Mercury is poured into a tall glass. Ethyl alcohol (which does not mix with mercury) is then poured on top of the mercury until the height of the ethyl alcohol itself is 112 cm. The air pressure at the top of the ethyl alcohol is one atmosphere. What is the absolute pressure at a point that is 9.20 cm below the ethyl alcohol-mercury interface? The density of mercury = 13 600 and the density of ethyl alcohol is 806. Use these values accordingly.
To determine the absolute pressure at a point below the ethyl alcohol-mercury interface, we need to consider the pressure contributions from both the ethyl alcohol and the mercury.
1. First, let's calculate the pressure contribution from the ethyl alcohol:
Given:
- Height of ethyl alcohol = 112 cm
- Density of ethyl alcohol = 806
Convert the height of ethyl alcohol to meters:
Height_ethanol = 112 cm * (1 m / 100 cm) = 1.12 m
Calculate the pressure contribution from the ethyl alcohol using the hydrostatic pressure equation:
Pressure_ethanol = Density_ethanol * g * Height_ethanol
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Pressure_ethanol = 806 kg/m³ * 9.8 m/s² * 1.12 m
2. Next, let's calculate the pressure contribution from the mercury:
Given:
- Density of mercury = 13,600
Since the ethyl alcohol and mercury do not mix, the pressure at the interface between them is the same. So, the pressure at the ethyl alcohol-mercury interface is one atmosphere.
Convert one atmosphere to Pascals:
Pressure_interface = 1 atm * 101,325 Pa/atm
Now we can calculate the absolute pressure at a point 9.20 cm below the ethyl alcohol-mercury interface:
Given:
- Height below the interface = 9.20 cm
Convert the height below the interface to meters:
Height_below_interface = 9.20 cm * (1 m / 100 cm) = 0.0920 m
Calculate the pressure below the interface using the hydrostatic pressure equation:
Pressure_below_interface = Pressure_interface + Density_mercury * g * Height_below_interface
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Pressure_below_interface = 101,325 Pa + 13,600 kg/m³ * 9.8 m/s² * 0.0920 m
Finally, the absolute pressure at the point 9.20 cm below the ethyl alcohol-mercury interface is the sum of the pressure contributions from both the ethyl alcohol and the mercury:
Absolute_pressure = Pressure_ethanol + Pressure_below_interface