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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 .
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. [1] The ideal gas concept is useful because it obeys the ideal gas law , a simplified equation of state , and is amenable to analysis under statistical mechanics .
In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
Therefore, the kinetic energy per kelvin of one mole of monatomic ideal gas (D = 3) is = =, where is the Avogadro constant, and R is the ideal gas constant. Thus, the ratio of the kinetic energy to the absolute temperature of an ideal monatomic gas can be calculated easily:
The classical equipartition theorem predicts that the heat capacity ratio (γ) for an ideal gas can be related to the thermally accessible degrees of freedom (f) of a molecule by = +, =. Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: γ = 5 3 = 1.6666 … , {\displaystyle \gamma ={\frac {5}{3}}=1. ...
With that said, R is just a constant, e.g. 1, 2, 3, etc., and n is a measure of the exact number atoms or molecular units in the ideal gas system, e.g. if n = 3.2, then there would be 1.93E24 atoms (or molecular units) in the gas phase system.
The Loschmidt constant or Loschmidt's number (symbol: n 0) is the number of particles (atoms or molecules) of an ideal gas per volume (the number density), and usually quoted at standard temperature and pressure. The 2018 CODATA recommended value [1] is 2.686 780 111... × 10 25 m −3 at 0 °C and 1 atm.