 π and using the standard reference temperature for the cold junction, what is the temperature of the hot junction closest too? A. 0 B. 21.7 C. 24.5 D. 27.3
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SOLUTION 1:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 0Β°πΆ
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Plugging in the given values for the voltage output, cold junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
3 Γ 10ST
π 0.082 π = Β°πΆ π β 0Β°πΆ
Solving for the temperature of the hot junction, we find: π = 27.3 Β°πΆ
Therefore, the correct answer choice is D. ππ. π
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PROBLEM 2: A thermocouple is placed in a moist environment with an ambient temperature of β100Β°πΆ. Which is the ANSI code of the thermocouple being used? A. π½ B. πΎ C. π D. πΈ
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SOLUTION 2:
The table for the PROPERTIES OF THERMOCOUPLES can be referenced under the topic of MEASUREMENT on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. As we are told the thermocouple will be used in an environment with an ambient temperature of β100Β°πΆ, we should evaluate the temperature range of each thermocouple. As this temperature is valid for multiple thermocouples, we need to look for an additional characteristic of the environment to guide us on which one to use. As we are told the environment is also moist, we notice that the thermocouple with ANSI Code T is said to be good for environments where moist is present.
Therefore, the correct answer choice is C. π
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PROBLEM 3: Given a class B resistance temperature detector with a reference temperature of 0 Β° πΆ, what is the tolerance value in units of ohms for a given temperature of 500Β°πΆ. A. 0.0 B. 0.5 C. 1.0 D. 1.5
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SOLUTION 3: The graph for the TOLERANCE VALUES OF THERMOCOUPLES can be referenced under the topic of MEASUREMENT on page 124 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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A RTD relies on the predictable behavior of the electrical resistance of materials changing with temperature as defined the temperature coefficient, πΌ. As we are told we have a class B resistance temperature detector, we can use the graph for the tolerance values of thermocouples to determine the tolerance value at the given temperature of 500Β°πΆ.
Drawing a vertical line from the stated temperature of 500Β°πΆ to where the class B line intersects, we find the tolerance value is Β±1.0, represented in units of ohms.
Therefore, the correct answer choice is C. π. π
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PROBLEM 4: A thermocouple composed of Chromel and another unknown metal with a total resistance of 810 πΊ is used to measure a thermodynamic system with a hot junction temperature of 740Β°πΆ. Given that the standard reference temperature is used, what is the sensitivity in units of ππ/Β°πΆ of the thermocouple if an ammeter measures an output of 0.75 ππ΄. A. 2 B. 8 C. 10 D. 25
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SOLUTION 4:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are not given the output in voltage, we can use Ohmβs Law to calculate the voltage output as a product of the given resistance (810 πΊ) and current output (0.75 ππ΄).
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The formula for the OHMβS LAW can be referenced under the topic of RESITIVITY on page 201 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
Plugging in the given values for current and resistance, we can calculate the voltage as:
π = πΌπ
π = 0.75 Γ 10ST π΄ 810 πΊ
π = 0.6075 π
As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 0Β°πΆ Plugging in the given value for the hot junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
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0.6075 π 740Β°πΆ β 0Β°πΆ
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Solving for the sensitivity of the thermocouple, we find:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: = 0.0008
π ππ =8 Β°πΆ Β°πΆ
Therefore, the correct answer choice is B. π
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PROBLEM 5: A thermocouple composed of two unknown metals is used to measure a thermodynamic system with a hot junction temperature of 120Β°πΉ. It is assumed the resistance of wire 1 is π g = 80 πΊ and the resistance of wire 2 is π h = 130 πΊ. Given that the standard reference temperature is used, what is the sensitivity in units of ππ/Β°πΉ of the thermocouple if an ammeter measures an output of 10.75 ππ΄. A. 2.5 B. 10 C. 26 D. 41
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SOLUTION 5:
The formula for THERMOCOUPLE SENSITIVITY is not provided in the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We must memorize this formula and understand its application independent of the NCEES Supplied Reference Handbook. The THERMOCOUPLE SENSITIVITY is the ratio of change in electrical signal magnitude to change in temperature.
The thermocouple sensitivity defines the
relationship of how much the voltage output will increase or decreases depending on the magnitude of the difference between the reference cold junction temperature and the specified hot junction temperature.
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
πΈππππ‘πππππ ππππππ π = πΆβππππ ππ ππππππππ‘π’ππ π β πN
Where: β’ π is the voltage output given in units of volts (V) β’ π is the specified hot junction temperature or temperature of interest given in units of Β°πΆ ππ Β°πΉ β’ πN is the specified cold junction temperature or reference temperature given in units of Β°πΆ ππ Β°πΉ As we are not given the output in voltage, we can use Ohmβs Law to calculate the voltage output as a product of the equivalent resistance (not given), and the current output (10.75 ππ΄).
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However, we are not given the equivalent resistance of the circuit, so we will need to calculate the equivalent resistance of circuits as two resistors in series. The formula for RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 201 of the NCEES Supplied Reference Handbook, 9.4 Version for Computer Based Testing. When resistors are in SERIES, the resistors act like a single resistor whose value is the sum of the resistors: π i = π g + π h Plugging in the given values for the resistance in each wire, we calculate the equivalent resistance as: π i = 80 πΊ + 130 πΊ = 210 πΊ The formula for the OHMβS LAW can be referenced under the topic of RESITIVITY on page 201 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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Plugging in the given values for current and calculated equivalent resistance, we can calculate the voltage as: π = πΌπ k
π = 10.75 Γ 10ST π΄ 210 πΊ
π = 2.258 π
As we are told to use standard reference temperature, the temperature of the cold junction is assumed to be 0Β°πΆ ππ 32Β°πΉ, such that: πN = 32Β°πΉ Plugging in the given value for the hot junction reference temperature, and sensitivity, we can re-write the expression for the thermocouple sensitivity as:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: =
2.258 π 120Β°πΉ β 32Β°πΉ
Solving for the sensitivity of the thermocouple, we find:
ππππ ππ‘ππ£ππ‘π¦89:;=?@A: = 0.0257
π ππ = 25.7 Β°πΉ Β°πΉ
Therefore, the correct answer choice is C.ππ
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