A uniform capillary 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 the air column was 5×10^-2m,when it was held vertically with the closed end downwards the length was 4.5×10^-2m.Determine the value of the atmospheric pressure.g=10m/s, density of mercury 1.36×10^4kg/m^-3
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To determine the value of the atmospheric pressure, we can use the principle of hydrostatic pressure.
First, let's calculate the pressure of the air column when the tube is held horizontally. The pressure in the air column is equal to the pressure exerted by the height of the air column itself plus the pressure exerted by the height of the mercury column.
1. Calculate the pressure exerted by the height of the air column:
Use the formula for hydrostatic pressure: P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the column.
P_air = ρ_air * g * h_air
Given:
h_air = 5×10^-2 m (height of the air column)
2. Calculate the pressure exerted by the height of the mercury column:
P_mercury = ρ_mercury * g * h_mercury
Given:
ρ_mercury = 1.36×10^4 kg/m³ (density of mercury)
h_mercury = 8.5×10^-2 m (height of the mercury column)
3. Calculate the atmospheric pressure:
The atmospheric pressure is the sum of the pressures exerted by the air and the mercury.
P_atmosphere_horizontal = P_air + P_mercury
Now, let's calculate the pressure when the tube is held vertically with the closed end downwards.
1. Calculate the pressure exerted by the height of the air column:
P_air_vertical = ρ_air * g * h_air_vertical
Given:
h_air_vertical = 4.5×10^-2 m (height of the air column when held vertically)
2. Calculate the pressure exerted by the height of the mercury column:
The height of the mercury column is now equal to the initial height minus the length of the air column.
h_mercury_vertical = h_mercury - h_air
3. Calculate the atmospheric pressure:
P_mercury_vertical = ρ_mercury * g * h_mercury_vertical
P_atmosphere_vertical = P_air_vertical + P_mercury_vertical
Finally, to determine the value of the atmospheric pressure, compare the values of P_atmosphere_horizontal and P_atmosphere_vertical. The atmospheric pressure should be the same in both cases.