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The Measurement of Temperature
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Because temperature is difficult to define, equality of
temperature is defined. Two bodies have equality of
temperature if no change in any observable property occurs
when they are in thermal communication.

Since pressure, volume, electrical resistance, expansion
coefficients, etc., are all related to temperature through the
fundamental molecular structure, they change with
temperature, and these changes can be used to measure
temperature.
Phil. U., M Eng Dep., Measurements, Chap#8
The Measurement of Temperature
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There are two scales for temperature; Fahrenheit and
Celsius. These scales are based on a specification of the
number of increments between the freezing point and
boiling point of water at standard atmospheric pressure. The
Fahrenheit scale is 180 units while the Celsius scale is 100
unit.
The absolute Celsius scale is called the Kelvin scale, while
the absolute Fahrenheit scale is termed the Rankine scale.
The ratio of two absolute temperature values is the same;
regardless of the scale used.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Scales
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Temperature Scales
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Scales
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Temperature Scales
Phil. U., M Eng Dep., Measurements, Chap#8
Ideal-Gas Thermometer
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pV = mRT
where V is the volume occupied by the
gas, m is the mass, and R is the gas
constant R is the gas constant for the
particular gas, given by
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where is the universal gas constant,
having a value of 8314.5 J/kg · mol · K,
andM is the molecular weight of the gas
Temperature Measurement by
Mechanical Effects
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(1) The liquid-in-glass thermometer: (Figure 8.4)
- This device is one of the most common types of
temperature measurement devices.
- Working method:…
- Alcohol and mercury are the most commonly used
liquids. Alcohol has the advantage that it has a higher
coefficient of expansion than mercury, but it is limited to
low-temperature measurement because it tends to boil at
high temperatures. Mercury can not be used below its
freezing point of -37.8C.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects
- These thermometers can serve as a calibration standards
for other temperature-measurements devices.
- Mercury-in-glass thermometers are generally applicable
up to about 600F. By filling the space above the mercury
with a pressuring gas, their range can be extended to
1000F.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects

(2) The bimetallic strip: (Figure 8.5)
- Two pieces of metal with different coefficients of thermal
expansion are bonded together to from the bimetallic stripdevice.
- Working method:…
- It can be shown that the radius of curvature for this
bimetallic strip may be calculated as:
(equation 8.5)
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects
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When the strip is subjected to a temperature
higher than the bonding temperature, it will bend in
one direction;
when it is subjected to a temperature lower than the
bonding temperature, it will bend in the other
direction.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects
- For the moved bimetallic strip
shown aside:
d = y sin 
where:
y = 2r sin /2
 = L/r

r
y
L
Phil. U., M Eng Dep., Measurements, Chap#8
d
Temperature Measurement by
Mechanical Effects

(3) Fluid-expansion thermometer: (Figure 8.6)
- This type of device represents one of the most economical,
versatile, and commonly used devices for industrial
temperature-measurement applications.
- Principle of operation:…
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Mechanical Effects
Fluid-expansion thermometers are usually
low in cost, stable in
operation, and accurate within ±1◦C.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
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The electrical temperature-measurement methods are very
convenient because they provide a signal that is easily
detected, amplified, or used for control purposes.
Many types:
(1) Resistance temperature detector (RTD):
- It consists of a resistive element, which is exposed to the
temperature to be measured. The temperature is indicated
through a measurement of the change in resistance of the
element.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
- The resistance-temperature relationship can be given as:
I. For linear R-variation with temperature: (used over narrow
ranges of temperature)
 = (R2-R1)/[R1(T2-T1)]
where:
: the linear temperature coefficient of the resistive material
(table 8.2)
R2 and R1: the resistances of the material at temperatures
T1 and T2
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
II. For wide ranges of temperature where the R-T
relationship is nonlinear:
2
R = Ro(1 + aT + bT )
where:
R: the resistance at temperature T
Ro: the resistance at reference temperature To
a, b: experimentally determined constants
- RTD is normally connected with some type of bridge
circuit.
Phil. U., M Eng Dep., Measurements, Chap#8
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The resistance wire is free of mechanical stresses and so
mounted that moisture cannot come in contact with the wire
and influence the measurement.
One construction technique involves winding the platinum on a
glass or ceramic bobbin followed by sealing with molten glass.
This technique protects the platinum RTD element but is subject
to stress variations over wide temperature ranges.
RTD sensors may also be constructed by depositing a platinum
or metal-glass slurry on a ceramic substrate. The film can then
be etched and sealed to form the resistance element. This
process is less expensive than the mechanical-winding ceramic
but is not as accurate.
Phil. U., M Eng Dep., Measurements, Chap#8
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SENSITIVITY OF PLATINUM RESISTANCE THERMOMETER.
Aplatinum resistance . thermometer is used at room
temperature. Assuming a linear temperature variation with
resistance, calculate the sensitivity of the thermometer in ohms
per degrees Fahrenheit.
Solution
The meaning of a linear variation of resistance with temperature
is
where R0 is the resistance at the reference temperature T0. The
sensitivity is thus
Phil. U., M Eng Dep., Measurements, Chap#8
Dr. Safwan A. Altarazi
Temperature Measurement by
Electrical Effects
(2) Thermistors:

- This is a semiconductor device that has a negative
temperature coefficient of resistance, in contrast to the
positive coefficient displayed in most metals. The
numerical value of β varies between 3500 and 4600 K,

depending on the thermistor material and temperature.
- For a thermistor:
R = Ro exp[(1/T – 1/To)]
where Ro is the resistance at the reference temperature To
and  is an experimentally determined constant.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
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- See figures 8.8 and 8.9.
- Thermistor is a very sensitive device, and consistent
performance within 0.01C may be anticipated with proper
calibration.
because its resistance changes so rapidly with temperature;
however, it has the disadvantage of highly nonlinear
behavior.
- Moreover, the thermistor may be used to counteract the
increase in resistance of a circuit with a temperature
increase.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
(3) Thermocouples:
- This is the most common
electrical method of
temperature measurement.
Material (2)
A
Junction
- When two dissimilar metals
are joined together, a voltage
(emf) will exist between the
two point (A) and (B), which is
primarily a function of the
junction temperature.
Phil. U., M Eng Dep., Measurements, Chap#8
B
Material (1)
Temperature Measurement by
Electrical Effects
- This phenomenon is called the Seebeck effect.
- If the two materials are connected to an external circuit in
such a way that a current is drawn, the emf may be altered
slightly owing to phenomenon called the Peltier effect.
- Further, if a temperature gradient exists along either or
both of the materials, the junction emf may undergo an
additional slight alteration. This is called the Thomson
effect.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
- If the emf generated at the junction is carefully measured
as a function of temperature, then such a junction may be
utilized for the measurement of the temperature.
- When the emf is measured, attention must be given to the
emf generated at the connection of the thermocouple
material and the wire connecting material.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
- Two rules are available for the analysis of thermoelectric
circuits:
a) “law of intermediate metals”: If a third metal is connected
in the circuit, figure 8.13, the net emf of the circuit is not
affected as long the new connections are at the same
temperature.
b) “law of intermediate temperatures”: Consider figure 8.14,
……….
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
- All thermoelectric circuits must involve at least two
junctions. If one junction is known, then the temperature of
the other junction may be easily calculated using the
thermoelectric properties of the materials. The known
temperature is called the reference temperature.
- Figure 8.15 presents some common arrangement for
establishing the reference temperature. 8.15a is necessary if
the binding posts at the voltage-measuring instrument were
at different temperatures, while the connection in 8.15b is
satisfactory if the binding posts were at the same
temperature.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
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- Standard thermocouple tables have been prepared with a
reference junction at 0C, (table 8.3). The output E of a
thermoelectric circuit is usually written as:
E = AT + BT 2/2 + CT 3/3
where T is the temperature in degrees Celsius and E is
based on a reference junction temperature of 0◦C. The
constants A, B, and C are dependent on the thermocouple
2 power, of a
material. The sensitivity, or thermoelectric
thermocouple is given by:
S = dE/dT = A + BT + CT
(see table 8.4)
Phil. U., M Eng Dep., Measurements, Chap#8
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
-
If each of the “hot” junctions is at a different temperature
while all the “cold” are at a same temperature, an average
emf is given by:
Eavg = E/n
then the average temperature corresponding to the average
emf is determined from table 8.3 or equation 8.13.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
- In order to provide a more sensitive circuit,
thermocouples are occasionally connected in series as
shown in figure 8.19. This arrangement is called thermopile.
For a three junction situation, the output would be three
times that of a single thermocouple provided the temperature
of the hot and cold junctions is uniform.
Phil. U., M Eng Dep., Measurements, Chap#8
Temperature Measurement by
Electrical Effects
-
The parallel connection shown in figure 8.21 may be used
for obtaining the average temperature of a number of points.
Each of the four junctions may be at a different temperature
and hence generate a different emf. The generated emf will
be the average of the four junction potentials.
Phil. U., M Eng Dep., Measurements, Chap#8