an equation of state (for gases) mathematical model used describe or predict state properties of gas. @ present, there no single equation of state accurately predicts properties of gases under conditions. therefore, number of more accurate equations of state have been developed gases in specific temperature , pressure ranges. gas models discussed perfect gas , ideal gas , real gas . each of these models has own set of assumptions facilitate analysis of given thermodynamic system. each successive model expands temperature range of coverage applies.
ideal , perfect gas models
the equation of state ideal or perfect gas ideal gas law , reads
p
v
=
n
r
t
,
{\displaystyle pv=nrt,}
where p pressure, v volume, n amount of gas (in mol units), r universal gas constant, 8.314 j/(mol k), , t temperature. written way, called chemist s version , since emphasizes number of molecules n. can written as
p
=
ρ
r
s
t
,
{\displaystyle p=\rho r_{s}t,}
where
r
s
{\displaystyle r_{s}}
specific gas constant particular gas, in units j/(kg k), , ρ = m/v density. notation gas dynamicist s version, more practical in modeling of gas flows involving acceleration without chemical reactions.
the ideal gas law not make assumption specific heat of gas. in general case, specific heat function of both temperature , pressure. if pressure-dependence neglected (and possibly temperature-dependence well) in particular application, gas said perfect gas, although exact assumptions may vary depending on author and/or field of science.
for ideal gas, ideal gas law applies without restrictions on specific heat. ideal gas simplified real gas assumption compressibility factor z set 1 meaning pneumatic ratio remains constant. compressibility factor of 1 requires 4 state variables follow ideal gas law.
this approximation more suitable applications in engineering although simpler models can used produce ball-park range real solution should lie. example ideal gas approximation suitable inside combustion chamber of jet engine. may useful keep elementary reactions , chemical dissociations calculating emissions.
real gas
21 april 1990 eruption of mount redoubt, alaska, illustrating real gases not in thermodynamic equilibrium.
each 1 of assumptions listed below adds complexity of problem s solution. density of gas increases rising pressure, intermolecular forces play more substantial role in gas behavior results in ideal gas law no longer providing reasonable results. @ upper end of engine temperature ranges (e.g. combustor sections – 1300 k), complex fuel particles absorb internal energy means of rotations , vibrations cause specific heats vary of diatomic molecules , noble gases. @ more double temperature, electronic excitation , dissociation of gas particles begins occur causing pressure adjust greater number of particles (transition gas plasma). finally, of thermodynamic processes presumed describe uniform gases velocities varied according fixed distribution. using non-equilibrium situation implies flow field must characterized in manner enable solution. 1 of first attempts expand boundaries of ideal gas law include coverage different thermodynamic processes adjusting equation read pv = constant , varying n through different values such specific heat ratio, γ.
real gas effects include adjustments made account greater range of gas behavior:
compressibility effects (z allowed vary 1.0)
variable heat capacity (specific heats vary temperature)
van der waals forces (related compressibility, can substitute other equations of state)
non-equilibrium thermodynamic effects
issues molecular dissociation , elementary reactions variable composition.
for applications, such detailed analysis excessive. examples real gas effects have significant impact on space shuttle re-entry extremely high temperatures , pressures present or gases produced during geological events in image of 1990 eruption of mount redoubt.
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