Thermal Sensor

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					Thermal Sensor
          Thermal Sensors
• The control of process needs to be able to
  sense controlled or regulated variables
• One physical variable that is important in
  industrial process control is temperature
  Definition of Thermal Energy
• Substances around us are composed of
• When substance received energy, it will
  – Vibrates at equilibrium – solid
  – Vibrates and rotating – liquid
  – Vibrates and rotating and moving freely - gas
    Definition of Temperature
• Temperature is the measurement of
  thermal energy containing in each
  molecule of substance (Joules/Molecule)
• Example 10,000 J of energy
  – In a glass of water
  – In a tank of water
 Temperature Scale
and Calibration Points
  Absolute Temperature Scale
• Assigns zero temperature to a material
  that has no thermal energy
  – Kelvin (K) Scale
  – Rankine (°R) Scale
• The transformation between the two
  scales is
                 T ( K )  T ( R)
   Relative Temperature Scale
• Shift the zero index up; zero degree does
  not mean zero thermal energy
• Celsius scale relates to Kelvin
               T ( C )  T ( K )  273.15

• Fahrenheit relates to Rankine

               T ( F )  T ( R)  459.6
 Relationship between F and C
• To transform from Celsius to Fahrenheit,
  note that the two scales differ by size of
  degree and scale shift of 32

               T ( F )  T ( C )  32
Relationship to Thermal Energy
• Average thermal energy WTH of a
  molecule can be found from the absolute
  temperature in K from
                 WTH    kT

• Where k = 1.38x10-23 J/K is Boltzmann’s
 A material has a temperature of 335 K.
 Find the temperature in °R
 Given temperature of 144.5 °C, express
 this temperature in (a) K and (b) °F
 A sample of oxygen gas has a
 temperature of 90 °F. If its molecular
 mass is 5.3x10-26 kg, find the average
 thermal speed of a molecule.
Metal Resistance and Temperature
• Metal is composed of atoms.
• Add up all atoms vibrations constitutes thermal
  energy stored in the metal
• The energy bands of metal is shown below

• Valance band and conduction band are
• Valance electron can stay in the
  conduction band and moves freely,
  conducting current
• As metal received energy, stationary atom
  vibrates more and more
• Conduction electrons collide more and
  more with vibrating atoms. Thus, resists
  the flow of current (increase in resistance)
Graph of Temperature
   vs. Resistance
Resistance vs. Temp
      Resistance vs. Temperature
• A straight line approximation of resistance
  vs. temperature

                       R(T )  R(T0 ) 1  0T 

  R(T )  approximation of resistance at temperature T
  R(T0 )  resistance at temperature T0
    T  T  T0
     0  fractional change in resistance per degree of temperature at T0

               1  R2  R1 
        0          T T 
             R(T0 )  2 1 
 A sample of metal resistance vs.
 temperature has the following measured

 Find the linear approximation of resistance
 vs temperature between 60° and 90° F
Resistance Temperature Detectors
• A temperature sensor based on the
  changed of resistance of metal due to the
  change in temperature
• Metals used are
  – Platinum (Repeatable, expensive)
  – Nickel (No quite repeatable, inexpensive)
       Characteristics of RTD
• Sensitivity
  – Value of α0 is sensitivity
  – on the order of 0.004/°C for platinum and
    0.005/°C for nickel
• Response time
  – Due to the slowness of thermal conductivity,
    the response time is 0.5 to 5 s or more
• Construction
  – Metal wire is wound into coil and is protected
    in sheath or productive tube
• Signal conditioning
  – The RTD is generally used in a bridge circuit
    with compensate line
• Dissipation constant
  – Because RTD is resistance, there is an I2R
    power dissipation in the device (Self-heating)
  – Can cause erroneous reading
  – Dissipation constant (PD) is provided in RTD
     • A power required to raise the RTD temp by 1 C
     • The increase in temperature is found as
                        T 
    T  temperature rise becuase of self-heating in C
      P  power dissipated in the RTD from the circuit in W
     PD  dissipation constant of the RTD in W/ C
 An RTD has α0 = 0.005/°C , R = 500 , and
 a dissipation constant of PD = 30 mW/°C at
 20 °C. The RTD is used in a bridge circuit
 with R1 = R2 = 500  and R3 a variable
 resistor used to null the bridge. If the
 supply is 10 V and the RTD is placed in a
 bath at 0 °C, find the value of R3 to null the
• Thermistor is made of semiconductor
  instead of metal
• The gap energy ΔWg exists between the
• When the temperature of material
  increases, valance electrons gain
  additional energy until exceeds the band
• Valence electrons are free to move and
  conduct current as temperature increase
• As current conducts more, resistance
Resistance vs. Temperature
    Thermistor Characteristics
• Sensitivity
  – Typically, 10% resistance change per 1 °C
• Construction
  – Can be fabricated in discs, bead, and rods
• Response time
  – Typically, 0.5 s
  – For poor thermal contact, response time can
    be 10 s
• Signal conditioning
  – Bridge circuit
• Dissipation constants
  – In milliwatts/°C
 A thermistor is to monitor room
 temperature. It has a resistance
 of 3.5 k at 20 °C with a slope of
 -10%/C. The dissipation
 constant is PD = 5 mV/C. It is
 proposed to use the thermistor in
 the divider circuit as shown to
 provide a voltage of 5.0 V at 20 °
 C. Evaluate the effect of self-
• When any conductor (such as a metal) is
  subjected to a thermal gradient, it will
  generate a voltage
• Two different metals A and B are used to
  close the loop with connecting junction at
  T1 and T2
Seebeck Effect
• Seebeck effect

                       QA  QB dT

• where

            emf produced in voltage
      T1 , T2  junction temperatures in K
    QA , QB  thermal transport constants of the two metals
• In practice, an approximation linear
  relationship exists as

                     T2  T1 

• where

                constant in V/K
           T1 , T2  junction temperatures in K
 Find the Seebeck emf for a material with α
 = 50 V/°C if the junction temperatures are
 20 °C and 100 °C.
 Thermocouple Characteristics
• The setup of thermocouple is arranged as

• Junction TM is exposed to temperature to be
• The reference junction TR is a known
• The voltage produce is a function of (TM-
       Thermocouple Types
• Certain standard configuration of
  thermocouples have been adopted
Each type has its particular features such as range,
linearity, inertness to hostile environments sensitivity
       Thermocouple Polarity
• If the reference temperature is less than
  the measured temperature, the output
  would be positive
        Thermocouple Tables
• Table gives the voltage output related to
  reference and measured temperature with
  TR = 0 °C                          increment

   TM            VM
• To find a corresponding temperature to a
  certain output voltage, need interpolation

                       TH  TL 
            TM  TL            VM  VL 
                      VH  VL 

• To find a measured voltage for a particular
                      VH  VL 
            VM  VL            TM  TL 
                       TH  TL 
 A voltage of 23.72 mV is measured with a
 type K thermocouple at a 0 °C reference.
 Find the temperature of the measurement
 Find the voltage of a type J thermocouple
 with a 0 °C reference if the junction
 temperature is -172 °C.
      Thermocouple Sensors
• Sensitivity
  – Type J: 0.05 mV/°C
  – Type K: 0.006 mV/°C
• Construction
  – Welded or twisted
    junction between 2
  – Protective cover
• Time response
  – Related to size of the wire and any protective
  – Small TC, 10 to 20 ms
  – Large TC, 10 to 20 s
• Signal conditioning
  – Output is very small, need high gain
    differential amplifier

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