What is the Equation of State for an Ideal Gas?

AI Thread Summary
The discussion focuses on the equation of state for an ideal gas, specifically the relationship p = ρc_s^2, where p is pressure, ρ is density, and c_s is the speed of sound. It contrasts this with the ideal gas law pV = NkT, leading to p = ρkT, raising the question of whether c_s^2 equals k_BT. Participants clarify that the density (ρ) in the two equations refers to different quantities: mass density in the first equation and number density in the second. Additionally, they note that the equations lack critical parameters, such as the adiabatic index (γ) and molar mass. Understanding these distinctions is crucial for correctly applying the equations of state for ideal gases.
Niles
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Homework Statement


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?
 
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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.
 
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