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                       series for average temperature, while the current devices are connected in series for minimum and parallel
                       for average. In addition to such simple applications of constant current or voltage sources based upon
                       temperature, there are a wide variety of novel circuits to derive almost any function imaginable as a basis
                       of temperature measurement.
                         Although there is a very small area on the silicon chip of the IC, which is temperature sensitive, it is
                       convenient to regard the entire chip, its case, and the bonded lead wires as the sensor. This increase in
                       thermal mass lowers the time response of the device to several seconds. Self-heating and heat transfer
                       through the leads are also of concern and limit the applicability of these devices in critical measurements.


                       Noncontact Thermometers
                       All of the previously discussed temperature monitoring systems implied that the sensor of whatever type
                       is in physical contact with the object being monitored, or in some special cases is the actual object being
                       measured. Often times it is impractical to make this physical connection and noncontact modes of
                       temperature measurement have been developed to overcome this objection. Almost all of these techniques
                       require that the infrared emissions from the surface of the object be measured, but in a few special cases
                       other surface optical properties such as reflectance can be exploited to determine the temperature
                       remotely.

                       IR Emission Thermometers
                       Any object above absolute zero emits electromagnetic radiation whose spectrum is related to its surface
                       temperature and surface emissivity. By characterizing the spectrum, the temperature of the object can be
                       determined directly and absolutely. The microwave background of the universe at 3 K, and the temperature-
                       dependent color of stars are extreme examples of this phenomena. Temperature can still be determined
                       from the emitted surface without using a spectrometer. If two bodies are allowed to come into thermal
                       equilibrium with each other and the temperature of one body is known, the temperature of the other is
                       also known. This is the basis of all previously discussed temperature-measuring devices assuming conduc-
                       tion as the principle means of heat transfer. This can be extended to noncontact thermometers since
                       radiation heat transfer is also a valid means of two bodies coming into thermal equilibrium. Many IR
                       thermometers are based upon this phenomenon.
                         In its simplest form, an IR thermometer would consist of a temperature sensor for monitoring the
                       temperature of an isolated object called the detector, and this detector would only be subject to radiative
                       heat transfer with the surface whose temperature is to be measured. This would work assuming that both
                       the surface and detector behave as black bodies, that there is no heat loss from the detector to the
                       surroundings, and that the field of view of the detector is restricted to the object under measurement
                       and otherwise totally unobstructed. Each one of these assumptions has to be considered when going
                       from the ideal case to a real IR thermometer.
                         The concept of a black body is an idealization where all radiant energy is completely absorbed by the
                       surface. Under this assumption, the radiant energy is a function only of the temperature of the surface.
                       The only alternatives to being absorbed by the surface are to be reflected by the surface or transmitted
                       through the material. The emissivity, which describes the deviation of a real surface from a black body,
                       is then just one minus its reflectance minus its transmittance. If the emissivity is less than one but
                       independent of wavelength, then it is a gray body. Few real materials are either black bodies or gray
                       bodies, thus emissivity corrections must be made which will often be a function of the temperature being
                       measured. If the surface behaves like a gray body over a limited range of wavelengths, the intensity at a
                       few wavelengths in this range can be measured to estimate the entire spectral shape. It is fortunate that
                       many real objects are close to gray over a narrow range of wavelengths around 750 nm and the spectral
                       shape as a function of temperature for gray objects in the temperature range of 500–3000°C is well
                       enough behaved at these wavelengths that the spectral shape, and thus the temperature, can be measured
                       with just two points. The emissivity of a surface can be determined in conjunction with taking its



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