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I know there's no such thing like a perpetual motion machine but I missing something in my reasoning.

Assume there's a gas giant planet where the immense pressure of the core causes it to heat and create a convection current of its gases. If there's no atmosphere gases losses to space that means we have a perpetual motion machine?

Is work being done to move all that gas (or not?). The energy to compress gases is coming from gravity but the total energy of the system remains the same?

Now assume some heat is being dissipated in space, that means the system is losing energy.

Can this possible go forever or will the planet reach a equilibrium where all gases and heat will be distributed in a way the convection cease? Or even can possible it loss energy enough to loss mass (and cease the heavy gravity effects)?

Bonus: Consider we got two kinds of life forms: one breathing XY and exhaling X+Y and another doing the inverse and using the heat from some (goldilock zone) atmosphere layer (some kind of XY + Energy => X + Y, X + Y + Energy => XY cycle). Will life perse consume the energy and cooldown the planet (eventually in billions years)?

Edit

There's a bit of confusing about this question due to my difficult in express my doubts. Sure it's impossible to achieve total "isolation". I'm just pondering about an hypothetical scenario. I see now the forever convection is just equivalent to a frictionless object spinning foerever in the void.

Any energy removed from the system will "slow down" it.

The true question is: What if the energy of this isolated system is used to fuel life and this life is inside the system and is part of the system? It still means energy is lost?

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    $\begingroup$ Life needs an energy source to breath. Trees can turn Oxygen into CO2, but only under sunlight. Mammals and others can turn O2 back into CO2, but only if they consume food. There's no balance of life without an energy source to keep it going. In theory a system that radiated zero heat could perhaps enter a type of perpetual motion, but it's not possible for a system to radiate zero heat. But on the scale of gas giants, the internal heat lasts a crazy-long time, perhaps trillions of years. $\endgroup$ – userLTK Oct 8 '16 at 8:31
  • $\begingroup$ You can improve your question by proofreading and spellchecking. $\endgroup$ – James K Oct 8 '16 at 15:28
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It is not a perpetual motion machine. Energy is being converted from gravitational potential energy in the gas, to motion, and eventually to heat which is lost as heat radiation. As this happens the planet shrinks and cools. This takes a long time, a lot longer than the few billion years of the the solar system. But ultimately convection will stop.

All life forms depend on capturing energy. All life processes increase entropy. Life can have a significant effect on a planet, but not by "consuming energy" rather by changing the composition of the atmosphere.

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You don't have a perpetual motion machine because you are losing energy to space in the form of heat, light, solar wind, etc. Even if you want to restrict it to the case where you are not expelling gas, you are always going to lose energy to heat radiation. The Sun loses mass all the time. It will keep doing this until it cannot generate enough internal heat to counterbalance its tendency to contract due to gravity. There is a whole progression where it burns its hydrogen, then its helium, etc. Finally, when it runs out of stuff to burn, it collapses and "blows up" in a nova or supernova, or it could just fizzle out. Its fate depends upon its mass.

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