1. Cold water generally sinks
2. The earth is pretty thick, so the bottom of the ocean is just a *tiny* fraction of the distance towards the core
3. A lot of the heat the surface of the earth gains is directly from the sun, not the core, so going down insulates you from that. If the sun were to just disappear, the surface would freeze over.
The deepest parts of the ocean *combined* with the thinnest parts of the earth’s crust are, surprising to some, *incredibly* hot. Known as [hydrothermal vents](https://en.wikipedia.org/wiki/Hydrothermal_vent), these places are where scientists study extremophile (things that can live in extreme conditions) lifeforms because of the massive pressure and temperature.
But generally, when talking about how far from the earth’s core there’s no particular difference between land and ocean. So the reason the seabed isn’t affected by the core more than the beach is because there’s still a *huge* amount of rock between it and the outer parts of magma.
The ocean is about 11km at its deepest. The Earth has a radius of ~6371km. The deepest part of the ocean is *much* closer to being part of the surface than it is to being part of the core.
In addition, the water in the ocean doesn’t stay put. If you have a pocket of heated water at the bottom of the ocean, it will rise up towards the top (hot things rise), and new cool water will sink down.
The Earth’s crust is like a big blanket that keeps the heat inside. It’s not a very good conductor at that thickness, which is why the ground doesn’t feel hot underfoot.
The oceans are on top of the crust also. A bit less of it, but still quite a lot of it in most places.
There are exceptions, points where the crust is thin, sometimes to the point of having underwater volcanoes. But we get that on land too. Iceland is close enough to our planet’s rich, creamy center that they use a lot of geothermal power.
The earth’s core is indeed hot. However, the earth is also *really* big and rock is a really good insulator. So most of the heat that finds it’s way to the surface is not radiated through the rocks themselves, but rather the gaps in the rocks via tectonic plates. Things like volcanoes are the result of this.
There *are* places at the bottom of the ocean that are hot as a result of this, basically underwater volcanoes called “hydrothermal vents.”
But the vast, vast majority of the energy we get on the surface comes from the sun. It heats things up far more than the center of the earth. The bottom of the ocean is cold because there is no sunlight there.
There’s still a lot of crust between the ocean floor and the mantle of the Earth.
There are volcanic vents underneath the ocean floor, but that newly heated water rises up rather than staying on the ocean floor.
The cold ocean floor is at about 4°C because that is the temperature at which water is densest, so slightly colder water will rise, and slightly warmer water will rise.
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