# Thermodynamic temperature (kelvin)

The definition of the unit of thermodynamic temperature was given in substance by the 10th CGPM (1954) which selected the triple point of water as the fundamental fixed point and assigned to it the temperature 273.16 K, so defining the unit. The 13th CGPM (1967/68) adopted the name kelvin, symbol K, instead of “degree Kelvin,” symbol °K, and defined the unit of thermodynamic temperature as follows (1967/68):

The kelvin, unit of thermodynamic temperature, is the fraction $$\dfrac{1}{273.16}$$ of the thermodynamic temperature of the triple point of water.

It follows that the thermodynamic temperature of the triple point of water is exactly 273.16 kelvins, TTPW = 273.16 K. The symbol TTPW is used to denote the thermodynamic temperature of the triple point of water. At its 2005 meeting, the CIPM affirmed that: This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.00015576 moles of 2H per mole of 1H, 0.0003799 moles of 17O per mole of 16O, and 0.0020052 moles of 18O per mole of 16O.

Because of the manner in which temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, regarding its difference from the reference temperature T0 = 273.15 K, the ice point. This difference is called the Celsius temperature, symbol T, which is defined by the quantity equation: T = T − T0

The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in magnitude to the kelvin. A difference or interval of temperature may be expressed in kelvins or degrees Celsius (13th CGPM, 1967/68), the numerical value of the temperature difference is the same. However, the numerical value of a Celsius temperature expressed in degrees Celsius is related to the numerical value of the thermodynamic temperature expressed in kelvins by the relation:

$\dfrac{\textrm{t}}{^{\circ}\textrm{C}}=\dfrac{\textrm{T}}{\textrm{K}-273.25}$

The kelvin and the degree Celsius are also units of the International Temperature Scale of 1990 (ITS-90) adopted by the CIPM in 1989 in its Recommendation 5.

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