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The Boltzmann constant, and therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin (J⋅K −1) in the International System of Units (or kg⋅m 2 ⋅s −2 ⋅K −1 in terms of base units). The entropy of a substance is usually given as an intensive property — either entropy per unit mass ...
As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380 649 × 10 −23 joules per kelvin. [1]
The SI system after 1983, but before the 2019 revision: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second), with the constants of nature and artefacts used to define them (such as the mass of the IPK for the kilogram).
Entropy increases with temperature, and is discontinuous at phase transition temperatures. The change in entropy (ΔS°) at the normal phase transition temperature is equal to the heat of transition divided by the transition temperature. The SI units for entropy are J/(mol·K). Absolute entropy of strontium. The solid line refers to the entropy ...
If there are N moles, kilograms, volumes, or particles of the unit substance, the relationship between h (in bits per unit substance) and physical extensive entropy in nats is: = where ln(2) is the conversion factor from base 2 of Shannon entropy to the natural base e of physical entropy.
When measuring entropy using the natural logarithm (ln), the unit of information entropy is called a "nat", but when it is measured using the base-2 logarithm, the unit of information entropy is called a "shannon" (alternatively, "bit"). This is just a difference in units, much like the difference between inches and centimeters.
[1]: 139 The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same ...
Hence the SI derived units on both sides of the equation are same as heat capacity: [] = [] = This definition remains meaningful even when the system is far away from equilibrium. Other definitions assume that the system is in thermal equilibrium , either as an isolated system , or as a system in exchange with its surroundings.