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It's said that at boiling point the pressure of the liquid is equal to the pressure of its vapor. That way, bubbles can form in the liquid phase. However, unless I'm mistaken, while the pressure of a gas is (mostly) uniform, the pressure of a liquid changes appreciably with depth. How can one talk about the pressure of the liquid being equal to the pressure of its vapor when the pressure of the liquid doesn't take on a single fixed value?

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How can one talk about the pressure of the liquid being equal to the pressure of its vapor when the pressure of the liquid doesn't take on a single fixed value?

If is an approximation, which is reasonable for many practical situations.

The atmospheric pressure is about $14.7$psi. The pressure at the bottom of a kettle, filled with $6$" of water, is going to be about $0.21$psi or $1.4$% greater than the pressure at the top.

On the other hand, the temperature of the water at the bottom of the kettle will be slightly higher than the temperature at the top.

These two factors are not significant on their own and also, at least partially, cancel each other, making the approximation reasonable.

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