All air particles in the atmosphere are drawn by the downward force of gravity.
But the pressure in the air creates an upward force working opposite gravity's pull.
Air density builds to whatever level balances the force of gravity, because
at this point gravity isn't strong enough to pull down a greater number of
particles.
This pressure level is highest right at the surface of the Earth because the
air at this level is supporting the weight of all the air above it -- more
weight above means a greater downward gravitational force. As you move up
through levels of the atmosphere, the air has less air mass above it, and so
the balancing pressure decreases. This is why pressure drops as you rise in
altitude.
This difference in air pressure causes an upward buoyant force in the air
all around us. Essentially, the air pressure is greater below things than it
is above things, so air pushes up more than it pushes down. But this buoyant
force is weak compared to the force of gravity -- it is only as strong as
the weight of the air displaced by an object. Obviously, most any solid
object is going to be heavier than the air it displaces, so buoyant force
doesn't move it at all. The buoyant force can only move things that are
lighter than the air around them.
For buoyancy to push something up in the air, the thing has to be lighter
than an equal volume of the air around it. The most obvious thing that is
lighter than air is nothing at all. A vacuum can have volume but does not
have mass, and so, it would seem, a balloon with a vacuum inside should be
lifted by the buoyancy of the air around it. This doesn't work, however,
because of the force of surrounding air pressure. Air pressure doesn't crush
an inflated balloon, because the air inside the balloon pushes out with the
same force as the outside air pushing in. A vacuum, on the other hand,
doesn't have any outward pressure, since it has no particles bouncing
against anything. Without equal pressure balancing it out, the outside air
pressure will easily crush the balloon. And any container strong enough to
hold up to the air pressure at the earth's surface will be much too heavy to
be lifted by the buoyant force.
Another option would be to fill the balloon with air that is less dense than
the surrounding air. Because the air in the balloon has less mass per unit
of volume than the air in the atmosphere, it would be lighter than the air
it was displacing, so the buoyant force would lift the balloon up. But
again, fewer air particles per volume means lower air pressure, so the
surrounding air pressure would squeeze the balloon until the air density
inside was equal to the air density outside.
All of this is assuming that the air in the balloon and the air outside the
balloon exist under exactly the same conditions. If we change the conditions
of the air inside the balloon, we can decrease density, while keeping air
pressure the same. As we saw in the last section, the force of air pressure
on an object depends on how often air particles collide with that object, as
well as the force of each collision. We saw that we can increase overall
pressure in two ways:
* Increase the number of air particles so there is a greater number of
particle impacts over a given surface area.
* Increase the speed of the particles so that the particles hit an area more
often and each particle collides with greater force.
There are fewer air particles per unit of volume inside the balloon, but
because those particles are moving faster, the inside and outside air
pressure are the same.
So, to lower air density in a balloon without losing air pressure, you
simply need to increase the speed of the air particles. You can do this very
easily by heating the air. The air particles absorb the heat energy and
become more excited. This makes them move faster, which means they collide
with a surface more often, and with greater force.
For this reason, hot air exerts greater air pressure per particle than cold
air, so you don't need as many air particles to build to the same pressure
level. So a hot air balloon rises because it is filled with hot, less dense
air and is surrounded by colder, more dense air.
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