Video: Determining the Relation between the Atmospheric Pressure and the Pressure of a Gas in a Liquid Column Manometer

The diagram shows a liquid column manometer connected at one end to a gas reservoir and at the opposite end to the atmosphere. Which of the following correctly relates the pressure of the gas and the pressure of the atmosphere, 𝑃_gas and 𝑃_atm? [A] 𝑃_gas = 𝑃_atm [B] 𝑃_gas < 𝑃_atm [C] 𝑃_gas > 𝑃_atm

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Video Transcript

The diagram shows a liquid column manometer connected at one end to a gas reservoir and at the opposite end to the atmosphere. Which of the following correctly relates the pressure of the gas and the pressure of the atmosphere, 𝑃 gas and 𝑃 atmosphere? (A) 𝑃 gas equals 𝑃 atmosphere. (B) 𝑃 gas is less than 𝑃 atmosphere. (C) 𝑃 gas is greater than 𝑃 atmosphere.

We need to recall that a manometer is a U-shaped tube filled with a liquid that is used to measure the pressure of a gas. In a manometer, the pressure on one side, in this case, the pressure of the atmosphere, pushes down on the liquid on one end of the tube. And the pressure on the other end of the tube, in this case, the pressure from the gas reservoir, pushes down on the liquid on the other end. The relative pressure of the gases will determine what height the liquid will go to on either end of the tube.

We can see in our diagram that we have a difference in height between the liquid on one end of the tube to the liquid on the other end of the tube. In this case, the height of the liquid that’s in the tube attached to the atmosphere is lower than the height of the liquid in the tube that’s attached to the gas reservoir. This implies that the pressure the atmosphere puts on the liquid provides a greater push than the pressure the gas reservoir puts on the liquid. Or another way to put it would be that the pressure of the atmosphere is greater than the pressure of the gas in the gas reservoir. Therefore, we can say that when we compare the pressure of the gas in the gas reservoir to the pressure of the atmosphere that the pressure of the gas is going to be less than the pressure of the atmosphere or answer choice (B).

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