If you wanted to make a barometer that had a column of liquid about 6 feet tall, what would
the density of the liquid have to be? 1 meter = 3.28 ft 1 inch = 2.54 cm Density Hg = 13.6
g/mL 1atm = 760 torr
To calculate the density of the liquid needed for the barometer, we can use the fact that the height of the liquid column in the barometer is directly related to the pressure it can measure. The pressure exerted by a column of liquid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column.
In this case, we want the barometer to have a column of liquid about 6 feet tall, which is equivalent to 1.83 meters (6 feet * 1 meter/3.28 feet). The pressure we are interested in measuring is atmospheric pressure, which is approximately 760 torr.
We know the density of mercury (Hg) is 13.6 g/mL. To convert this density to g/cm³ (which is the same as g/mL), we divide by 1,000 since 1 mL is equal to 1 cm³. So, the density of mercury in g/cm³ is 13.6 g/cm³.
Now, let's rearrange the equation P = ρgh to solve for ρ:
ρ = P / (gh)
Substituting the known values:
ρ = 760 torr / (1.83 meters * 9.8 m/s²)
To convert torr to pascals (Pa), we use the conversion factor: 1 torr = 133.32 Pa. So:
ρ = (760 torr * 133.32 Pa/torr) / (1.83 meters * 9.8 m/s²)
Simplifying:
ρ = 101,325.6 Pa / (17.934 meters²/s²)
Finally:
ρ ≈ 5628.5 Pa / meters²
So, the density of the liquid needed to create a barometer with a 6 feet tall column is approximately 5628.5 Pa/m².