A uniform capillarity tube closed at one end contained dry air trapped by a thread of Mercury 8.5*10-2m long when the tube was held horizontally the length of air column was 5.0*10-2m, when it is held vertically with the closed end downward the length was 4.5*10-2m.
Determine the volume of the atmospheric pressure.?
To determine the volume of atmospheric pressure, we need to understand the concept of atmospheric pressure and how it affects the length of the air column in a capillarity tube.
First, let's define some terms:
- Atmospheric pressure: The pressure exerted by the Earth's atmosphere on the surface of objects. It is usually measured in units of pascals (Pa).
- Capillarity tube: A small tube with a narrow diameter used to measure small pressure differences or changes.
In this scenario, the capillarity tube is closed at one end, and the length of the air column inside the tube changes when the tube is held horizontally or vertically.
To find the volume of the atmospheric pressure inside the capillarity tube, we can start by understanding the relationship between pressure and length of the air column.
In a capillarity tube, the pressure inside is the sum of two pressures:
- The pressure exerted by the length of the air column inside the tube.
- The atmospheric pressure pushing down on the mercury thread.
When the tube is held horizontally, the length of the air column is 5.0 * 10^-2 m. This length can be used to determine the pressure exerted by the air column.
Similarly, when the tube is held vertically with the closed end downward, the length of the air column is 4.5 * 10^-2 m. Again, this length can be used to calculate the pressure exerted by the air column.
To determine the volume of the atmospheric pressure, we need to find the pressure difference between the horizontal and vertical positions.
The pressure difference can be calculated using the equation:
Pressure difference = Pressure(horizontal) - Pressure(vertical)
To find the pressure exerted by the air column, we can use the equation:
Pressure = Density * g * Height
In this case, the height is the length of the air column, and g is the acceleration due to gravity (approximately 9.8 m/s^2). The density of dry air is approximately 1.225 kg/m^3.
Now, let's calculate the pressure difference.
Pressure(horizontal) = Density * g * Height(horizontal)
Pressure(horizontal) = 1.225 kg/m^3 * 9.8 m/s^2 * 5.0 * 10^-2 m
Pressure(vertical) = Density * g * Height(vertical)
Pressure(vertical) = 1.225 kg/m^3 * 9.8 m/s^2 * 4.5 * 10^-2 m
Pressure difference = Pressure(horizontal) - Pressure(vertical)
Now that we have the pressure difference, the volume of the atmospheric pressure can be determined using Boyle's Law.
Boyle's Law states that at constant temperature, the product of pressure and volume is constant.
Pressure difference * Volume(atmospheric pressure) = Constant
Solving for Volume(atmospheric pressure):
Volume(atmospheric pressure) = Constant / Pressure difference
To find the constant value, we need to use the initial length of the air column (8.5 * 10^-2 m).
Pressure(constant) = Density * g * Height(constant)
Pressure(constant) = 1.225 kg/m^3 * 9.8 m/s^2 * 8.5 * 10^-2 m
Now we can calculate the volume of the atmospheric pressure:
Volume(atmospheric pressure) = (Density * g * Height(constant)) / Pressure difference
Substituting the values, plug in the numbers into the equation to find the volume of the atmospheric pressure inside the capillarity tube.
Note: Make sure to pay attention to unit conversions while plugging in the values and calculate the final volume accurately.