A container filled with gas is connected to an open-end manometer that is filled with mineral oil.The pressure in the gas container is 763 mm Hg and atmospheric pressure is 734 mm Hg.How high will the level rise in the manometer if the densities of Hg and mineral oil are 13.6 g/mL and 0.822 g/mL respectively?
A) 1.75 mm
B) 23.8 mm
C) 29.0 mm
D) 480 mm

Question

Quizplus · Accepted Answer

The difference in pressure between the gas and the atmosphere is 763 mm Hg - 734 mm Hg = 29 mm Hg. To convert this pressure difference into a height of mineral oil, we use the fact that the pressure exerted by a column of fluid is given by $P = \rho gh$, where $P$ is the pressure, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the height of the fluid column. Since the densities of mercury and mineral oil are given, we can set up a ratio using the fact that the pressure exerted by the mercury column (29 mm Hg) is equal to the pressure that will be exerted by the mineral oil column. Given the density of mercury is 13.6 g/mL and the density of mineral oil is 0.822 g/mL, the height of the mineral oil column can be calculated as follows:$$\frac{29 \, \text{mm Hg} \times 13.6 \, \text{g/mL}}{0.822 \, \text{g/mL}} \approx 480 \, \text{mm}$$Thus, the correct answer is D, 480 mm.

A Container Filled with Gas Is Connected to an Open-End