Mechanical temperature measurement processes are founded on the physical expansion of gaseous, liquid or solid matter under the influence of temperature. Where the functional dependence of the thermal expansion of a material is known and reproducible from physical calculations or empirical processes, this material characteristic can be employed in the measurement of temperature.

Bimetallic Thermometers

The temperature-sensitive sensor element is a bimetallic strip in the form of a spiral or coil spring.
A bimetallic strip is a measuring element consisting of two materials with different thermal expansion coefficients. The material coefficients are selected in such a way as to give the largest possible difference in their coefficient of heat expansion. The angle of twist of a bimetallic spiral therefore changes dependent on temperature.

The relation between angle of twist and temperature can be described by the following formula:

, where

a: specific thermal expansion

l: length of bimetallic strip

s: thickness of bimetallic strip

Gas Pressure Thermometers

In gas pressure spring thermometers the entire closed system is filled with an inert gas or gas mixture. The temperature-dependent change in gas pressure is transmitted to a display by means of a capillary lead and an elastic measurement spring.

Van der Waal's equation of state is used to calculate the relation between pressure and temperature.

 

Liquid-in-Glass Thermometers

The liquid-in-glass thermometer is a widely used type of expansion thermometer. The method of operation is based on the thermal expansion of liquids. The sensitivity of the thermometer can be influenced by variation of the volume of the thermometer vessel. The most common thermometer liquids are mercury, gallium and alcohol.

Metal resistance thermometers change their electrical resistance dependent on temperature. The change in electrical resistance under temperature influence is caused by the conduction mechanism of the metals. The freely moving electrons in the atomic grid are the basis for the conductivity of metals. Their quantity and movement energy are temperature-dependent. When energy is supplied to the metal atoms by means of an increase in temperature, the metal atoms oscillate with correspondingly greater amplitude and frequency. An increasing resistance is set against the electron movement, this corresponds to the increase in electrical resistance. Since the electrical resistance rises in proportion to temperature the expression positive temperature coefficient is used.

The metal with the best characteristics is platinum and as a result the Pt resistance thermometer is the most important in measurement technology. Further metals that are used in temperature measurement are copper (Cu), nickel (Ni) and molybdenum (Mo).

The platinum resistance thermometer is described in detail in EN 60751. The so-called Pt100 resistance thermometer is the most commonly used. The thermometer has a nominal resistance of R = 100 W
at t = 0 °C and obeys the following equation:

In the range -200 to 0°C:

in the range 0 to 850°C:

where:

R₀ = 100,00 W

A = 3,9083 x 10^-3 °C^-1

B = -5,775 x 10^-7 °C^-2

C = -4,183 x 10^-12 °C^-4

The Pt100 resistance thermometer is divided into two accuracy classes:

Class A: ( 0.15 + 0.002 | t | ) °C

Class B: ( 0.30 + 0.005 | t | ) °C

Thermocouples

The measurement principle of the thermocouple is based on the effect discovered by Seebeck, that a voltage arises at the ends of two wires of different materials, when the temperature at the junction point of the two materials is different to the temperature of the measuring instrument terminals.

According to latest knowledge this effect is based on a material-specific characteristic of electrically conductive materials. A displacement of electron density is apparent within a conductor (volume diffusion effect) if a thermal gradient exists over the conductor. The collection of electrons is denser in the lower temperature range.

If one uses a thermocouple from two suitable materials, for example NiCr and Ni, the contact potential of this pair of materials can be measured. The thermoelectric voltage range against platinum at 100°C measuring junction temperature and 0°C reference junction temperature is presented in the following table.

Material	Voltage in mV
Tellurium	50
Silicon	45
Silit	27
Antimonite	4,8
Nickel-Chromium (85Ni-10Cr)	2,55
Iron	1,9
Platinum-Rhenium	1,5
Molybdenum, Uranium	1,2
Brass	1,1
Iridium-Rhodium (40IR, 60Rh)	1,0
Tungsten, High-Grade Steel (V2A)	0,8
Copper	0,75
Silver, Gold, Zinc	0,7
Manganese (86Cu, 12Mn, 2Ni)	0,68
Rhodium	0,65
Iridium-Rhodium (40Ir, 66Rh)	0,64
Platinum-Rhodium (10%)	0,64
Ididium	0,63
Phosphorus-Bronze	0,52
Tantalum, Caesium	0,5
Lead, Iridium-Rhodium	0,45
Aluminium, Magnesium, Zinc	0,4
Graphite	0,2
Platinum, Mercury	0,0
Thorium	-0,1
Sodium	-0,21
Palladium	-0,3
Potassium	-0,94
German Silver (Cu, Ni, Zn)	-1,0
Nickel	-1,55
Cobalt	-1,6
Constantan (55Cu, 45Ni)	-3,5
Bismuth, perpendicular to axis	-5,2
Bismuth, parallel to axis	-7,7

 

Thermocouples and compensating conductors are defined by colour codes. Unfortunately, these codes are often country-specific. The colour coding of the most common thermocouple types can be found at the following Internet addresses:

http://world.omega.com/germany/techref/thcpref1.html

http://world.omega.com/germany/techref/thcpref2.html

http://world.omega.com/germany/techref/thcpref3.html

Reference Junction Compensation for Thermocouples:

In thermocouples two wires of different materials are joined at the point of measurement. When these so-called thermoconductors are joined with copper conductors this transition point is known as the reference junction. The contact potential measured at the reference junction is directly proportional to the temperature difference between measurement point and reference junction. A Type K thermocouple is presented in the example below.

Total voltage U_ges is calculated as follows:

The contact potential proportional to temperature is obtained by deducting the contact potential arising at the reference junction. For reasons of simplicity the reference junction temperature is usually set to zero, since all thermocouples then have a contact potential of 0mV and thereby the voltage at the measurement point is equal to the total voltage.

Semiconductor Sensors

Resistance thermometers based on semiconductors use the temperature-dependent change of the electrical resistance of semiconductive, mostly ceramic materials for temperature measurement.

To this category belong:

Cold conductors (PTC)

Hot conductors (NTC)

Silicon sensing resistors

A cold conductor (PTC-Resistor) is a temperature-dependent semiconductor resistor, whose resistance value rises in step form on reaching a certain reference temperature. In the manufacturers' data the corresponding resistance value, the transition temperature and the maximum operating voltage are given for a specific reference temperature. Cold conductors are manufactured from implanted polycrystalline ceramic on the basis of barium nitrate.

Hot conductors are also commonly known as Thermistors or NTC-Resistors. The resistance of hot conductors dependent on temperature is almost exponential. Hot conductors consist of polycrystalline mixed oxide ceramic. Manufacturers provide information in the form of characteristic curves. The following formula applies approximately to the characteristic curve:

, where

: Temperature in K

: Reference Temperature in K

: Resistance at Temperature T

: Resistance at Temperature T₀

: Constant dependent on form and material in K

Silicon Measurement Resistors (spreading resistance sensor) have a positive temperature coefficient. The graph is characterised by a small non-linearity, which can be compensated by simple switching.

As well as heat exchange through conduction and convection, solids also exchange heat with their surrounding environment through radiation. The heat radiation of a measurement object is optically filtered and concentrated on a radiation detector. The electrical reaction consists of a change in resistance, voltage or current of the radiation detector, directly induced, or induced indirectly by an increase in temperature, dependent on the principle applied. The electrical change is amplified, measured and processed (see also VDI 3511, Page 4).

The following is a list of other temperature measurement processes (more detailed observations are not made here):

• Optical measurement process (determination of the intensity or wavelength of the electromagnetic radiation of a solid)
• Temperature measurement colours (physical effects of materials whose colour changes dependent on temperature)
• Liquid crystal (for indication of surface temperatures and optical presentation of temperature fields)
• Quartz crystal temperature sensors (the resonance frequency changes dependent on temperature)
• Acoustic measurement process (temperature-dependent speed of propagation of sound)
• Noise thermometers (temperature dependence of mean electron speed ® Brown movement)
• Capacitive temperature sensors (temperature dependence of dielectricity constants)
• Inductive temperature sensors (temperature dependence of the magnetic moment)