# /EOS/IDEAL-GAS or /EOS/IDEAL-GAS-VE

Block Format Keyword Describes the ideal gas equation of state $P=\left(\gamma -1\right)\left(1+\mu \right)E$ .

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/IDEAL-GAS/mat_ID/unit_ID or /EOS/IDEAL-GAS-VE/mat_ID/unit_ID
eos_title
$\gamma$ P0 Psh T0 ${\rho }_{0}$

## Definitions

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit Identifier.

(Integer, maximum 10 digits)

eos_title EOS title.

(Character, maximum 100 characters)

$\gamma$ Heat capacity ratio $\gamma =\frac{{C}_{p}}{{C}_{v}}$ .

(Real)

P0 Initial pressure.

(Real)

$\left[\text{Pa}\right]$
Psh Pressure shift.

(Real)

$\left[\text{Pa}\right]$
T0 Initial temperature.

(Real)

$\left[\text{K}\right]$
${\rho }_{0}$ Reference density.

Default = material density (Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$

## Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDRO/7/1
AIR
#              RHO_I               RHO_0
1.22e-6                   0
#                Knu                Pmin
1.5E-2                   0
/EOS/IDEAL-GAS/7/1
EoS for Air at atmospheric pressure
#              GAMMA                  P0                 PSH                  T0                RHO0
1.4                0.10                   0               300.0             1.22E-6
/ALE/MAT/7

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

1. Ideal-gas thermal EOS is:(1)
$Pv=RT$
Where,
$v$
Specific volume
$R$
Specific gas constant
$T$
Temperature

Previous form of $P=\mathrm{P}\left(v,T\right)$ can be written in the $P=\mathrm{P}\left(\mu ,E\right)$ form.

Where,(2)
$µ=\frac{\rho }{{\rho }_{0}}-1$
(3)
$E=\frac{{E}_{int}}{{V}_{0}}$
(4)
$\mathrm{P}\left(\mu ,E\right)=\left(\gamma -1\right)\left(1+\mu \right)E$
with (5)
$\gamma =\frac{{C}_{p}}{{C}_{v}}$

Where, ${C}_{p}$ and ${C}_{v}$ are constant parameters.

Consequently, the same equation of state can be built using /EOS/IDEAL-GAS-VT (Volume Temperature) defining the special case of a constant function:(6)
${C}_{p}\left(T\right)=\frac{\gamma r}{\gamma -1}$
2. Some characteristics of this equation of state:
Ideal Gas
$\mathrm{P}\left(v,T\right)$
$Pv=RT$
$\mathrm{P}\left(\mu ,E\right)$
$\left(\gamma -1\right)\left(1+µ\right)E$
Sounce speed $c$
$c=\sqrt{\frac{\gamma P}{\rho }}$
${E}_{0}=\mathrm{E}\left(0\right)$
$\frac{{P}_{0}}{\gamma -1}$
3. For this equation of state, $\gamma$ , ${C}_{p}$ and ${C}_{v}$ are constant parameters.

In other cases, /EOS/IDEAL-GAS-VT (Volume Temperature) must be used.

The heat capacity ${C}_{v}$ is computed from the initial data:(7)
${C}_{v}=\frac{{E}_{0}}{{\rho }_{0}{T}_{0}}$
This parameter enables the calculation of the gas temperature since (8)
$\text{Δ}e={C}_{v}\text{Δ}T$
Where,
$e=\frac{{E}_{int}}{m}$
Specific energy by mass
4. Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws:
• /MAT/LAW3 (HYDPLA)
• /MAT/LAW4 (HYD_JCOOK)
• /MAT/LAW6 (HYDRO or HYD_VISC)
• /MAT/LAW10 (DPRAG1)
• /MAT/LAW12 (3D_COMP)
• /MAT/LAW49 (STEINB)
• /MAT/LAW102 (DPRAG2)
• /MAT/LAW103 (HENSEL-SPITTEL)