handbook of modern sensors

96 3 Physical Principles of Sensing
the other point at 96 degrees which is “…found in the blood of a healthy man…”. 14
On his scale, the melting point of water was at 32 ◦ and boiling at 212 ◦ . In 1742,
Andreas Celsius, professor of astronomy at the University of Uppsala, proposed a
scale with zero as the melting point of ice and 100 at the boiling point of water.
Currently, in science and engineering, Celsius and Kelvin scales are generally
employed. The Kelvin scale is arbitrarily based on the so-called triple point of water.
There is a fixed temperature at a unique pressure of 4.58 mm Hg, where water vapor,
liquid, and ice can coexist. This unique temperature is 273.16 K (kelvin) which
approximately coincides with 0 ◦ C. The Kelvin scale is linear with zero intercept (0
K) at a lowest temperature where the kinetic energy of all moving particles is equal
to zero. This point cannot be achieved in practice and is a strictly theoretical value.
It is called the absolute zero. Kelvin and Celsius scales have the same slopes 15 (i.e.,
1 ◦ C=1 Kand0K=−273.15 ◦ C):
◦ C = ◦ K − 273.15 ◦ (3.107)
The boiling point of water is at 100 ◦ C=373.15 K. A slope of the Fahrenheit scale is
steeper, because 1 ◦ C=1.8 ◦ F. The Celsius and Fahrenheit scales cross at temperature
of −40 ◦ C and ◦ F. The conversion between the two scales is
◦ F = 32 + 1.8 ◦ C, (3.108)
which means that at 0 ◦ C, temperature in the Fahrenheit scale is +32 ◦ F.
3.11.2 Thermal Expansion
Essentially, all solids expand in volume with an increase in temperature. This is a result
of vibrating atoms and molecules. When the temperature goes up, an average distance
between the atoms increases, which leads to an expansion of a whole solid body. The
change in any linear dimension (length, width, or height) is called a linear expansion.
A length, l 2 , at temperature, T 2 , depends on length, l 1 , at initial temperature T 1 :
l 2 = l 1 [1 + α(T 2 − T 1 )], (3.109)
where α, called the coefficient of linear expansion, has different values for different
materials. It is defined as
α = l 1
l T , (3.110)
14 After all, Fahrenheit was a toolmaker and for him 96 was a convenient number because to
engrave the graduation marks he could easily do so by dividing by 2: 96, 48, 24, 12, and
so forth. With respect to nationality of the blood, he did not care if it was of Englishman or
not. Now, it is known that the blood temperature of a healthy person is not really constant
and varies between approximately 97 ◦ F and 100 ◦ F (36 ◦ C and 37.7 ◦ C), but during his time
he did not have a better thermostat than the human body.
15 There is a difference of 0.01 ◦ between Kelvin and Celsius scales, as Celsius’ zero point is
defined not at a triple point of water as for the Kelvin, but at temperature where ice and
air-saturated water are at equilibrium at atmospheric pressure.