Answer:
a) The difference in mercury levels in the manometer is 2 centimeters.
b) The gage of the gas is 2.670 kilopascals.
Explanation:
a) Pressure in gases is absolute. A manometer helps to determine the hydrostatic difference between pressure of the gas ([tex]P_{g}[/tex]) and atmospheric pressure ([tex]P_{atm}[/tex]), both measured in pascals. A kilopascal equals 1000 pascals and 1 meter equals 100 centimeters. That is:
[tex]P_{g}-P_{atm} = \rho \cdot g \cdot L[/tex] (1)
Where:
[tex]\rho[/tex] - Density of mercury, measured in kilograms per cubic meter.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]L[/tex] - Difference in mercury levels, measured in meters.
If we know that [tex]P_{g} = 104000\,Pa[/tex], [tex]P_{atm} = 101330\,Pa[/tex], [tex]\rho = 13590\,\frac{kg}{m^{3}}[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], the difference in mercury levels in the manometer is:
[tex]L = \frac{P_{g}-P_{atm}}{\rho\cdot g}[/tex]
[tex]L = \frac{104000\,Pa-101330\,Pa}{\left(13590\,\frac{kg}{m^{3}} \right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}[/tex]
[tex]L = 0.020\,m[/tex]
[tex]L = 2\,cm[/tex]
The difference in mercury levels in the manometer is 2 centimeters.
b) The gage pressure is the difference between gas pressure and atmospheric pressure: ([tex]P_{g} = 104000\,Pa[/tex], [tex]P_{atm} = 101330\,Pa[/tex])
[tex]P_{gage} = P_{g}-P_{atm}[/tex] (2)
[tex]P_{gage} = 104000\,Pa-101330\,Pa[/tex]
[tex]P_{gage} = 2670\,Pa[/tex]
[tex]P_{gage} = 2.670\,kPa[/tex]
The gage of the gas is 2.670 kilopascals.
