Polytropic index

Polytropic index The equation of state for a polytropic fluid is:

Equation 3: Equation of state for a polytropic fluid

Where:

• P is the pressure [Pa]

• K is a constant [null]

• ρ is the fluid density [kg/m3]

• Γ is a quantity called the polytropic index [null].

Note

Γ does not need to be the adiabatic index (or ratio of specific heats), and in fact often it is not. This is sometimes a cause for confusion.

• In the case of an isentropic ideal gas, the polytropic index Γ is equal to the adiabatic index γ, which is the ratio of specific heats: Γ = γ = Cp / Cv (1.4 for air).

• In the case of an isothermal ideal gas, the polytropic index Γ differs from the adiabatic index γ, and in particular it is equal to one: Γ = 1

After differentiation of Equation 3:

K is replaced by Equation 4:

Which can be written:

The bulk modulus of a polytropic fluid is:

Equation 4: Bulk modulus for a polytropic fluid