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a go, no-go indication. The spots can be made reversible for real-time indications or irreversible to
indicate the maximum temperature reached over the monitoring period, although the irreversible ones
are much more common than the reversible kind.
Although waxes are widely used, any material that has a distinct phase change at a defined temperature
can be used in such a monitor. Imaging techniques other than visual can also be used to determine the
phase change. One such application involves using gadolinium or another element that readily absorbs
neutrons in a suitable form and observing the melting within the interior of an assembly by means of
neutron radioscopy. The temperature range for systems based upon observing melting solids ranges
from near ambient to several thousand Kelvin.

Electrical Temperature Sensors and Transducers
A sensor in this context is an element that varies an electrical parameter as a function of temperature.
This electrical parameter is then converted to a useful electrical function, such as linear voltage to
temperature, with added electronics. The sensor and added electronics make up a transducer. The
variation of electrical characteristics with temperature is both a source of measurement possibilities as
well as the bane of all electrical measuring systems, since the unwanted change of such things as the gain
of an amplifier with temperature causes thermal errors to occur. More effort is expended on eliminating
temperature induced electrical variations than is spent exploiting them for temperature measurement.
Thermocouples
There is a relationship between the temperature of a conductor and the kinetic energy of the free
electrons. Thus, when a metal is subjected to a temperature gradient, the free electrons will diffuse from
the high temperature region to the low temperature region where they have a lower kinetic energy. The
electron concentration gradient creates a voltage gradient since the lattice atoms that constitute the
positive charges are not free to move. This voltage gradient will oppose the further diffusion of electrons
in the wire and a stable equilibrium will be established with no current flow.
The “thermal power” of a material relates the balance of thermal diffusion of the electrons to the
electrical conductivity of the metal and is unique for every conductor and usually varies with temperature.
The electrical conductivity of the material has a strong influence on the thermal power since it defines
the ability of a material to support a voltage gradient. Thus, a SINGLE conductor with its ends at differing
temperatures will have a voltage difference between the ends. The trick is to be able to measure the voltage
at both ends of the conductor and thus determine the temperature difference between those ends. If we
use the same type of wire to measure the voltage across the original wire, the second wire will develop
exactly the same voltage difference when its ends are exposed to the same temperatures as the original
wire. Therefore, this effect cannot be measured with a pair of similar wires. But because the voltage
gradient is a function of the thermal power, which is different for each type of metal, a second conductor
of a different type of wire can be used to measure the original voltage gradient. Only a conductor with
either no electron mobility or infinite conductivity could be used to measure the absolute voltage gradient
associated with the temperature gradient of the original conductor. This is not a practical proposition,
so only the difference in the temperature-induced electron gradient between two conductors can ever be
measured. This is the basis of thermocouples.
In practical terms, whenever two metals are joined together and the junction is at a different temper-
ature than the free ends of the conductors, the free ends will have a potential difference between them,
that is a function of the absolute temperature at the junction and the temperature of the free ends. The
relationship between voltage difference and temperature difference will be characteristic of the chosen
pair of conductors. Rather than speak of the free ends of the two wires, it is normal to refer to a second
junction in the circuit. This is valid and reminds us that there is always a second junction to consider
even if the two wires from the thermocouple are attached to a metering circuit. Somewhere within the
meter, the circuit is completed and the second junction is formed.
From the previous explanation, all of the classic thermocouple laws can be derived. These laws can be
summarized and find application as follows:

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