Video Transcript
In this lesson, we will learn how
to describe atmospheric pressure using various units, including the height of a
mercury column. Before we learn about this process,
let’s first refresh our memory on how to find the pressure of a liquid. We need to recall that when we’re
looking for the pressure in a liquid at different heights, we can use the formula:
𝑃, the pressure in the fluid, is equal to 𝜌, the density of the fluid, times 𝑔,
the acceleration due to gravity, times ℎ, the height of the fluid above the point we
are considering.
Going deeper into our liquid is the
same thing as saying that the height of the liquid above us is increasing, which
means that the pressure in the liquid is also increasing. We can connect this to the fact
that the pressure at the bottom of a swimming pool is greater than the pressure at
the top of a swimming pool. The height of the water above us
when we’re at the bottom of the swimming pool is much greater than the height of the
water above us when we’re at the top. Let’s apply what we just recalled
about the pressure in a liquid to an experiment done by Torricelli in 1646, what we
call today a barometer.
In the experiment, Torricelli
placed a tube of approximate height of one meter filled with mercury into a dish
that also contained mercury. The dish was open such that the
atmosphere could apply pressure to the liquid mercury. Torricelli stated that some of the
mercury would drain from the tube into the dish, until the pressure of the column of
mercury in the tube was equal to the atmospheric pressure pushing down on the
mercury in the dish. The height of the mercury column is
0.760 meters or 760 millimeters, as measured from the surface of the mercury rather
than from the bottom of the tube.
If the pressure within the column
of mercury is equal to the atmospheric pressure, then we can use our height of 0.760
meters and our equation that we discussed earlier for pressure within a fluid to
determine the atmospheric pressure. To plug in our values, you must
first look up the density of mercury. For this example, the 𝜌 or density
of mercury is 13,595 kilograms per meter cubed. Next, we need to plug in our value
for acceleration due to gravity.
Assuming that our experiment takes
place on Earth, we can use the acceleration due to gravity of 9.81 meters per second
squared. And finally, we need to plug in our
value for our height. In this case, we found the height
to be 0.760 meters. When we multiply 13,595 kilograms
per meter cubed by 9.81 meters per second squared by 0.760 meters, we get a pressure
of 101,358.88 pascals. Our acceleration due to gravity and
our height are given to three significant figures. Therefore, we should report our
pressure back to three significant figures, which rounds our pressure to 101,000
pascals.
Commonly, when we deal with such
large numbers, we use a prefix to make our number more manageable. The prefix kilo- represents
1,000. So one kilopascal is the same thing
as 1,000 pascals, which means that 101,000 pascals becomes 101 kilopascals. Now that we know how to measure
atmospheric pressure, let’s look at different units that the pressure can be
reported in. We know that the atmospheric
pressure is approximately 101 kilopascals. We should remember that one
atmosphere or one atm is equal to 101 kilopascals. Therefore, the atmospheric pressure
at sea level is the same thing as one atm, one atmosphere, and 101 kilopascals.
Millimeters mercury or mmhg is
essentially the height that the mercury column will rise to given a specific
pressure. The conversion factor between
kilopascals and millimeters mercury is that one kilopascal is equal to 7.50
millimeters mercury. In our example, we had an
approximate pressure of 101 kilopascals. Converting this to millimeters
mercury would make it be around 758 millimeters mercury. The height of our mercury in our
example was 0.760 meters or 760 millimeters. Due to reporting our final answer
to three significant figures causing us to round our pressure in kilopascals, our
approximation of 758 millimeters mercury is slightly lower than the 760 millimeters
that we had in the experiment.
Another unit of pressure is the
bar. One bar is equal to 100
kilopascals. Therefore, 101 kilopascals will be
equivalent to 1.01 bar. And the final unit of pressure we
will discuss is the torr named after Torricelli, which has the same conversion
factor of one kilopascal to 7.50 torrs as the millimeters mercury had to
kilopascals. With approximately 101 kilopascals,
the pressure in torr will be 758. Now that we have learned about how
to measure atmospheric pressure from the height of the liquid column of mercury as
well as how to convert between the units of kilopascals and millimeters mercury,
kilopascals and bar, as well as kilopascals and torr, let’s apply our understanding
to some example questions.
The apparatus shown in the diagram
is used to measure atmospheric pressure. Which of the following occupies
region A of the test tube? (a) Air, (b) mercury vapor, (c)
glass, (d) vacuum.
The apparatus in the diagram is
from the Torricelli experiment, what we would call today a barometer. It has a dish on the bottom that is
filled with mercury that is open to the atmospheric pressure and a test tube in the
middle that is also filled with mercury. When the test tube is first placed
into the dish, it is filled with mercury all the way to the top. The mercury then flows out of the
test tube and into the dish below, leaving the space that we see in our diagram
between the top of the mercury and the test tube. Because the test tube was full
before and now it’s not, that means that there is a vacuum left in this space,
leading us to answer choice (d). Vacuum is what occupies region A of
the test tube.
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.
The apparatus shown in the diagram
is used to measure atmospheric pressure. Find the upward pressure on the
mercury column. Use a value of 13,595 kilograms per
meters cubed for the density of mercury.
In the diagram, we have an
apparatus which is filled with liquid mercury. The apparatus contains a test tube
that is filled with mercury as well as a dish that’s filled with mercury. The dish is open to the atmosphere
such that the atmosphere applies a pressure as represented by the blue arrows onto
the liquid mercury. This atmospheric pressure provides
the upward pressure on the mercury column inside the test tube.
How do we find this pressure? Well, we know that the atmospheric
pressure is equal to the pressure of the liquid column of mercury inside the test
tube. And we know that the pressure of a
fluid 𝑃 is equal to the density of the fluid 𝜌 times the acceleration due to
gravity 𝑔 times the height of the fluid ℎ. So if we calculate the pressure of
the liquid column of mercury based on the density of mercury, acceleration due to
gravity, and height of the column, we will therefore know the atmospheric
pressure.
The pressure of our column liquid
mercury is equal to the density of mercury, 13,595 kilograms per meter cubed, times
the acceleration due to gravity, 9.81 meters per second squared, times the height of
the liquid mercury, 0.760 meters. When we multiply out these three
values, we get a pressure of 101,358.88 pascals.
Looking at our values, we can see
that the acceleration due to gravity and the height of our liquid column are
reported to three significant figures. Therefore, we must report our
answer to three significant figures, which rounds our pressure to 101,000
pascals. When dealing with such large
numbers, we typically use a prefix to make the numbers more manageable. In this case, we can use the prefix
kilo-, which means 1,000. So one kilopascal is the same thing
as 1,000 pascals. So 101,000 pascals becomes 101
kilopascals. Our final answer for the upward
pressure on the mercury column is 101 kilopascals.
Key Points
A column of mercury can be used to
measure atmospheric pressure. One atmosphere is equal to 101
kilopascals. 7.50 millimeter mercury is equal to
one kilopascal. One bar is equal to 100
kilopascal. 7.50 torr is equal to one
kilopascal.
