Why can't hot air balloons fly higher then helium balloons? I have read these questions:
Hot air balloon trajectory predictions
Do atmospheric physics prevent hot air balloons from ascending over 60,000ft?
What is precisely the reason that a helium balloon ascends?
I have read that hot air balloons can just fly 11 miles up, while helium ones can go much higher.
I do not know whether hot air rises, as long as there is atmosphere.
Helium is one of the lightest gases, so it rises too.
The density for air is : 1.29 kg/m3
The density for helium is : 0.178 kg/m3
I have found a calculator for hot air density.
https://www.gribble.org/cycling/air_density.html
It says that the density of hot air reaches the density of helium at 1700C.
None of these questions said why hot air balloons can't fly higher then 11 miles.
Question:


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*Why can't hot air balloons fly higher then helium balloons?

 A: Although it is pretty obvious that helium balloons should be able to rise higher than hot air balloons due to much lower molecular weight of helium vs air, it could be still informative to look at how they rise and why they stop rising.
Both helium and hot air balloons rise because the lifting force, equal to the weight of air displaced by a balloon, exceeds the weight of the balloon (including the gas, helium or hot air, inside the balloon).
Both helium and hot air balloons stop rising because the density of air is decreasing with altitude and, with it, the lifting force. This is not the case with water, which has practically the same density at different depth levels and therefore keeps pushing objects less dense than water all the way up to the surface.
For helium balloons, this drop in density with altitude is partially compensated by the expansion of their volume, but still, at some altitude the weight will exceed the lifting force.
For hot air balloons the drop in density could be partially compensated by expelling more and more air, which could be achieved by raising the temperature in the balloon to progressively higher levels. But, again, at some point the weight of the balloon will exceed the lifting force.
So, even if the weight of the gas inside a balloon was zero, there would be a limit due to the finite weight of the balloon itself and the payload. This limit is lower for hot air balloons because they tend to weigh more and because, at any given pressure level, the density of helium will be lower than the density of hot air (for any practical temperature) and therefore helium balloons will have a greater lifting force for the same volume ($(\rho_{out}-\rho_{in})\times V$). 
