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One mole of atoms contains an Avogadro number of atoms, so that the energy of one mole of atoms of a monatomic gas is =, where R is the gas constant. In an adiabatic process , monatomic gases have an idealised γ -factor ( C p / C v ) of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also ...
A closely related property of a substance is the heat capacity per mole of atoms, or atom-molar heat capacity, in which the heat capacity of the sample is divided by the number of moles of atoms instead of moles of molecules. So, for example, the atom-molar heat capacity of water is 1/3 of its molar heat capacity, namely 25.3 J⋅K −1 ⋅mol ...
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.
An equivalent statement of the Dulong–Petit law in modern terms is that, regardless of the nature of the substance, the specific heat capacity c of a solid element (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole).
It follows that the heat capacity of the gas is 3 / 2 N k B and hence, in particular, the heat capacity of a mole of such gas particles is 3 / 2 N A k B = 3 / 2 R, where N A is the Avogadro constant and R is the gas constant. Since R ≈ 2 cal/(mol·K), equipartition predicts that the molar heat capacity of an ideal gas ...
Helium is the least water-soluble monatomic gas, [95] and one of the least water-soluble of any gas (CF 4, SF 6, and C 4 F 8 have lower mole fraction solubilities: 0.3802, 0.4394, and 0.2372 x 2 /10 −5, respectively, versus helium's 0.70797 x 2 /10 −5), [96] and helium's index of refraction is closer to unity than that of any other gas. [97]
1.365. In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). It is sometimes also known as the isentropic expansion factor and is denoted by γ ...
Sackur–Tetrode equation. 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. [4]
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