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is the specific gas constant [L 2 T −2 θ −1] (287.05 J/(kg K) for air), is the density [M 1 L −3]. If the temperature is increased, but the volume kept constant, then the Knudsen number (and the mean free path) doesn't change (for an ideal gas). In this case, the density stays the same.
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 .
For any substance, the number density can be expressed in terms of its amount concentration c (in mol/m 3) as = where N A is the Avogadro constant. This is still true if the spatial dimension unit, metre, in both n and c is consistently replaced by any other spatial dimension unit, e.g. if n is in cm −3 and c is in mol/cm 3 , or if n is in L ...
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Consider a steady diffusion between two regions of the same gas with perfectly flat and parallel boundaries separated by a layer of the same gas. Both regions have uniform number densities, but the upper region has a higher number density than the lower region. In the steady state, the number density at any point is constant (that is ...
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume.In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
When reduced temperature is greater than two (T R > 2), ideal-gas behavior can be assumed regardless of pressure, unless pressure is much greater than one (P R ≫ 1). Gases deviate from ideal-gas behavior the most in the vicinity of the critical point. [6]