Temperature Measurement

Changes in body temperature have been considered a sign of local or general illness from the time of Hippocrates. However, only the discovery of the thermometer in the half of the 17th century allowed the quantification of temperature.

The temperature scale constructed independently of any thermal medium is called the thermodynamic temperature, and its unit is the Kelvin [K]. The Kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

The triple point of water is the temperature at which ice-water-vapour are in equilibrium.

0 Celsius = 273.15K = 32 Fahrenheit

The normal body temperature corresponds to 37 degrees Celsius.

Different methods are used to measure temperature under special conditions. They can be divided into:

  • contact measurement
  • contactless measurement

Contact thermometric methods:

A) Thermal volume increase of liquids – Volume of the liquid increases with temperature.

The most common liquid to be used in thermometers is mercury (Hg). It is usually situated in a cylindrical reservoir from which the mercury can expand into a thick walled capillary. The sensitivity of this thermometer is given by the change of length of the liquid column in the capillary for temperature change of 1 degree Celsius.

The medical mercury thermometer is narrowed above the reservoir to prevent the mercury from spontaneously returning back into the reservoir in case there is a sudden temperature drop. To reuse the thermometer it must be shaken so that the Hg will return to the reservoir.

B) Thermal expansion of metals – The shape of the metal changes with temperature.

Two metallic plates having different thermal longitudinal expansion coefficients and being tightly connected represent a bimetallic thermometer. The plates will change their shape with increasing temperature, and return to their initial shape with decreasing temperature, or further continue to change shape.

The deformation can be calibrated for a range of temperatures with an accuracy of approx. 1 degree Celsius.


C) Changes in electrical properties of materials

  1. The resistance of some metals increases with temperature linearly over a broad range of temperatures. This can be used to determine temperature
  2. With increasing temperature the free-electron density of semiconductors increases rapidly. Thermistors, semiconductor components with thermal dependence of resistance, can also be used to determine temperature.
  3. A combination of two metals, two identical conductors with another conductor, in a junction forms two thermoelectric couples (thermocouple). If those thermocouples are held at different temperatures, a thermoelectric voltage U arises between them. Usually one of the thermocouples is kept at a reference temperature. The voltage depends on the temperature difference between the two couples and the difference of thermoelectric coefficients(α) of the metals used.

U = (α1 – α2) * (temperature1 – temperature2)

The advantage of a thermocouple temperature measurement is its very short time-constant. A disadvantage is the necessity of a reference temperature.

Contactless temperature measurement:

In this method, the temperature is determined by measuring the electromagnetic infrared radiation emitted by the human body. The wavelength distribution of the radiation energy depends on the temperature and nature of the source.

In theory, the temperature can be simply determined using Wien’s shift law:

T = b / λ max

where b is a constant and λ max is the wavelength of radiation with maximum intensity. However, for more precision radiation thermometers are used. They absorb a total amount of radiation, E, and determine the temperature using Stefan-Boltzmann law:

T = (E/σ)^(0.25)

where σ is a constant.

The emitted radiation is focused on a detector where radiation enegy is transformed into an electrical signal which can be easily measured an displayed. The sensitivity of a radiation thermometer is 0.05 degrees Celsius.