Video Transcript
The magnitude of the atmospheric
pressure at different heights above sea level is shown in the diagram. The atmospheric pressure is shown
at two heights, ℎ one and ℎ two, where ℎ two equals two times ℎ one. The change in the pressure between
the top of Earth’s atmosphere and ℎ two is equal to Δ𝑃 sub 𝐴. The change in the pressure between
ℎ two and ℎ one is equal to Δ𝑃 sub 𝐵. How does the atmospheric pressure
change as the height above sea level decreases?
Starting off, let’s notice that our
graph shows height above sea level on the vertical axis and atmospheric pressure on
the horizontal. The height above sea level goes
from the very top of Earth’s atmosphere, all the way down to sea level. Likewise, the atmospheric pressure
on the horizontal axis ranges from zero pressure here, all the way up to one
atmosphere. Notice that the pressure of zero
pressure corresponds to a height above sea level at the top of Earth’s
atmosphere. In other words, if we’re at the
very top of this atmosphere, the pressure would effectively be zero.
As we decrease in altitude, though,
getting all the way down to sea level, we eventually reach an atmospheric pressure
of one atmosphere. We know that this is a greater
pressure than zero pressure because it’s farther away from the origin of our
graph. More than this, if we look at the
shape of our graph overall, we see that for any two points at different altitudes,
the point at the higher altitude, the one higher above sea level, will have a
corresponding lower pressure. This makes sense if we think about
moving down through the layers of Earth’s atmosphere. The farther downward we move, the
more layers are on top of us, so to speak, and the higher the atmospheric pressure
is. As height above sea level
decreases, atmospheric pressure increases.
Now let’s look at part two of our
question.
How does the rate of change of the
atmospheric pressure change as the height above sea level decreases?
This question is different from the
one we just answered because now we’re talking about the rate at which atmospheric
pressure changes as the height above sea level decreases. So what does that mean? Well, notice that this curve is not
a straight line. That tells us that for some changes
in altitude, the atmospheric pressure will vary more than it does for other equally
sized changes in altitude. To understand this better, let’s
consider these two heights, ℎ two and ℎ one.
Imagine we begin with our elevation
above sea level being equal to ℎ two. Then, say, from there we move
downward in elevation until we reach ℎ one. The atmospheric pressure at a
height ℎ two is marked out as 𝑃 two. That pressure at a height ℎ one is
𝑃 one. As we move down from ℎ two to ℎ one
then, the atmospheric pressure increases from 𝑃 two up to 𝑃 one. We can see that according to our
graph, as we move from ℎ two to ℎ one, we’ve moved through a vertical distance of
Δℎ.
Starting now at ℎ one, if we move
downward through that same vertical distance, we reach sea level. This is the same change in height
Δℎ. But now notice that the resulting
change in atmospheric pressure is from 𝑃 one all the way up to one atmosphere. So if we move through some height
in the lower atmosphere, that results in a relatively large change in pressure. If we move downward through the
same height but higher up in the atmosphere, that results in a much smaller change
in atmospheric pressure. What we’re finding then is that as
the height above sea level decreases, the rate of change of atmospheric pressure is
increasing. This then is our answer. As height above sea level
decreases, the rate of change of atmospheric pressure increases.
