What is the Equation of State for an Ideal Gas?

In summary, the conversation discusses the equation of state for an ideal isothermal gas, which relates pressure, density, and speed of sound. The question is whether c_s^2 is equal to k_BT, and the response clarifies that the ρ in the two equations represents different quantities. The first equation uses mass density, while the second uses number density, and the molar mass is missing.
  • #1
Niles
1,866
0

Homework Statement


Hi

Often I bump into the relation [itex]p=\rho c_s^2[/itex], 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 [itex]pV=NkT[/itex], which becomes [itex]p=\rho kT[/itex], but does this mean that [itex]c_s^2=k_BT[/itex]?
 
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  • #3
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.
 

Related to What is the Equation of State for an Ideal Gas?

What is the Equation of State for an ideal gas?

The Equation of State for an ideal gas is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

What is the purpose of the Equation of State?

The purpose of the Equation of State is to describe the relationship between the physical properties of an ideal gas, such as pressure, volume, and temperature. It allows scientists to make predictions and calculations related to the behavior of ideal gases.

How does the Equation of State differ from real gases?

The Equation of State assumes that the gas particles have zero volume and do not interact with each other, which is not the case for real gases. Real gases also experience deviations from ideal behavior at high pressures and low temperatures.

Can the Equation of State be used for all gases?

No, the Equation of State is only applicable to ideal gases, which are theoretical gases that follow certain assumptions. Real gases, such as those found in nature, do not always behave according to the Equation of State.

What are the units of the gas constant, R, in the Equation of State?

The units of the gas constant, R, in the Equation of State depend on the units used for pressure, volume, temperature, and the number of moles. Common units include joules per mole-kelvin (J/mol-K) and liters-atmospheres per mole-kelvin (L-atm/mol-K).

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