handbook of modern sensors

98 3 Physical Principles of Sensing
temperature change. This assumes that at a reference temperature (we may call it calibration
temperature), the plate is flat; however, any convenient shape at a calibration
temperature may be selected. In effect, a bimetal plate is a transducer of temperature
into a displacement.
Most of such transducers are made of the bimetal plates (iron–nickel–chrome
alloys). They are useful in a temperature range from −75 ◦ C and up to +600 ◦ C. In
reality, for relatively small temperature changes, the radius of curvature is quite large
(several meters) and thus the tip deflection is rather small.Abimaterial plate deflection
can be computed from
[
= r 1 − cos
( 180L
πr
)]
, (3.114)
where r is found from Eq. (3.113) and L is the length of the plate. For example,
for a bimetal plate of L = 50 mm and thickness j = 1 mm and made of brass
(α = 20 × 10 −6 ) and chromium (α = 6 × 10 −6 ) with a 10 ◦ C gradient, the deflection
≈ 0.26 mm. This deflection is not easy to observe with the naked eye; thus, in a
practical thermometer, a bimetal plate is usually preshaped in the form of a coil (Fig.
3.38B). This allows for a dramatic increase in L and achieve a much larger . In
the same example, for L = 200 mm, the deflection becomes 4.2 mm—a significant
improvement. In modern sensors, the bimaterial structure is fabricated by employing
a micromachining technology.
3.11.3 Heat Capacity
When an object is warmed, its temperature increases. By warming, we mean the
transfer of a certain amount of heat (thermal energy) into the object. Heat is stored in
the object in the form of the kinetic energy of vibration atoms. The amount of heat
which an object can store is analogous to the amount of water which a water tank
can store. Naturally, it cannot store more than its volume, which is a measure of a
tank’s capacity. Similarly, every object may be characterized by a heat capacity which
depends on both the material of the object and its mass, m:
C = cm, (3.115)
where c is a constant which characterizes the thermal properties of material. It is
called the specific heat and is defined as
c =
Q
mT
(3.116)
The specific heat describes the material, whereas a thermal capacity describes an
object made of that material. Strictly speaking, specific heat is not constant over an
entire temperature range of the specific phase of the material. It may change dramatically
when a phase of the material changes, say from solid to liquid. Microscopically,
specific heat reflects structural changes in the material. For instance, the specific heat
of water is almost constant between 0 ◦ C and 100 ◦ C (liquid phase)—almost, but not
exactly: It is higher near freezing and decreases slightly when the temperature goes