When a baseball player hits a ball
during an unusually humid night will the ball travel further than it
would during a drier atmosphere. First,we should consider how many
molecules there are in a certain volume of air. Avagadros number,
6.022 times ten to the twenty-third power, was initially discovered
by tying a number of reactive molecules in a certain volume of air.
For example, it was discovered that a certain volume of Hydrogen gas,
22.4 liters, contained two grams of Hydrogen. When two of these molar
volumes are reacted with 22.4 liters of Oxygen (one mole), which
happened to weigh 32 grams, it produced 36 grams of water, H2O (and
two moles of vapor.) Although there are slight constants
adjustments, the gases of both Hydrogen and Oxygen contain exactly
the same volume, despite their differences in mass. And,with the one
to one reaction of theses gas molecule, one could be assured that
there is indeed the exact same number of constituent molecules.
Therefore we can assume, with slight adjustments, that the air
containing the Water molecule, as humidity, also has the exact same
number of molecules as the air that is more constituted of the
representative Nitrogen, Oxygen, and lesser amount gases, in its
constitution. So now, with equal numbers of molecules in the
atmosphere, but with differing densities, it can be shown that the
high humidity air is much less dense than the air without H2O in high
concentration. The weight of a di-atomic Oxygen molecule is two times
sixteen (the weight of an oxygen molecule), or thirty-two grams per
mole (22.4 liters), similarly, Nitrogen gas is two times fourteen, or
28 grams per mole. Water is two hydrogen and one oxygen which has a
weight of Eighteen grams per mole. So in equivalent amounts of gas,
you have molecules averaging about 29 or so grams per mole, and, when
water vapor is added, a much less dense average weight per mole. The
pressure of the lighter gases needs to be assimilated into the
equation of which gas is easier for a baseball to pass through, since
the lighter molecules are moving faster (on average) than the heavier
counterparts, so they would hit with a higher momentum against a ball
traveling through it. In fact it is the same momentum effect on the
ball because, even though the bigger molecules are traveling slower
as they impact the ball, their heft of mass imparts a similar impact
of kinetic energy. So it seems that there should be an equal impact
of the gases with lighter density and faster kinetic speed against
higher mass and slower speed molecules against the momentum of the
baseball. Then there is the kinetic energy of the baseball itself.
The baseball would hit less high H2O concentrated gas molecules,
because the molecules become more widely dispersed from their higher
velocity, and the baseball can plough through easier, much like a
racked pool balls slammed hard travel over further areas of a pool
table, or in our case, the area in front of the hit ball, and the
baseball will travel further in a high humidity atmosphere.
This combined video shows the fall of a heated centimeter-sized steel sphere through water. From left to right, the sphere is at 25 degrees C (left), 110 degrees C (middle), and 180 degrees C, demonstrating how the Leidenfrost effect—which vaporizes the water in immediate contact with the sphere—can substantially reduce the drag on a submerged object. In the middle video, the vaporization of the water around the sphere is sporadic and incomplete, only slightly reducing the sphere’s drag relative to the room temperature case. The much hotter sphere on the right, however, has a complete layer of vapor surrounding it, allowing it to travel through a gas rather than the denser liquid. (Video credit: I. Vakarelski and S. Thoroddsen; from a review by D. Quere)
(Source: annualreviews.org)
