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The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. [ 1 ] It is named for Hugo Martin Tetrode [ 2 ] (1895–1931) and Otto Sackur [ 3 ] (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.
Boltzmann's equation—carved on his gravestone. [1]In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...
For the expansion (or compression) of an ideal gas from an initial volume and pressure to a final volume and pressure at any constant temperature, the change in entropy is given by: = = Here is the amount of gas (in moles) and is the ideal gas constant. These equations also apply for expansion into a finite vacuum or a throttling ...
Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1.The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
In the case of an ideal gas, the heat capacity is constant and the ideal gas law PV = nRT gives that α V V = V/T = nR/p, with n the number of moles and R the molar ideal-gas constant. So, the molar entropy of an ideal gas is given by (,) = (,) + . In this expression C P now is the molar heat capacity. The entropy of inhomogeneous ...
A major use of the integrated equation is to estimate a new equilibrium constant at a new absolute temperature assuming a constant standard enthalpy change over the temperature range. To obtain the integrated equation, it is convenient to first rewrite the Van 't Hoff equation as [ 2 ]
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant , expressed in units of energy per temperature increment per amount of substance , rather than energy per temperature increment per particle .