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It seems as if the 'lowest energy' state for the Earth is to not have any mountains and that given enough time, the oceans would erode all land. Essentially it's an argument like entropy. And I mean in the far future, once tectonic activity has ceased.

Is this the case, and if so how long might it take? If it is not the case, why not?

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    $\begingroup$ Related question. I also remember seeing somewhere that the sun will expand and evaporate all water before the heat that drives tectonic activity dissipates. In that case, the situation that you describe is not relevant since it will never happen. $\endgroup$ – Gimelist May 17 '15 at 0:16
  • $\begingroup$ It's not just a matter of erosion, but also re-balancing the uneven weight distribution of rock below the surface - which is why continents exist, the thicker continental crust floats on top of the heavier oceanic crust. The weight evens out. I don't know if it would ever balance out, certainly it would take hugely long time if it did. Granite is harder and lighter so it's good continental material. I don't think erosion would be sufficient to re-distribute the cooled mantle. mlms.loganschools.org/~mlowe/lowehome/DictionaryPictures/… $\endgroup$ – userLTK May 17 '15 at 22:40
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Continents are made up of different, lighter materials than oceans and both continents and oceans "float" on the mantle. Continents are also thicker than oceans so erosion does not only need to take care of the ~5 km which is above sea level but it should also erode away the continental root (which can be several 10's of kilometers until the continental crust is actually slightly thinner than oceanic crusts are today.

However tectonics is not the only source of topography which can easily be seen if we look at Mars where a hotspot has created an enormous mountain on a tectonically inactive planet.

So if you want to end up with a topography free planet you need to shut down all possible mantle plumes too.

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I would argue that plate tectonics is the major reason their is elevation on the surface of the earth. But let me be clear that the oceans are not the major eroders of land - running water on the land is (from rain and snow). You are correct to assume that as the earth cools, plate tectonics will subside and the rate of erosion will overcome the rate of uplift due to plate tectonics.

As for making estimates about how long it will take to do this, I would not wish to hazard a guess. Earth has been going strong for billions of years and it probably has a few billion more years left.

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    $\begingroup$ Nearly all the water that falls as some sort of precipitation originates as evaporation from the oceans. Without the oceans, there would be very little, if any, snow and rain. Erosion is enhanced by the dissolution of CO2 with H2O forming carbonic acid (H2C03). $\endgroup$ – BillDOe Jul 4 '15 at 5:15
  • $\begingroup$ I think you have missed my point. The question asks will the "ocean" erode all land. Oceans can only erode through wave action along the coasts. The evaporation of water has nothing to do with erosion on land. Precipitation and subsequent water runoff on land is the major reason the land erodes. This includes carrying sediment in suspension and dissolution in chemical weathering through water runoff. I suppose there is semantics involved here but most would not relate erosion by runoff directly to the ocean. $\endgroup$ – see you Jul 4 '15 at 21:29
  • $\begingroup$ This reminds me of when I read a children's book that mentioned river meanders being cut off and wondered if all the rivers in the world will become straight in enough millions of years. There's actually a river in North Vietnam that's just like what I imagined. It's so ludicrously straight. Check it out. $\endgroup$ – ItsMyPostAndIllWriteIfIWnt2Wri Jul 4 '15 at 22:49
  • $\begingroup$ @MarcDefant, No, I don't believe I missed your point. But I think making your statement, "...oceans are not the major eroders of land.." without also mentioning their rather important contribution to the source of precipitation, could cause uninformed readers to draw the wrong conclusion. $\endgroup$ – BillDOe Jul 5 '15 at 1:39

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