Image 1 Caption: The pressure of the
classical ideal gas
(see also Wikipedia: Ideal gas law)
and
ideal quantum gases
(i.e., the Fermi gas and
the Bose gas)
as a function
of temperature
(i.e., Kelvin temperature)
for a fixed particle density.
The ideal gases
are for the case of non-relativistic limit
(i.e., they are consist of massive particles
moving at velocities
asymptotically close to
zero relative to the
vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns)
in 3-dimensional Euclidean space.
Features:
- The
classical ideal gas
pressure P = (Nk/V)T,
where N is particle number,
V is volume,
the
Boltzmann contant
k = 1.380649*10**(-23) J/K = (8.617333262 ... )*10**(-5) eV/K (exact) ≅ 10**(-4) eV/K
≅ 10**(-10) MeV/K,
and
the slope is of Nk/V
when P is plotted as function
of temperature.
- As temperature increases,
the Fermi gas and
the Bose gas both
approach the
classical ideal gas
asymptotically in
slope though with
a vertical offset???
that usually immeasurably small for
room temperature and above???.
UNDER CONSTRUCTION BELOW
- The Fermi gas
is always higher in pressure
than the
classical ideal gas
due the
Bose attraction effect
(i.e., the exchange interaction).
The Bose gas
is always lower in Pressure
due to boson attraction.
- Even at 0 temperature, the Fermi gas maintains a nonzero pressure, known as degeneracy pressure or Fermi pressure.
- The
★
marker indicates the upper temperature of Bose condensation.
Moving below this temperature, the pressure drops rapidly as more and
more particles are absorbed into the condensed phase.
- The figure has been scaled in a way that the particle degeneracy factor, density, mass, etc. are all factored out and irrelevant."
(Somewhat edited.)
The ideal gas law
is the simplest of all laws relating
thermodynamic variables:
PV=nRT ,
where for a system of
ideal gas
P is pressure,
V is volume,
n is the number of moles
R is the universal gas constant
and
T is temperature
on the Kelvin temperature scale.
If temperature is fixed, then
pressure is decreases with
volume as the plot shows.
Isotherms are curves of constant
temperature.
Real gases approach ideal gas in the limit of low
density.
The ideal gas law
is often an excellent approximation to real gases.
Images:
- Credit/Permission: User:Nanite,
2020 /
Public domain.
Image link: Wikimedia Commons:
File:Quantum ideal gas pressure 3d.svg.
- Credit/Permission: ©
USER:LVD,
2014 /
CC BY-SA 3.0.
Image link: Wikimedia Commons:
File:Emissive Power.png.
Local file: local link: gas_classical_quantum.html.
File: Thermodynamics file:
gas_classical_quantum.html.