/EOS/IDEALGAS or /EOS/IDEALGASVE
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/IDEALGAS/mat_ID/unit_ID or /EOS/IDEALGASVE/mat_ID/unit_ID  
eos_title  
$\gamma $  P_{0}  P_{sh}  T_{0} 
Definition
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) 

P_{0}  Initial
pressure. (Real) 
$\left[\text{Pa}\right]$ 
P_{sh}  Pressure
shift. (Real) 
$\left[\text{Pa}\right]$ 
T_{0}  Initial
temperature. (Real) 
$\left[\text{K}\right]$ 
Example (Air)
#12345678910
/UNIT/1
unit for mat
g mm ms
#12345678910
/MAT/HYDRO/7/1
AIR
# RHO_I RHO_0
1.22e6 0
# Knu Pmin
1.5E2 0
/EOS/IDEALGAS/7/1
EoS for Air at atmospheric pressure
# GAMMA P0 PSH T0
1.4 0.10 0 300.0
#12345678910
#enddata
Comments
 Idealgas thermal EOS is:$$Pv=RT$$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,
$$\mu =\frac{\rho}{{\rho}_{0}}1$$$$E=\frac{{E}_{int}}{{V}_{0}}$$$$\mathrm{P}\left(\mu ,E\right)=\left(\gamma 1\right)\left(1+\mu \right)E$$with
$$\gamma =\frac{{C}_{p}}{{C}_{v}}$$Where, ${C}_{p}$ and ${C}_{v}$ are constant parameters.
Consequently, the same equation of state can be built using /EOS/IDEALGASVT (Volume Temperature) defining the special case of a constant function:
$${C}_{p}(T)=\frac{\gamma r}{\gamma 1}$$  Some characteristics of this equation of state:
 Ideal Gas
 $\mathrm{P}\left(v,T\right)$
 $Pv=RT$
 $\mathrm{P}\left(\mu ,E\right)$
 $\left(\gamma 1\right)\left(1+\mu \right)E$
 Sounce speed $c$
 $c=\sqrt{\frac{\gamma P}{\rho}}$
 ${E}_{0}=\mathrm{E}\left(0\right)$
 $\frac{{P}_{0}}{\gamma 1}$
 For this equation of state,
$\gamma $
,
${C}_{p}$
and
${C}_{v}$
are constant parameters.
In other cases, /EOS/IDEALGASVT (Volume Temperature) must be used.
The heat capacity ${C}_{v}$ is computed from the initial data:
$${C}_{v}=\frac{{E}_{0}}{{\rho}_{0}{T}_{0}}$$This parameter enables the calculation of the gas temperature since
$$\text{\Delta}e={C}_{v}\text{\Delta}T$$Where, $e=\frac{{E}_{int}}{m}$
 Specific energy by mass
 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 (HENSELSPITTEL)
 /MAT/LAW109