Question Video: Drawing an Inference about the Height above Sea Level through Inspecting the Height of a Mercury Column

The apparatus shown in the diagram is used to measure atmospheric pressure. In which case is the apparatus at the greatest height above sea level? [A] I [B] II [C] III [D] There is no difference in the apparatus’s height above sea level in the three cases.

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Video Transcript

The apparatus shown in the diagram is used to measure atmospheric pressure. In which case is the apparatus at the greatest height above sea level? (a) Roman numeral I, (b) Roman numeral II, (c) Roman numeral III, (d) there is no difference in the apparatus’s height above sea level in the three cases.

In the diagram, we have an apparatus for Roman numeral I, II, and III, which in each case is filled with liquid mercury. In each case, there is a dish filled with mercury on the bottom and a test tube that’s filled with mercury that’s flipped upside down inside the dish. To determine which of the apparatuses is at the greatest height above sea level, let’s discuss how the apparatus works. In each of the three cases, the atmosphere applies a pressure to the liquid mercury in the dish, as shown by the blue arrows drawn into the diagram. Depending on how great the atmospheric pressure is, we’ll determine how high the mercury in the column goes.

The atmospheric pressure is equal to the pressure 𝑃 of the liquid column of mercury. And the pressure of the liquid column mercury 𝑃 is equal to 𝜌, density of the liquid mercury, times 𝑔, acceleration due to gravity, times ℎ, the height of the column of liquid mercury in the tube. This equation tells us that if the atmospheric pressure is higher or the pressure of the liquid column of mercury is higher, then the height of the liquid column of mercury would also be higher. But how does that help us determine which of the apparatuses is at the greatest height above sea level?

Well, the higher we go above sea level, the lower the pressure is going to be due to the atmosphere. This is because there’s gonna be less atmosphere above us pushing down. So if we’re at our greatest high above sea level, that means that we have the smallest atmospheric pressure pushing on our apparatus. So we’re looking for the case that would then have the smallest height within the test tube. When comparing the height of liquid mercury in each of the test tubes, we can see that in case III, it has the smallest height. This means that the case in which the apparatus is at the greatest height above sea level is answer choice (c), Roman numeral III.

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