Kelvin, thermometers and temperature scales – how it works

Temperature has always played a central role in human life, but despite this it was not until the 18th century that common temperature scales began to be developed, giving us common references to describe temperature.

Philo and Galileo

The first devices to measure temperature, thermoscopes, could be used to compare temperatures or observe temperature changes. However, these thermoscopes did not give an accurate indication of how hot or cold it actually was. One of the first thermoscopes was developed around 2,000 years ago by the Greek engineer Philo of Byzantium. Philo's thermoscope consisted of a hollow sphere filled with air and water, connected to an open water container. When the sphere was heated by the sunlight, the volume of the water in the sphere increased, which pushed out the air and in turn increased the volume of the water in the container.

This principle of the thermoscope was developed in the 17th century by Galileo Galilei and Santorio Santorio, among others. The thermoscope was gradually equipped with scales, including by Robert Fludd in 1638. However, each scientist or instrument maker had his own scale and it was difficult or impossible to compare readings from different instruments.

Universal temperature scales

In the 18th century, thermometry developed, and several scientists proposed universal temperature scales. Fahrenheit created his temperature scale in 1724, where the freezing point of water was set at 32 degrees and the boiling point at 212 degrees. Fahrenheit also invented the mercury thermometer in 1714.

The Swede Anders Celsius set the boiling point to 0 °C and the freezing point to 100 °C for his temperature scale. After his death, the scale was turned so that 0 °C corresponded to the freezing point of water. In our everyday life, it is this scale that we use to measure temperature.

Kelvin scale

The confusion with different scales led physicists to seek a scale based on the basic physics of temperature. This resulted in the Kelvin scale, which was introduced by Lord Kelvin (1824-1907). The scale sets the zero point at the lowest possible temperature for matter (-273.15°C) and the kelvin has been the official SI unit for thermodynamic temperature since 1954.

The steps on the Kelvin scale and the Celsius scale are the same, which means that the relationship between temperature expressed in degrees Celsius and Kelvin is:

t = T - 273.15

where t is the temperature in degrees Celsius and T is the temperature in Kelvin.

The definition of a kelvin

In 1954, the kelvin was defined as 1/273.16 of the thermodynamic temperature at the triple point of water. The triple point is the specific temperature and pressure where water can exist in all three states simultaneously - solid (ice), liquid (water) and gas (steam). As this temperature differs depending on the composition of the water, an internationally agreed composition of water called Vienna Standard Mean Ocean Water is used.

Since 2018, the unit is defined based on Boltzmann constant, which relates thermodynamic energy in a substance to its temperature.

Thermodynamic temperature

In everyday life, we often think of temperature as a comparison - how hot or cold something feels compared to something else. However, thermodynamic temperature is a measure of an object's internal energy, which includes the average kinetic energy of the object's atoms and molecules. Simply put, you can say that the more the atoms move, the higher the thermodynamic temperature. According to classical physics, motion ceases at absolute zero (but according to quantum theory, there is still random motion, so-called "zero-point motion", even at absolute zero, due to Heisenberg's uncertainty principle).

Because it is very difficult to measure the internal energy directly, scientists instead measure its effect as it moves as heat between objects. It is this effect that we use when we compare whether something is cold or hot. When heat no longer flows between the objects, that is, when they are in thermal equilibrium, that is their thermodynamic temperature.

How is kelvin realised?

Internal energy and temperature are different but directly related. To connect energy and temperature, Boltzmann's constant is used:

E = kT

where E is the material's kinetic energy, k is Boltzmann's constant and T is the material's temperature.

Realisation of an SI unit, that is, "making" the unit in the real world from its definition, is done through established and approved methods called mises en pratique. There are several mises en pratique to realise the kelvin, all of which are relatively complex, such as measuring the speed of sound in an ideal gas (the speed of sound depends on the temperature of the gas, which allows you to calculate the temperature from the speed). Although the triple point of water no longer defines the kelvin, the method is still used as a practical realisation with sufficiently low measurement uncertainty for calibrating thermometers.

The temperature scale ITS-90

Because of the difficulties in realising kelvin, practically useful temperature scales have long been used for calibrating thermometers. The first version came in 1889. Today there are two temperature scales, PLTS-2000 for very low temperatures (0.9 mK to 1 K) and ITS-90 for other temperatures. It is ITS-90 that we use for calibrations at RISE. The triple point of water is a good reference point to use for calibrations, but it is only one point. ITS-90 therefore contains 17 different fix points which are based on phase transitions (freezing or melting) or triple points in several different substances. At these points, the temperature is known with very low measurement uncertainty. This makes it possible to calibrate thermometers at many different temperatures.

Some of the fix points:

• Triple point of hydrogen = 13.8033 K (-259.3467 °C)
• Triple point of oxygen = 54.3584 K (-218.7916 °C)
• Triple point of mercury = 234.3156 K (-38.8344 °C)
• Freezing point of tin = 505.078 K (231.928 °C)
• Freezing point of aluminum = 933.473 K (660.323 °C)
• Freezing point of gold = 1337.33 K (1064.18 °C)

How is a thermometer calibrated?

The principle is simple. The reading from a reference thermometer is compared with the reading of the thermometer to be calibrated. The reference thermometer is usually a so-called platinum resistance thermometer, but at high temperatures a radiation thermometer is used which measures the radiation from the object.

The reference thermometer is in turn calibrated against ITS-90. When calibrating against ITS-90, fix point cells are used: prepared containers with the correct pressure and composition of the substance, which are heated or cooled. When, for example, gold changes from liquid to solid form, i.e. freezes, the temperature is known to be 1337.33 K. The reading of the reference thermometer is then compared with the temperature of the fix point cell.

The video shows a simplified view of calibrating a thermometer.