# Equation of State, ideal gas

1. Dec 11, 2013

### Niles

1. The problem statement, all variables and given/known data
Hi

Often I bump into the relation $p=\rho c_s^2$, where p is the pressure, rho the density and cs the speed of sound in the ideal gas. It is apparently called the equation of state for an ideal isothermal gas.

I know about $pV=NkT$, which becomes $p=\rho kT$, but does this mean that $c_s^2=k_BT$?

2. Dec 11, 2013

### Niles

3. Dec 11, 2013

### nasu

The ρ in your two equations is not the same quantity.
In the first equation it may be mass density (but it looks like you are missing a γ), in the second is number density. But again, the molar mass is missing.