A gas bulb is connected to an open end manometer. The pressure in the bulb is 0.355 Torr more than atmospheric pressure. If the manometer is filled with mineral oil (density = 0.888 g/cm3), what will be the difference in height between the two sides of the manometer? Density of mercury is 13.6 g/cm3.
To determine the difference in height between the two sides of the manometer, we need to calculate the pressure difference between the gas bulb and the atmosphere.
First, let's convert the density of mineral oil from grams per cubic centimeter (g/cm3) to grams per cubic millimeter (g/mm3) since the pressure measurements are in Torr.
Density of mineral oil = 0.888 g/cm3
To convert g/cm3 to g/mm3, we divide the density by 1000 since there are 1000 cubic millimeters in a cubic centimeter:
Density of mineral oil = 0.888 g/cm3 / 1000 = 0.000888 g/mm3
Next, we need to calculate the difference in pressure between the gas bulb and the atmosphere. The pressure difference can be obtained by subtracting the atmospheric pressure from the pressure in the bulb.
Given that the pressure in the bulb is 0.355 Torr more than atmospheric pressure, we can set up the equation:
Pressure difference = Pressure in bulb - Atmospheric pressure
Pressure difference = 0.355 Torr
Now, let's convert the pressure difference from Torr to grams per square millimeter (g/mm2) to match the units of density.
The conversion factor between Torr and g/mm2 for mercury is:
Conversion factor = 13.6 g/cm3 * 1 cm / 1.33 g/mm3 * 760 Torr / 1 atm
This conversion factor can be used to convert Torr to g/mm2.
Pressure difference in g/mm2 = Pressure difference in Torr * Conversion factor
Substituting the values:
Pressure difference in g/mm2 = 0.355 Torr * 13.6 g/cm3 * 1 cm / 1.33 g/mm3 * 760 Torr / 1 atm
Now, let's calculate the pressure difference:
Pressure difference in g/mm2 = 3.647 g/mm2
Since the manometer is filled with mineral oil, we can assume it has the same density as mineral oil.
Now, we can calculate the height difference between the two sides of the manometer using the pressure difference and density of mineral oil.
Height difference = Pressure difference / (density of mineral oil * g)
where g is the acceleration due to gravity.
Substituting the values:
Height difference = 3.647 g/mm2 / (0.000888 g/mm3 * 9.8 m/s2)
Simplifying:
Height difference = 4134 mm
Therefore, the difference in height between the two sides of the manometer is 4134 mm.
To find the difference in height between the two sides of the manometer, we need to consider the pressure difference between the gas bulb and the atmospheric pressure.
Given:
Pressure difference = 0.355 Torr
Density of mineral oil = 0.888 g/cm^3
Density of mercury = 13.6 g/cm^3
Now let's calculate the pressure difference in terms of the height difference using the equation:
pressure difference = density x gravity x height difference
First, let's calculate the pressure difference in terms of the height difference using mineral oil:
0.355 Torr = (0.888 g/cm^3) x (9.8 m/s^2) x height difference
Converting the pressure difference to Pascals:
1 Torr = 133.322 Pa
0.355 Torr = (0.355 Torr) x (133.322 Pa/Torr) = 47.146 Pa
Next, we can rearrange the equation to solve for the height difference:
height difference = (pressure difference) / (density x gravity)
height difference = (47.146 Pa) / ((0.888 g/cm^3) x (9.8 m/s^2))
Converting the density of mineral oil from g/cm^3 to kg/m^3:
0.888 g/cm^3 = (0.888 g/cm^3) x (1000 kg/m^3 / 1 g/cm^3) = 888 kg/m^3
height difference = (47.146 Pa) / ((888 kg/m^3) x (9.8 m/s^2))
height difference ≈ 0.006 m
The difference in height between the two sides of the manometer when filled with mineral oil will be approximately 0.006 meters.