Glycerin is poured into an open U-shaped tube until the height in both sides is 18 cm . Ethyl alcohol is then poured into one arm until the height of the alcohol column is 18 cm . The two liquids do not mix.
What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?
To find the difference in height between the top surface of the glycerin and the top surface of the alcohol, we need to consider the difference in pressure caused by the two liquids.
In this case, the pressure at the top surface of the glycerin is equal to the atmospheric pressure (since it is an open U-shaped tube), which we can assume to be constant.
However, the pressure at the top surface of the alcohol is equal to the sum of the atmospheric pressure and the pressure due to the column of alcohol.
Using the hydrostatic pressure formula:
Pressure = Density × Gravity × Height,
The pressure due to the glycerin is:
Pressure_glycerin = Density_glycerin × Gravity × Height_glycerin,
And the pressure due to the alcohol is:
Pressure_alcohol = Density_alcohol × Gravity × Height_alcohol.
Since the two liquids do not mix, the pressure at the top surface of the alcohol (Pressure_alcohol) must equal the atmospheric pressure (Pressure_glycerin) plus the pressure due to the column of alcohol.
So,
Pressure_alcohol = Pressure_glycerin + Pressure_alcohol
Density_alcohol × Gravity × Height_alcohol = Density_glycerin × Gravity × Height_glycerin + Density_alcohol × Gravity × Height_alcohol.
Simplifying the equation, we can cancel out the Gravity factor and rearrange the terms:
Height_glycerin = (Density_alcohol / Density_glycerin) × Height_alcohol.
Since we know the heights of both the glycerin and alcohol columns are both 18 cm, we can substitute those values into the equation:
Height_glycerin = (18 cm) × (Density_alcohol / Density_glycerin).
Now we need the densities of glycerin and alcohol. The density of glycerin is approximately 1.26 g/cm^3, and the density of alcohol (ethyl alcohol) is approximately 0.79 g/cm^3.
Substituting these values into the equation, we can calculate the difference in height:
Height_glycerin = (18 cm) × (0.79 g/cm^3 / 1.26 g/cm^3)
= (18 cm) × (0.79 / 1.26)
≈ 11.34 cm.
Therefore, the difference in height between the top surface of the glycerin and the top surface of the alcohol is approximately 11.34 cm.