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fbs7

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Sorry if the question sounds idiotic, but this morning I was watching a program on Jupiter and then I couldn't wrap my head around this. Say a slowly changing gas planet that is cold enough to have very little convection, and that by assumption does not lose its mass to space. Then draw some radius around a fixed mass M1 around it center (say 1 trillion tons); that will have a volume V which is very slowly changing. Then I know that pV = nRT. Now consider the rest of the gas outside that volume; that that's M2 = 1 quatrillion tons.

Now it gets very complicated for me, and here's the thinking. The planet will always lose heat through radiation; so let 1 trillion years pass. Whatever T it started with, in the long term T must end up being very small (for the reason that a higher T will lead to more heat loss due to radiation).

As R is constant and under my definition n is constant too, then pV is going to be very small. But there is a huge weight of the fixed mass M2 pushing down through gravity on my volume. So p cannot be very small. Therefore, V must be very small, and given that the radius of the volume is very small and the mass M2 is fixed, then p must be large.

As T is very small and p is large, then the core of a large enough gas planet must at some point freeze or liquefy. Therefore, above some size it should be impossible for a gas planet to remain gaseous forever. But that sounds preposterous, because it means that in the long term there would be no more large, completely gaseous planets, for thermodynamics alone...

I appreciate any insight where may train of thought has gone off tracks on that.