Ideal Gas| 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 = 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];
Taskov a2007 [Boltzmann distribution];
> 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)-a1108 [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.
> Online resources:
see Wikipedia page.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 28 aug 2020