# Perfect gas

In physics, a perfect gas is a theoretical gas model that differs from real gases in ways that makes certain calculations easier to handle. Its behaviour is also simplified compared to an ideal gas (which is itself a theoretical gas model). In perfect gas models, intermolecular forces are neglected. This means that one can neglect many complications that may arise from the Van der Waals forces.

## Perfect gas nomenclature

The terms perfect gas and ideal gas are sometimes used interchangeably, depending on the particular field of physics and engineering. Sometimes, other distinctions are made, such as between thermally perfect gas and calorically perfect gas, or between imperfect, semi-perfect, perfect, and ideal gases. Two of the common sets of nomenclatures are summarized in the following table.

Nomenclature 1

Nomenclature 2

Heat capacity at
constant V, ${\displaystyle C_{V}}$ ,
or constant P, ${\displaystyle C_{P}}$ .
Ideal-gas law
${\displaystyle pV=nRT}$  and ${\displaystyle C_{p}-C_{V}=nR}$
Calorically perfect Perfect Constant Yes
Thermally perfect Semi-perfect T-dependent Yes
N/A Ideal May or may not be T -dependent Yes
N/A Imperfect T and p-dependent No

### Thermally and calorically perfect gas

Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition.

A thermally perfect gas

• is in thermodynamic equilibrium
• is not chemically reacting
• has internal energy e, enthalpy h, and heat capacities CV,CP that are functions of temperature only and not of pressure, i.e., ${\displaystyle e=e(T)}$ , ${\displaystyle h=h(T)}$ , ${\displaystyle de=C_{v}(T)dT}$ , ${\displaystyle dh=C_{p}(T)dT}$ .

It can be proved that an ideal gas (i.e. satisfying the ideal gas equation of state) is thermally perfect.[1]

This type of approximation is useful for modeling, for example, an axial compressor where temperature fluctuations are usually not large enough to cause any significant deviations from the thermally perfect gas model. Heat capacity is still allowed to vary, though only with temperature, and molecules are not permitted to dissociate. The latter implies temperature limited to 2500 K.[2]

Even more restricted is the calorically perfect gas for which, in addition, the heat capacity is assumed to be constant: ${\displaystyle e=C_{v}T}$  and ${\displaystyle h=C_{p}T}$ .

Although this may be the most restrictive model from a temperature perspective, it is accurate enough to make reasonable predictions within the limits specified. A comparison of calculations for one compression stage of an axial compressor (one with variable Cp, and one with constant Cp) produces a deviation small enough to support this approach. As it turns out, other factors come into play and dominate during this compression cycle. These other effects would have a greater impact on the final calculated result than whether or not Cp was held constant. (examples of these real gas effects include compressor tip-clearance, separation, and boundary layer/frictional losses, etc.)