# Thermal Sensor by malj

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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
atoms
• When substance received energy, it will
vibrates
– 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
5
T ( K )  T ( R)
9
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

9
T ( F )  T ( C )  32
5
Relationship to Thermal Energy
• Average thermal energy WTH of a
molecule can be found from the absolute
temperature in K from
3
WTH    kT
2

• Where k = 1.38x10-23 J/K is Boltzmann’s
constant
Example
A material has a temperature of 335 K.
Find the temperature in °R
Example
Given temperature of 144.5 °C, express
this temperature in (a) K and (b) °F
Example
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
overlapped
• 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
Approximation
Resistance vs. Temperature
Approximation
• A straight line approximation of resistance
vs. temperature

R(T )  R(T0 ) 1  0T 

Where
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
where

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

Find the linear approximation of resistance
vs temperature between 60° and 90° F
Resistance Temperature Detectors
(RTD)
• 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
spec.
• A power required to raise the RTD temp by 1 C
• The increase in temperature is found as
P
T 
PD
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
Example
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
bridge.
Thermistors
• Thermistor is made of semiconductor
• The gap energy ΔWg exists between the
band
• When the temperature of material
increases, valance electrons gain
additional energy until exceeds the band
gap
• Valence electrons are free to move and
conduct current as temperature increase
• As current conducts more, resistance
decreases
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
Example
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-
heating
Thermocouples
• 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
T2

    QA  QB dT
T1

• 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
Example
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
shown

• Junction TM is exposed to temperature to be
measured
• The reference junction TR is a known
temperature
• The voltage produce is a function of (TM-
TR)
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
temperature
VH  VL 
VM  VL            TM  TL 
 TH  TL 
Example
A voltage of 23.72 mV is measured with a
type K thermocouple at a 0 °C reference.
Find the temperature of the measurement
junction.
Example
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
metals
– Protective cover
• Time response
– Related to size of the wire and any protective
material
– 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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