what pressure (in atm) is exerted by a column of mercury 1.4O high? The density of mercury is 13.5951 g/cm3.
what pressure (in atm) is exerted by a column of mercury 1.4O WHAT high? The density of mercury is 13.5951 g/cm3.
1.40 m high
To find the pressure exerted by a column of mercury, we can use the formula:
Pressure = Density x Gravity x Height
Given:
Height (h) = 1.40 m (since 1.4O high could be a typo)
Density (ρ) = 13.5951 g/cm³ = 13.5951 × 1000 kg/m³ (converting g/cm³ to kg/m³)
Gravity (g) = 9.8 m/s² (acceleration due to gravity on Earth)
Let's substitute these values into the formula:
Pressure = (13.5951 × 1000 kg/m³) x (9.8 m/s²) x (1.40 m)
Note: We have converted the density to kg/m³ and used standard gravity in meters per second squared.
Calculating the pressure:
Pressure = 13,595.1 kg/m³ x 9.8 m/s² x 1.40 m
= 189,835.88 Pascal (Pa)
Since 1 atm (atmosphere) is equal to 101325 Pa, we can convert the pressure to atm:
Pressure = 189,835.88 Pa ÷ 101325 Pa/atm
≈ 1.874 atm (rounded to three decimal places)
Therefore, the pressure exerted by the column of mercury 1.40 m high is approximately 1.874 atm.
To find the pressure exerted by a column of mercury, we can use the formula:
Pressure = Density × gravitational acceleration × height
First, we need to convert the height from centimeters to meters, as the SI unit for density and gravitational acceleration are in kilograms per cubic meter and meters per second squared, respectively.
Given:
Height = 1.40 cm
Density of mercury = 13.5951 g/cm³
1 atm = 101325 Pa
Converting height from cm to m:
Height = 1.40 cm = 1.40 / 100 m = 0.0140 m
Next, we need to convert the density from g/cm³ to kg/m³:
Density of mercury = 13.5951 g/cm³ = 13.5951 × 1000 kg/m³ = 13595.1 kg/m³
The acceleration due to gravity is approximately 9.8 m/s².
Now we can plug these values into the formula:
Pressure = Density × gravitational acceleration × height
Pressure = 13595.1 kg/m³ × 9.8 m/s² × 0.0140 m
Calculating the pressure:
Pressure = 2067.03188 Pa
Lastly, we can convert the pressure from Pascal to atmospheres (atm):
Pressure in atm = 2067.03188 Pa / 101325 Pa/atm
Calculating the final answer:
Pressure in atm ≈ 0.0204 atm
Therefore, a column of mercury 1.40 m high exerts a pressure of approximately 0.0204 atm.