re: Why does a hot air balloon rise in the air?
Hot air in the balloon has less density and compared to the total volume it displaces- it is lighter than equal volume of the colder air.
And the hot air inside the balloon is roughly the same pressure as air outside it. At the bottom of balloon, which is open, the pressure is nearly equal; at the top of balloon there is slightly higher pressure, but this slightly higher pressure does not explain why a balloon has lift.