Page 452 - The Mechatronics Handbook

0066_Frame_C19 Page 74 Wednesday, January 9, 2002 5:27 PM

∗
TABLE 19.4 Fixed Points Used in ITS 90
Triple point of hydrogen 13.8033 K
Triple point of neon 24.5561 K
Triple point of oxygen 54.3584 K
Triple point of argon 83.8058 K
Triple point of mercury 234.3156 K
Triple point of water 273.16 K
Melting point of gallium 302.9146 K
Freezing point of indium 429.7485 K
Freezing point of tin 505.078 K
Freezing point of zinc 692.677 K
Freezing point of aluminum 933.573 K
Freezing point of silver 1234.93 K
Freezing point of gold 1337.33 K
Freezing point of copper 1357.77 K
∗
Magnum (1990) includes the full definition of these points.
the discussion of temperature measuring techniques presented here. While this definition may help us
understand the concept of temperature, it does not help us assign a numerical value to temperature or
provide us with a convenient method for measuring temperature. The zeroth law of thermodynamics,
formulated in 1931 more than half a century after the first and second laws, lays the foundation for all
temperature measurement. It states that if two bodies are in thermal equilibrium with a third body, they
are also in thermal equilibrium with each other. By replacing the third body with a thermometer, we can
state that two bodies are in thermal equilibrium if both have the same temperature reading even if they
are not in contact.
The zeroth law does not enable the assignment of a numerical value for temperature. For that we must
refer to a standard scale of temperature. Two absolute temperature scales are defined such that the
temperature at zero corresponds to the theoretical state of no molecular movement of the substance. This
leads to the Kelvin scale for the SI system and the Rankine scale for the English system. There are other
two-point scales derived by identifying two arbitrary defining points for temperature. These are usually
defined as the temperature at which a pure substance undergoes a change in phase. Familiar defining
points are the freezing and boiling point of water for 0°C and 100°C, respectively. A wide range of
such phase changes, many of them triple points where all three phases are in equilibrium, have been
accepted as the defining points of the International Practical Temperature Scale of 1990 (ITS 90 ) shown
in Table 19.4. These can be used directly as calibration points for temperature monitors as long as the
substances are pure and the other conditions, such as pressure, which are included in the defining points
are met. Within the ITS 90 guidelines are standard means of interpolating temperatures between the defined
points. For example, platinum resistors are used in the range from 13.8 to 1235 K. The resistance is fitted
to the temperature through a higher-order polynomial that may be simplified for more limited ranges
between defined temperature points. The difference between a linear interpolation of resistance between
the defined points and the higher-order polynomial interpolation never exceeds 2 mK (Magnum and
Furukawa, 1990).
Another complication that is encountered in any discussion of temperature measurement is the fact
that temperature is an intrinsic rather than an extrinsic property. Thus, temperature can not be added,
subtracted, and divided in the same way that measured extrinsic properties such as length or voltage can
be manipulated.
Any property that changes predictably in response to temperature can be used in a temperature sensor.
The discussion of temperature measuring devices given here subdivides the devices based on the mea-
suring principle. Discussion will begin with a series of thermometers that rely upon the differential
expansion coefficients of the materials, be they solid, liquid, or gas. Mercury thermometers, perhaps the
most well known and widely used of all temperature measuring devices, belong to this category. We will
then move on to devices that rely upon phase change. Next we will discuss electrical temperature sensors
and transducers. Included in this category are thermocouples, RTDs, and thermistors, as well as integrated

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