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If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

Molecules of a gas at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down. Signs of this progressively occur when $V \gg Nb$ is not true any more and the former is approaching the latter.

Additionally, at such a density, intemolecular interactions are not negligible.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure or density nor states near the critical state, as the model breaks physically much sooner than mathematically.

If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

Molecules of a gas ( or rather a fluid ) at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down. Signs of this progressively occur when $V \gg Nb$ is not true any more and the former is approaching the latter.

Additionally, at such a density, intermolecular interactions are not negligible.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure/density nor states near the critical state, as the model breaks physically much sooner than mathematically.

If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

Molecules of a gas at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down. Sign of this progressively occur when $V \gg Nb$ is not true any more and the former is approaching the latter.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure or density nor states near the critical state, as the model breaks physically much sooner than mathematically.

If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

Molecules of a gas at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down. Signs of this progressively occur when $V \gg Nb$ is not true any more and the former is approaching the latter.

Additionally, at such a density, intemolecular interactions are not negligible.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure or density nor states near the critical state, as the model breaks physically much sooner than mathematically.

If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

$$b'_2 = 4\pi d^3/3 = 8\times (4\pi r^3/3)$$ $$b' = b'_2/2 \quad \rightarrow \quad b'=4\times (4\pi r^3/3),$$ $$b = N_A b' .$$

Molecules at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure or states near the critical state, as it breaks physically much sooner than mathematically.

If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

Molecules of a gas at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down. Sign of this progressively occur when $V \gg Nb$ is not true any more and the former is approaching the latter.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. This model is not intended for high pressure or density nor states near the critical state, as the model breaks physically much sooner than mathematically.