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
Negative base and we have So every number formula_19 with a terminating fraction formula_20 added has two distinct representations. For example, in negaternary, i.e. formula_21 and formula_22, there is Such non-unique representations can be found by considering the largest and smallest possible representations with integral parts 0 and 1 respectively, and then noting that they are equal. (Indeed, this works with any integral-base system.) The rationals thus non-uniquely expressible are those of form with formula_25 Just as using a negative base allows the representation of negative numbers without an explicit negative sign, using an imaginary base allows the representation of Gaussian integers.