Ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma. The classical thermodynamic properties of an ideal gas can be described by two equations of state: The ideal gas law is the equation of state for an ideal gas, given by: where The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations. Real fluids at low density and
Positive real numbers numbers. For a given positive real number "x", the sequence {"x"} of its integral powers has three different fates: When "x" ∈ (0, 1) the limit is zero and when "x" ∈ (1, ∞) the limit is infinity, while the sequence is constant for "x" = 1. The case "x" > 1 thus leads to an unbounded sequence. formula_10 and the multiplicative inverse function exchanges the intervals. The functions floor, formula_11, and excess, formula_12, have been used to describe an element formula_13 as a continued fraction formula_14 which is a sequence of integers obtained from the floor function after the