## UNIT: kelvin

• PID: si:unit:kelvin
• Definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380 649 × 10-23 when expressed in the unit J K-1, which is equal to kg m2 s2 K-1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
• Source: SI Brochure 9th Ed. 2019, p 133
• Reference: CGPM Resolution 1 of the 26th CGPM (2018) "On the revision of the International System of Units (SI)"
• Status: Valid
• Valid: 2019-05-20 -
• Notes
1. This definition implies the exact relation $$k = 1.380\:649 \times 10^{-23}\ {\rm{kg\:m^{2}\:s^{2}\:K^{-1}}}$$. Inverting this relation gives an exact expression for the kelvin in terms of the defining constants $$k$$, $$h$$ and $${\Delta\nu_{\rm{Cs}}}$$: $$1\ {\rm{K}} = \left( \frac{1.380\:649}{k} \right) \times 10^{-23}\ {\rm{kg\:m^{2}\:s^{-2}}}$$ which is equal to $$1\ {\rm{K}} = \frac{1.380\:649 \times 10^{-23}}{(6.626\:070\:15 \times 10^{-34})(9\:192\:631\:770)}\frac{\Delta\nu_{\rm{Cs}}h}{k} \approx 2.266\:6653 \frac{\Delta\nu_{\rm{Cs}}h}{k}$$
2. The effect of this definition is that one kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy $$kT$$ by $$1.380\:649 \times 10^{-23} {\rm{J}}$$.
3. The previous definition of the kelvin set the temperature of the triple point of water, $$T_{\rm{TPW}}$$, to be exactly $$273.16\ {\rm{K}}$$. Due to the fact that the present definition of the kelvin fixes the numerical value of $$k$$ instead of $$T_{\rm{TPW}},$$ the latter must now be determined experimentally. At the time of adopting the present definition $$T_{\rm{TPW}}$$ was equal to $$273.16\ {\rm{K}}$$ with a relative standard uncertainty of $$3.7 \times 10^{-7}$$ based on measurements of $$k$$ made prior to the redefinition.
4. As a result of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol $$T$$, in terms of its difference from the reference temperature $$T_{0} = 273.15\ {\rm{K}}$$, close to the ice point. This difference is called the Celsius temperature, symbol $$t$$, which is defined by the quantity equation $$t=T-T_{0}$$
5. The unit of Celsius temperature is the degree Celsius, symbol $$^{\circ}{C}$$, which is by definition equal in magnitude to the unit kelvin. A difference or interval of temperature may be expressed in kelvin or in degrees Celsius, the numerical value of the temperature difference being the same in either case. However, the numerical value of a Celsius temperature expressed in degrees Celsius is related to the numerical value of the thermodynamic temperature expressed in kelvin by the relation $$t/^{\circ}{\rm{C}} = T/{\rm{K}}-273.15$$ (see 5.4.1 for an explanation of the notation used here).
6. 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 Recommendation 5 (CI-1989, PV, 57, 115). Note that the ITS-90 defines two quantities $$T_{90}$$ and $$t_{90}$$ which are close approximations to the corresponding thermodynamic temperatures $$T$$ and $$t$$.
7. Note that with the present definition, primary realizations of the Kelvin can, in principle, be established at any point of the temperature scale.
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