What is the Equation of State for an Ideal Gas?

[Niles]

Homework Statement

Hi

Often I bump into the relation $p=\rho c_s^2$, where p is the pressure, rho the density and c_s 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 $c_s^2=k_BT$?

 

[Niles]

Wiki explains it well...

https://en.wikipedia.org/wiki/Ideal_gas#Speed_of_sound

 

[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.