Ideal Gas |

**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* = *Nk*_{B}*T* ,

where *R* is the molar gas constant, and *k*_{B} 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)* Nk*_{B}*T* .

* __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* = *C*_{V} ln(*T*/*T*_{0})
+ *Nk*_{B} ln(*V*/*V*_{0}) .

* __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].

@ __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-a1311 [probability distribution for the relative velocity of colliding particles]; Montakhab et al PhyA-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].

@ __From particles to fluid__: Park a1310-proc [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.

> __Online resources__: see Wikipedia page.

main page – abbreviations – journals – comments – other
sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 24
may
2016