Using the Particle Theory, explain why liquids are less compressible than gases.
1 answer:
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Answer: 230.50 m
Explanation:
We have the following information:
the barometric reading at the top of the building
the barometric reading at the bottom of the building
density of air
density of mercury
gravity
And we need to find the height of the building.
In order to approach this problem, we will firstly use the following equations to find the pressure at the top of the building and the perssure at the bottom
:
(1)
(2)
From (1): (3)
From (2): (4)
Having the pressures at the top and the bottom of the building, we can calculate the variation in pressure :
(5)
(6)
On the other hand, we have a column of air with a cross-section area and the same height of the building, lets name it
.
As pressure is defined as the force exerted on a specific area
, we can write:
(7)
If we isolate we have:
(8)
Also, the force gravity exerts on this column of air (its weight) is:
(9)
Knowing the density of air is: (10)
where the volume of air can be written as: (11)
Substituting (1) in (10):
(12)
Isolating :
(13)
Substituting (13) in (9):
(14)
Matching (8) and (14)
(15)
Isolating :
(16)
Substituting the known and calculated values:
(17)
Finally:
This is the height of the building