# Perfect gas

By definition, a **perfect gas** is one in which intermolecular forces are neglected. So, along with the assumptions of an ideal gas, the following assumptions are added:

- Neglected intermolecular forces

By neglecting these forces, the equation of state for a perfect gas can be simply derived from kinetic theory or statistical mechanics.

This type of assumption is useful for making calculations very simple and easy to do. With this assumption we can apply the Ideal gas law without restriction and neglect many complications that may arise from the Van der Waals forces.

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. For the sake of clarity, these simplifications are defined separately.

#### Thermally perfect

- The gas is in thermodynamic equilibrium
- Not chemically reacting
- Internal energy, enthalpy, and specific heat are functions of temperature
*only*.

<math>e = e(T)</math> <math>h = h(T)</math> <math>de = C_vdT</math> <math>dh = C_pdT</math>

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.

#### Calorically perfect

Finally, the most restricted gas model is one where all the above assumptions apply and we also apply:

- Constant Specific Heats

<math>e = C_vT</math> <math>h = C_pT</math>

Although this may be the most restrictive model, it still may be accurate enough to make reasonable calculations. For example, if a model of one compression stage of the axial compressor mentioned in the previous example was made (one with variable <math>C_p</math>, and one with constant <math>C_p</math>) to compare the two simplifications, the deviation may be found at a small enough order of magnitude that other factors that come into play in this compression would have a greater impact on the final result than whether or not <math>C_p</math> was held constant (compressor tip-clearance, boundary layer/frictional losses, manufacturing impurities, etc).