Page 453 - The Mechatronics Handbook

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circuit temperature sensors. The final category of temperature sensors will be noncontact sensors. A
separate discussion of temperature measurements on the microscale is provided at the end. Many of the
techniques discussed in the microscale section will be derivatives of those introduced earlier in the
discussion, but alterations, ranging from minor to quite major, must be made to enable small-scale and/or
quick response temperature measurements.

Thermometers That Rely Upon Differential Expansion Coefficients
Thermometers that rely upon differential expansion coefficients are by far the most common and familiar
direct reading temperature monitors. These thermometers can be divided into categories depending on
the state of the materials used. Each of these deserves a separate discussion.
Gas vs. Solid
The gas bulb thermometer, which is used to determine absolute zero from extrapolation of the change
in pressure of a simple gas in a metal sphere with a change in temperature, is an example of a gas vs.
solid thermometer. If the metal bulb had the same expansion coefficient as the fill gas, the pressure inside
would remain constant and it would not be a thermometer. Instead, the gas follows the ideal gas law,
which indicates that, at a constant volume, the pressure is linearly related to the temperature and the
vessel containing the gas changes linearly with the volumetric expansion coefficient of the metal making
up the bulb. The thermal expansion coefficient of the metal is usually ignored unless very precise
predictions of absolute zero are required.
While a large metal sphere with a pressure gage attached is not a very convenient means of measuring
temperature, except as a demonstration or research tool, the bulb can be made quite small and connected
via a small capillary tube to a remote pressure gage. In this miniaturized configuration the gas bulb
thermometer becomes a practical means of measuring temperature. As long as the device operates in the
ideal gas region, the pressure gage can be graduated to read temperature directly, since pressure is linearly
related to temperature.
Some major limitations on gas bulb thermometers are that the instrument should be calibrated
specifically for a particular installation since the length of the heated capillary, as well as the ambient
pressure and temperature at the pressure gage, will influence the accuracy of the device. These limitations
can be overcome at the expense of complication by using bimetallic elements in the pressure gage to
compensate for the temperature at that point or by having a parallel capillary with no bulb follow the
main capillary up to the point of measurement and have the parallel capillary equipped with a pressure
gage linked to subtract its effects from the main gage. Also, any damage that changes the volume of the
bulb, such as a dent, will shift the calibration. This style of instrument should not be confused with vapor
pressure thermometers that can take on an identical exterior form, but instead of being filled with an
ideal gas, they contain a two-phase fluid and the saturation pressure of the fluid is measured. This type
of temperature sensor is discussed in further detail in another section.
Liquid vs. Solid
The common mercury and glass thermometer is an example of a liquid vs. solid temperature sensor. The
thermal expansion of liquids, although not as great as gasses, is generally much greater than that of solids
and for many applications the expansion coefficient of the glass can be ignored. However, for precision
measurements, the expansion of the glass can introduce significant errors. There are two common means
of dealing with the glass expansion coefficient. Thermometers intended for reading the temperature of
a liquid bath might have a specified submergence depth indicated by a mark on the stem. It is assumed
that the rest of the thermometer is at standard lab conditions. This is not always a good assumption,
however, and a more precise way of handling the glass expansion coefficient compared to that of mercury
is to use a pair of total submergence thermometers. One measures the temperature of the liquid and the
other measures the temperature in the immediate vicinity of the exposed stem. A simple stem correction
formula supplied by the thermometer manufacturer can then be applied to determine the temperature
of the bath.

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