Since there is no disorder in this state, the entropy can be defined as zero. Imagine cooling the substance to absolute zero and forming a perfect crystal (no holes, all the atoms in their exact place in the crystal lattice). The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium, down to 240 m/s for xenon. The absolute entropy of any substance can be calculated using equation (1) in the following way. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. This corresponds very well with experimental data. According to the equipartition of energy this means that there is a thermal energy of 3 / 2 k T per atom. Monatomic ideal gases (the six noble gases) possess three degrees of freedom per atom, corresponding to the three spatial directions. 1 It is named for Hugo Martin Tetrode 2 (18951931) and Otto Sackur 3 (18801914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.

In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. The SackurTetrode equation is an expression for the entropy of a monatomic ideal gas. This is generally true only for classical systems with a large number of particles, and in which quantum effects are negligible. Given a thermodynamic system at an absolute temperature T, the average thermal energy carried by each microscopic degree of freedom in the system is 1 / 2 k T (i.e., about 2.07 ×10 −21 J, or 0.013 eV, at room temperature). Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n and absolute temperature T: Roles of the Boltzmann constant Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant k = R / N A = n R / N (in each law, properties circled are variable and properties not circled are held constant) The Boltzmann constant is defined to be exactly 1.380 649 ×10 −23 J⋅K −1. They are used in various combinations to define the seven SI base units. It is named after the Austrian scientist Ludwig Boltzmann.Īs part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven ' defining constants' that have been given exact definitions. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant ( k B or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. Ludwig Boltzmann, the constant's namesake

Absolute entropy equation