In General > s.a. gas; fluids; states in statistical mechanics; thermodynamical systems [including geometry of state space].
* Idea: A large collection of particles with no internal structure, non-interacting except for collisions (small hard spheres).
* Equation of state: The ideal gas law, obtained combining Boyle's volume-pressure law, Gay-Lussac's pressure-temperature law and Charles' law,

pV = nRT = NkBT ,

where R is the molar gas constant, and kB the Boltzmann constant (> see constants); First stated in 1834 by Émile Clapeyron; It does not hold at very low temperatures or high densities, when quantum effects have to be taken into account.
* Remark: Most gases at room T and p behave like ideal gases, but as T → 0 they can't because of quantum effects.
* Internal energy: If s is the number of degrees of freedom (s = 3 for a monatomic gas),

U = (s/2) NkBT .

* Entropy: An explicit expression in terms of basic constants for a monatomic gas is given by the Sackur-Tetrode equation; The general form is given by

S = CV ln(T/T0) + NkB ln(V/V0) .

* Consequences: Aerosol cans get cold when used.
* In a gravitational field: The equilibrium pressure of a perfect gas in a constant gravitational field decreases exponentially with height (barometric formula).

Second-Order Quantities > see Compressibility; specific heat.

References
@ General: Creaco & Kalogeropoulos MPLB(09)-a0811 [thermodynamic limit, phase space measure]; Arnaud et al Ent(13)-a1105 [assumptions behind the ideal gas law]; Ferrando & Sáez CQG(19)-a1910 [kinematic approach].
@ Quantum: Meyer IJMPC(97)qp [quantum lattice gas]; Bloch pw(04)apr [in optical lattices]; Nattermann AJP(05)apr [scaling approach]; Velenich et al JPA(08) [Brownian gas, Poissonian ground state]; Dodonov & Vieira Lopes PLA(08) [temperature increase from sudden expansion]; Pérez & Sauer AHES(10)-a1004 [Einstein's work]; Nakamura et al PRE(11)-a1105 [in an expanding cavity]; Quevedo & Zaldivar a1512 [geometrothermodynamic approach]; > s.a. gas [fermion gas, boson gas]; Susceptibility.
@ Relativistic: Becattini & Piccinini AP(08), Becattini & Tinti AP(10)-a0911 [rotating]; Chakrabarti et al PhyA(10) [non-extensive statistics]; Basu & Mondal a1103 [4-velocity distribution]; Cannoni PRD(14)-a1311 [probability distribution for the relative velocity of colliding particles]; Montakhab et al PhyA(14)-a1406 [morphological phase transition]; > s.a. deformed special relativity; quantum-gravity phenomenology; statistical-mechanical systems.
@ Modified: Das et al PRD(09)-a0908 [DSR, equation of state]; Chandra & Chatterjee PRD(12)-a1108 [DSR, thermodynamics]; > s.a. phenomenology of modified uncertainty relations; thermodynamic systems [non-commutative, etc].
@ Entropy: Kolekar & Padmanabhan PRD(11)-a1012 [in a strong gravitational field]; Oikonomou & Bagci SHPMP(13) [monatomic gas, Clausius versus Sackur-Tetrode entropies]; > s.a. Gibbs Theorem.
@ From particles to fluid: Park JPCS(14)-a1310 [phase transition at finite particle number for ideal Bose gas].
@ Related topics: Landsberg et al AJP(94)aug, Pantellini AJP(00)jan [in a constant g field]; Boozer AJP(10)jan [1D, details]; Kothawala PLB(13)-a1108 [in free fall in curved spacetime]; > s.a. Boltzmann Equation; Maxwell-Boltzmann Distribution.