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A thermometer is an instrument that measures the
temperature of a system in a quantitative way. The easiest way to do this
is to find a substance having a property that changes in a regular way
with its temperature. The most direct 'regular' way is a linear one:
t(x) = ax + b,
where t is the temperature of the substance and changes as the property
x of the substance changes. The constants a and b depend on the substance
used and may be evaluated by specifying two temperature points on the
scale, such as 32° for the freezing point of water and 212° for its
boiling point.
For example, the element mercury is liquid in the temperature range of
-38.9° C to 356.7° C (we'll discuss the Celsius ° C scale later). As a
liquid, mercury expands as it gets warmer, its expansion rate is linear
and can be accurately calibrated.
The mercury-in-glass thermometer illustrated in the above figure
contains a bulb filled with mercury that is allowed to expand into a
capillary. Its rate of expansion is calibrated on the glass scale.
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