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 and negative sets Positive and negative sets In measure theory, given a measurable space ("X",Σ) and a signed measure μ on it, a set "A" ∈ Σ is called a positive set for μ if every Σ-measurable subset of "A" has nonnegative measure; that is, for every "E" ⊆ "A" that satisfies "E" ∈ Σ, one has μ("E") ≥ 0. Similarly, a set "A" ∈ Σ is called a negative set for μ if for every subset "E" of "A" satisfying "E" ∈ Σ, one has μ("E") ≤ 0. Intuitively, a measurable set "A" is positive (resp. negative) for μ if μ is