1. The Measurement of Temperature
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

2. The Measurement of Temperature
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

3. Temperature Measurement by Mechanical Effects
(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

4. 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

5. 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 strip-device.
- 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

6. Temperature Measurement by Mechanical Effects
- Bimetallic strips are frequently used in simple on-off temperature-control devices (thermostats). Movements of the strip has sufficient force to trip control switches for various devices.
- Alternate construction methods…
Phil. U., M Eng Dep., Measurements, Chap#8

7. Temperature Measurement by Mechanical Effects
- For the moved bimetallic strip shown aside:
d = y sin 
where:
y = 2r sin /2
 = L/r L d r y 
Phil. U., M Eng Dep., Measurements, Chap#8

8. 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

9. Temperature Measurement by Electrical Effects
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

10. 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

11. Temperature Measurement by Electrical Effects
II. For wide ranges of temperature where the R-T relationship is nonlinear:
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. 2
Phil. U., M Eng Dep., Measurements, Chap#8

12. 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.
- 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

13. Temperature Measurement by Electrical Effects
- 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.
- 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

14. Temperature Measurement by Electrical Effects
(3) Thermocouples:
- This is the most common electrical method of temperature measurement.
- 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. A B
Material (1)
Material (2)
Junction
Phil. U., M Eng Dep., Measurements, Chap#8

15. 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

16. 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

17. 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

18. 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

19. Temperature Measurement by Electrical Effects
- 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 + CT /3
- The sensitivity, or thermoelectric power, of a thermocouple is given by:
S = dE/dT = A + BT + CT
(see table 8.4) 2 3 2
Phil. U., M Eng Dep., Measurements, Chap#8

20. Temperature Measurement by Electrical Effects
- In order to provide a more sensitive circuit,
thermocouples are occasionally connected in series as
shown in figure 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

21. 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

22. 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