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Question Video: Relating Atmospheric Pressure and Height above Sea Level Physics • 9th Grade

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, ℎ₁ and ℎ₂, where ℎ₂ = 2ℎ₁. The change in the pressure between the top of Earth’s atmosphere and ℎ₂ is equal to Δ𝑃_𝐴. The change in the pressure between ℎ₂ and ℎ₁ is equal to Δ𝑃_𝐵. How does the atmospheric pressure change as the height above sea level decreases? How does the rate of change of the atmospheric pressure change as the height above sea level decreases?

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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.

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