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 is equal to 𝑃
atmosphere. (B) 𝑃 gas is greater than 𝑃
atmosphere. (C) 𝑃 gas is less than 𝑃
atmosphere.
We need to remember that a
manometer is a U-shaped tube filled with a liquid that is used to measure the
pressure of a gas. For this problem, one end of the
tube is opened up to the atmosphere, and the other end is connected to a gas
reservoir. The atmosphere applies a pressure
𝑃 atmosphere onto the liquid in one side of the tube. On the other side of the tube, the
gas from the gas reservoir also applies a pressure onto the liquid. We can compare the pressure of the
atmosphere to the pressure of the gas by looking at the height that the liquid goes
to on either end of the tube.
We need to recall that the pressure
of a fluid 𝑃 is equal to the density of the fluid 𝜌 times the acceleration due to
gravity 𝑔 times the height of the fluid ℎ. If we wanna compare the two
pressures, we need to analyze the height that the liquid goes to on either end of
the tube. Because the liquid rises to the
same height on either end of the tube, this implies that both ends of the tube apply
the same amount of pressure. Or put another way, the pressure
that the gas applies on the liquid is gonna be equal to the pressure that the
atmosphere applies on the liquid. Therefore, we can say answer choice
(A) is correct. The pressure of the gas from the
gas reservoir is equal to the pressure from the atmosphere.
