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
Lucky numbers of Euler Lucky numbers of Euler Euler's “lucky” numbers are positive integers "n" such that for all integers "k" with , the polynomial produces a prime number. When "k" is equal to "n", the value cannot be prime anymore since is divisible by "n". Since the polynomial can be rewritten as , using the integers "k" with produces the same set of numbers as . Leonhard Euler published the polynomial which produces prime numbers for all integer values of "k" from 1 to 40. Only 7 lucky numbers of Euler exist, namely 1, 2, 3, 5, 11, 17 and 41 . The