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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,