You are correct that the tank itself does not change. It doesn’t get noticeably compressed, nor have a different volume of air inside it, regardless of where you’re diving.
What does change is the pressure of the surrounding ocean, at the depth you choose to dive to. And the way the regulator works is that it delivers air to your face at (approximately) the same pressure as submergence pressure for your depth. And density is proportional to pressure, for all intents and purposes here.
Ergo, if you dive twice as deep, when you pull a lungful of air, it’s twice as high in pressure, twice as dense, and depletes your tank twice as fast.
A standard tank is pressurized to *approximately* 20 atmospheres. At the surface (aka one standard atmosphere of pressure), if it were the size of your lungs, you could inhale 20 times. But for every ten meters (33 feet) below the surface you dive, you add another atmosphere of pressure. So ten meters down (2 atmospheres), you could only take 10 lungfuls. Thirty meters down (4 atmospheres), only 5 lungfuls.
Make sense?
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