What pressure (atm) is exerted by a column of ethanol 49.0 cm high? The density of ethanol is 0.789 g/cm3 and 9.8m/s2 as your gravitational constant.
http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
To calculate the pressure exerted by a column of a liquid, we can use the equation:
Pressure = density × g × height
Where:
- Pressure is the desired value in atmospheres (atm)
- Density is the density of the liquid in grams per cubic centimeter (g/cm^3)
- g is the acceleration due to gravity in meters per second squared (m/s^2)
- Height is the height of the liquid column in centimeters (cm)
Given values:
Density of ethanol (ρ) = 0.789 g/cm^3
Acceleration due to gravity (g) = 9.8 m/s^2
Height of ethanol column (h) = 49.0 cm
First, we need to convert the height of the column from centimeters (cm) to meters (m):
Height = 49.0 cm = 0.49 m
Next, we can substitute the known values into the formula:
Pressure = density × g × height
= 0.789 g/cm^3 × 9.8 m/s^2 × 0.49 m
To ensure consistent units, we need to convert grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3):
1 g/cm^3 = 1000 kg/m^3
So, the equation becomes:
Pressure = (0.789 g/cm^3 × 1000 kg/m^3) × 9.8 m/s^2 × 0.49 m
Substituting the values and performing the calculation:
Pressure = (789 kg/m^3) × 9.8 m/s^2 × 0.49 m
≈ 3805.22 kg/m^3
Now, to convert the pressure from kilogram per square meter (kg/m^3) to atmospheres (atm):
1 atm = 101325 kg/m^3
So, the equation becomes:
Pressure = 3805.22 kg/m^3 ÷ 101325 kg/m^3
≈ 0.0376 atm
Therefore, a column of ethanol with a height of 49.0 cm exerts a pressure of approximately 0.0376 atm.