(II) An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is
(b) 7.6 cm lower, than the mercury in the tube connected to the tank? See Fig. 13–10a.
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Verified step by step guidance

1. Identify the given values: atmospheric pressure (P_atm) is 1040 mbar, and the height difference in the mercury levels (h) is 7.6 cm.
2. Convert the atmospheric pressure from mbar to pascals (Pa) since 1 mbar = 100 Pa. Therefore, P_atm in pascals is 1040 mbar * 100 Pa/mbar.
3. Understand that the pressure in the tank (P_tank) is higher than the atmospheric pressure by the amount of pressure corresponding to the mercury column height difference. The pressure difference due to the mercury column can be calculated using the formula $\mathrm{\Delta }P=\rho gh$, where $\rho$ is the density of mercury, $g$ is the acceleration due to gravity, and $h$ is the height difference.
4. Convert the height difference from cm to meters for consistency in units, as 1 cm = 0.01 m.
5. Calculate the absolute pressure in the tank using the formula $P_{tank}=P_{atm}+\mathrm{\Delta }P$. This will give the pressure in the tank in pascals.

Key Concepts

Manometer Principle

A manometer is a device used to measure pressure by balancing a column of liquid against the pressure to be measured. In an open-tube manometer, the difference in height between two columns of liquid (usually mercury) indicates the pressure difference between the gas in the tank and the atmospheric pressure. The height difference is directly related to the pressure exerted by the gas.

Absolute Pressure

Absolute pressure is the total pressure exerted on a system, measured relative to a perfect vacuum. It is calculated by adding the atmospheric pressure to the gauge pressure (the pressure relative to atmospheric pressure). In this scenario, the absolute pressure in the oxygen tank can be determined by considering the height difference in the mercury column and the atmospheric pressure.

Pressure Conversion

Pressure is often measured in various units, such as pascals (Pa), millibars (mbar), and atmospheres (atm). To convert between these units, it is essential to know the relationships: 1 mbar equals 100 Pa. In this problem, converting the atmospheric pressure from mbar to pascals is necessary to find the absolute pressure in the oxygen tank accurately.