Ideal Gas: Non-Uniform Conditions Explained

[mikeph]

Hi,

If I have a container with fixed volume, and fill it entirely with a known quantity of CO2, and then heat the edges, I should be right in saying I have under my control the temperature, volume and molecule number, and the pressure is fixed by the ideal gas equation (assuming the assumptions of this model are valid).But what if these values are non-uniform? Does the restriction still apply? Can I specify temperature, pressure, volume and molecule density fields, and is there some generalised for of this ideal gas equation?

Or can I say that in theory, the restriction has been lifted, and does not apply for a container with a gas which is not in thermal equilibrium.

Thanks,

 

[Dadface]

Hello Mikey .the volume of the gas will be the volume of the container and if the container is tightly sealed the number of molecules is fixed.If there is a temperature variation throughout the container there will be a corresponding pressure and density variation.The ideal gas equation is followed more closely when the gas reaches thermal equilibrium but it should be remembered that the equation is an approximation only and becomes more in error as the pressures rises and if the temperature approaches values where the collisions become exciting or ionising.

 

[mikeph]

Ok- thanks for your reply. Can I ask as a further question, if the ideal gas equation breaks down under those conditions, does a different equation (whether we know it or not) "take over"? Or am I free to vary the fields in whatever way I like, as long as I don't forget that I no longer have thermal equilibrium?

 

[Dadface]

As far as I am aware there is not an equation which applies closely under all conditions but there are equations that are better approximations.Van der Waals equation is an improvement on the ideal gas equation particularly for when gases get close to liquification.

 

[PJC01]

I would like to clarify that the ideal gas equation assumes certain conditions, such as uniform temperature and pressure, to be valid. In a non-uniform system, these assumptions may not hold true and the ideal gas equation may not accurately predict the behavior of the gas.

In a non-uniform system, the temperature, pressure, volume, and molecule density may vary throughout the container. This can be due to external factors such as heating or cooling at different parts of the container. In this case, the ideal gas equation cannot be directly applied and a more complex equation, such as the Van der Waals equation, may be necessary to accurately describe the behavior of the gas.

Furthermore, it is important to note that the ideal gas equation is based on the assumption that the gas is in thermal equilibrium. If the gas is not in thermal equilibrium, the ideal gas equation will not accurately predict its behavior. In this case, the restriction of the ideal gas equation does not apply and a different approach may be needed to understand the system.

In summary, the ideal gas equation is a simplified model that assumes certain conditions to be valid. In non-uniform systems or systems that are not in thermal equilibrium, this equation may not be applicable and a more complex approach may be necessary. As scientists, it is important to carefully consider the assumptions and limitations of any model before applying it to real-world scenarios.