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.
