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Violation of conservation of energy thought experiment:

Let us imagine an air compressor is invented with incredible efficiency. This compressor will compress a gas and recover back 99% percent of that energy when the gas is released from the compression chamber. So far this violates no laws of physics.

Now imagine we were to take an enormous hydrogen balloon and lift a very large mass to a substantial height. The hydrogen balloon drops of the mass on some very high platform, then compresses its hydrogen to the point where it loses its buoyancy and it will descend. The balloon then reloads another mass, decompresses the hydrogen, and repeats. Were the 99% efficient compressor to waste less energy than the gravitation potential of the lifted masses, would we not have violated conservation of energy? So where is the flaw in this experiment?

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  • $\begingroup$ By allowing the balloon to rise, you are allowing the atmosphere to do work against gravity; hence, you're receiving energy from the environment. $\endgroup$
    – probably_someone
    Commented Feb 19, 2018 at 0:20
  • $\begingroup$ Ask yourself what happens once you've lifted all of the mass of the Earth up to your high platform, and then I think you'll see what's going on. $\endgroup$
    – DanielSank
    Commented Feb 19, 2018 at 1:36
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    $\begingroup$ @DanielSank That doesn't explain anything. We're still getting "free" work done. Let's say we stop at a quarter the mass of the earth. That's a ton of potential energy that we seem to have gotten out of nowhere. $\endgroup$
    – A Tyshka
    Commented Feb 19, 2018 at 3:44
  • $\begingroup$ I was trying to give a hint, not solve the problem. Maybe it's a bad hint. Why don't you consider the energy of everything in the problem before and after one cycle of the process and write your findings in the question post? You're more likely to get an answer out of someone if you show a bit more effort. $\endgroup$
    – DanielSank
    Commented Feb 19, 2018 at 3:46

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When you try to expand the gas to refill the balloon, you’re pushing against a higher pressure: you’ll need to add energy to get back to the original state.

To do a complete calculation is tricky, because you have to consider thermal effects: how does heat flow as the balloon rises (is the balloon insulated?) and during compression and expansion.

But the real problem is the difference in pressure environment.

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