The origin of SI units - K and °C

In the ancient times people know hot, cold and warm by their feelings. But sometimes feeling is not reliable. So people need a quantity to describe it, which is called temperature. There are two units of temperature in SI: the base unit kelvin (K) and the derived unit degree Celsius (°C).

To measure the temperature, people use an instrument called thermometer. Then people use different special points to define different  temperature scales  to measure the temperature. These temperature scales are called "empirical scales".  In the past Celsius was an empirical scale. In 1742, Swedish astronomer Anders Celsius (1701-1744) created a new temperature scale by water: 0 represented the boiling point of water, while 100 represented the freezing point of water. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure. He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere. The BIPM's 10th General Conference on Weights and Measures (CGPM) later defined one standard atmosphere to equal precisely 101.325 kPa.

In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Académie des sciences, belles-lettres et arts de Lyon, working independently of Celsius, developed a scale where zero represented the freezing point of water and 100 represented the boiling point of water. On 19 May 1743 he published the design of a mercury thermometer, the "Thermometer of Lyon" built by the craftsman Pierre Casati that used this scale.

In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carolus Linnaeus (1707-1778) reversed Celsius's scale. His custom-made "linnaeus-thermometer", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time and whose workshop was located in the basement of the Stockholm observatory. As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; Daniel Ekström, the instrument maker; and Mårten Strömer (1707-1770) who had studied astronomy under Anders Celsius.

Since the 19th century, the scientific and thermometry communities worldwide referred to this scale as the centigrade scale. Temperatures on the centigrade scale were often reported simply as degrees or °, when greater specificity was desired, as degrees centigrade. The symbol for temperature values on this scale is °C.

Because the term centigrade was also the Spanish and French language name for a unit of angular measurement (1/10000 of a right angle) and had a similar connotation in other languages, the term centesimal degree was used when very precise, unambiguous language was required by international standards bodies such as the BIPM. The 9th CGPM and the CIPM formally adopted "degree Celsius" (symbol: °C) in 1948.

Now  the Celsius scale was being used by everyone in the world. But the Celsius scale is an empirical scale depending on the properties of a particular material (water), so it does not signify the essence of temperature. With the development of science, thermodynamic temperature was founded.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, called absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

In 1848 Lord Kelvin (William Thomson), wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment. Thomson calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale. Thomson's value of "-273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.

In 1954, the Resolution 3 of the 10th CGPM gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to exactly 273.16 °K.

In 1967/1968 Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."

After redefining kelvin, degree Celsius was redefined as well. °C is derived by K: °C = K - 273.15. In this definition, the scale of K is the same as °C. So when the temperature increases/decrease 1 K, it will increase /decrease 1°C.

Unlike °C, the kelvin is not referred to or typeset as a degree. The kelvin is the primary unit of measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. Subtracting 273.16 K from the temperature of the triple point of water (0.01 °C) makes absolute zero (0 K) equivalent to −273.15 °C. The boiling point of water in 101.325 kPa is 373.15 K (100 °C).

K is used mainly in research and experiment, sometimes in engineering. While in our daily life we often use the derived unit °C. °C is commonly used in weather report, engineering, cooking, medical treatment, etc. Here are the rules of using these 2 units.

Kelvin is named after William Thomson, 1st Baron Kelvin. As with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (K). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (kelvin), except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.  When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm (e.g. "the triple point of water is exactly 273.16 kelvins"). When reference is made to the "Kelvin scale", the word "kelvin"—which is normally a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols (angle symbols, e.g. 45°3'4'', are the exception) there is a space between the numeric value and the kelvin symbol (e.g. "99.987 K").

Before the 13th General Conference on Weights and Measures (CGPM) in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time. It was distinguished from the other scales with either the adjective suffix "Kelvin" ("degree Kelvin") or with "absolute" ("degree absolute") and its symbol was °K. The latter (degree absolute), which was the unit's official name from 1948 until 1954, was rather ambiguous since it could also be interpreted as referring to the old Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute". The 13th CGPM changed the unit name to simply "kelvin" (symbol K).  The omission of "degree" indicates that it is not relative to an arbitrary reference point like °C, but rather an absolute unit of measure which can be manipulated algebraically (e.g. multiplied by two to indicate twice the amount of "mean energy" available among elementary degrees of freedom of the system).

The "degree Celsius" has been the only SI unit whose full unit name contains an uppercase letter since the SI base unit for temperature, the kelvin, became the proper name in 1967 replacing the term degree Kelvin. The plural form is degrees Celsius.

The general rule of the BIPM is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, e.g. "30.2 °C" (not "30.2°C" or "30.2° C"). Thus the value of the quantity is the product of the number and the unit, the space being regarded as a multiplication sign (just as a space between units implies multiplication). The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ', and '', respectively), for which no space is left between the numerical value and the unit symbol. Other languages, and various publishing houses, may follow different typographical rules.

In this post we talked about the origin of SI temperature units - K and °C. In the next post we will use these 2 units in an example. This is a new instance!