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I am quoting Chaikin, Lubensky, Principles of Condensed Matter Physics, p. 4.

Now suppose we have a closed container of water vapor at a density of 0.322 g/cc at room temperature. As the temperature is lowered...

It then proceeds to describe condensation, and says it is a continuous process because the system is at the critical density. However, it is definitely not at the critical temperature. How can it condense at a temperature lower than that? Is it a mistake?

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If this state is prepared at room temperature (somehow), condensation will happen immediately, and the temperature will rise so much that the water will be boiling hot (some water will stay in the vapor phase), although it will still be less hot than the critical point.

Yes, it is a mistake. You can only prepare/maintain water vapor (or more properly, a single water phase) at that density at the critical point. Any cooler and it will condense into two phases. It's possible to forestal condensation somewhat by eliminating condensation nuclei, but this won't work near the critical point where phase changes are smoother.

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