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Thus, the ratio of the kinetic energy to the absolute temperature of an ideal monatomic gas can be calculated easily: per mole: 12.47 J/K; per molecule: 20.7 yJ/K = 129 μeV/K; At standard temperature (273.15 K), the kinetic energy can also be obtained: per mole: 3406 J; per molecule: 5.65 zJ = 35.2 meV.
for the average kinetic energy per particle, the equipartition theorem can be used to derive the ideal gas law from classical mechanics. [6] If q = ( q x , q y , q z ) and p = ( p x , p y , p z ) denote the position vector and momentum of a particle in the gas, and F is the net force on that particle, then
M is molar mass of the substance, and thus may be calculated as a product of particle mass, m, and Avogadro constant, N A: =. For diatomic nitrogen ( N 2 , the primary component of air ) [ note 1 ] at room temperature ( 300 K ), this gives
M m = molar mass = = = ... Average kinetic energy per degree of freedom ... Thermodynamic equation calculator This page was last edited on 9 December 2024 ...
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. [2] It occurs in the definitions of the kelvin (K) and the gas constant , in Planck's law of black-body radiation and Boltzmann's entropy formula , and is used in ...
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount, n (in moles), is equal to total mass of the gas (m) (in kilograms) divided by the molar mass, M (in kilograms per mole): =.
Hence temperature was proportional to the average kinetic energy of the particles. [28] This article inspired further work based on the twin ideas that substances are composed of indivisible particles, and that heat is a consequence of the particle motion; movement that evolves in accordance with Newton's laws.
The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; this average total kinetic energy is related to the temperature of the system by the equipartition theorem.