Question

A vessel that contains a gas has two pressure gauges attached to it. One contains liquid mercury, and the other an oil such as dibutyl phthalate. The difference in levels of mercury in the two arms of the mercury gauge is observed to be 9.50 cm.

Given density of mercury is 13.60 g cm², density of oil is 1.045 g cm², acceleration due to gravity is 9.806 m s².
(a) What is the pressure of the gas?
(b) What is the difference in height of the oil in the two arms of the oil pressure gauge?

Answer 1

Pressure of the gas = 12669 (Pa) and height of the oil is 1,24 meters

Step-by-step explanation:

First, we can use the following sketch for an easy understanding, in the attached image we can see the two pressure gauges the one with mercury to the right and the other one with oil to left. We have all the information needed in the mercury pressure gauge, so we can determine the pressure inside the vessel because the fluid is a gas it will have the same pressure distributed inside the vessel (P1).

Since P1 = Pgas, we can use the same formula, but this time we need to determine the height of the column of oil in the pressure gauge.

The result is that the height of the oil column is higher than the height of the one that uses mercury, this is due to the higher density of mercury compared to oil.

Note: the information given in the units of the fluids is not correct because the density is always expressed in units of (mass /volume)