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A Closer Look: Helium vs. Hot Air Balloons
Airy ghosts in an ocean of air
In this video session, we stated that helium
balloons rise in air for the same reason that a piece of pinewood rises
in water — the buoyant
force upward is greater than the weight downward. We can also state
this as “the weight of the watery (or airy) ghost is more than
the weight of the object.”
If an object has an average density (mass
divided by volume displaced) that is less than that of the fluid in
which it is placed, it will rise.
If the average density is greater than the density of the fluid in
which it is placed, it will sink.
In the case of the wood, water molecules
bumping into the sides of the wood provide the pressure that causes it
to rise. With the balloon,
moving
molecules of nitrogen, oxygen, and argon collide with the outside
of the balloon to provide pressure and thus the buoyant force that causes
it to
rise.
But how can balloons be less dense than air? Let’s take
a closer look at two types of balloons that rise in air.
Helium
balloons: Why helium is less dense than air
 Recall that the particles
of a gas are, on average, very far apart and collide less frequently
than do particles of liquids or solids.
Consider
two balloons that contain gas and have equal volumes. If one
balloon is filled with air and the other is filled with
helium, the balloons will still contain the same number of
particles. Why? Since the spaces between particles are quite big (about
1000 times the
diameter of a single molecule), the size of the individual
particles
could be larger or smaller by a factor of two or three and
not change the total
volume of gas. Therefore, a liter of air contains the same
number of particles as a liter of helium.
Air is made mostly of the molecules
oxygen and nitrogen. The most common type of isotope for O_2 (oxygen)
[link to isotopes
ACL in
session 5]
contains eight protons and eight neutrons. The most common
type of isotope for N_2
(nitrogen) contains seven protons and seven neutrons. Helium
is made of single atoms of helium, the most common isotope
of which
contains
two protons
and two neutrons. Thus, the mass of one particle of helium
(a single atom) is about one eighth the mass of one particle
of
oxygen (a
molecule with
two atoms of oxygen). If the same volume of these two gases
contains the same number of particles but the mass of each
helium particle
is much less
than the mass of a particle of air, the density of the
helium will be less than that of air, thereby causing helium to
rise in air.
In summary, there are the same number of particles in
a helium balloon and an air balloon of equal volume,
but
each particle
of helium has
a smaller mass.
Hot air balloons: Why hot air is less
dense than room temperature air
Let’s compare a balloon with cool
air and one with hot air to help explain the differences in density.
As we’ll see in Session 7, as an object becomes
hotter, its particles move faster, collide more often,
and therefore
have larger spaces between
them. In this case, the balloon with the hot air
will have larger spaces between its particles and, as a result,
a smaller
number of particles in
the same volume.
Particles in a hot air balloon.
The particles of air in each balloon
individually weigh the same but, since there are fewer particles
in the
hot air
balloon, there is less
mass in
that air than in cooler, more dense air. Since
the two balloons have the same volume, the density of
the hot
air is less
than that of
the cool air
and the hot air balloon will float in air!
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