The basic energy equation of the airbag can be written as:
(1)
Where,
-
- Internal energy
-
- Pressure
-
- Airbag volume
-
- Incoming enthalpy
-
- Outgoing enthalpy
When the adiabatic condition is applied and assuming a perfect gas:
(2)
Where,
is the gas constant. For air,
= 1.4.
The two equations above allow the current airbag volume to be determined. The energy and
pressure can then be found. To know the current airbag volume, derive energy and thus
pressure.
Considering a gas such that the constant pressure and the constant volume heat capacities
per mass unit (respectively,
and
) vary in temperature
.
The following temperature dependency of the constant pressure heat capacity is
assumed:
(3)
Where,
,
and
are the constants depending to characteristics of the gas.
The
and
satisfy the Mayer relation:
(4)
With
is the universal gas constant depending to the unit system
(
):
(5)
Where,
-
- Specific energy
-
- Specific enthalpy per mass unit of the gas at temperature
You can then obtain:
(6)
and
(7)
Where, the lower index
refers to the reference temperature
.
Now, assuming an ideal mixture of gas:
(8)
with
the total number of moles:
(9)
Where,
-
- Mass of gas
-
- Molar weight of gas
It follows:
(10)
With
.