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In a hypothetical universe with a different Universal gravitational constant $G$, will the nature of ideal gas change by any means?

i.e, will $PV = nRT$ be no longer applicable in that case?

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There is no direct link between the Boltzmann constant $k$ (from which the gas constant $R$ is derived) and the gravitational constant $G$ such that causing one to have a different value would necessitate a change in the value of the other. As such, there is no reason to expect that the ideal gas law would not have the same form.

However, it is possible that the ideal gas law could end up being less useful. If $G$ were changed such to increase the strength of the gravitational force by many orders of magnitude, one could imagine it becoming increasingly less valid to ignore the gravitational forces between particles in a gas. One could end up with a situation where it is never practical to model a gas as having ideal behavior, because the strength of the gravitational interaction is too great (effectively breaking one of the postulates of the kinetic molecular theory of gases, that there are no inter-particle forces).

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