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
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.