TWO IDENTICAL mano METERS ARE FILLED WITH MERCURY. THE mano METERS ARE PLACED IN A CLOSED PRESSURIZED BOX CONTAINING AIR AT 1,000 TORR PRESSURE. ONE manometer CONTAINS GAS a, AND THE OTHER GAS B. WHAT IS THE DIFFERENCE BETWEEN THE PRESSURES OF THE TWO GASES? THE DENSITY IS 13.6 G/CM^3

Question

TWO IDENTICAL mano METERS ARE FILLED WITH MERCURY. THE mano METERS ARE PLACED IN A CLOSED PRESSURIZED BOX CONTAINING AIR AT 1,000 TORR PRESSURE. ONE manometer CONTAINS GAS a, AND THE OTHER GAS B. WHAT IS THE DIFFERENCE BETWEEN THE PRESSURES OF THE TWO GASES? THE DENSITY IS 13.6 G/CM^3

a.) 10 TORR
B.)30 TORR
C.)60 TORR
D.) 90 TORR
E.) 120 TORR

Answer 1

To find the difference between the pressures of gases A and B in the manometers, let's consider the principle of Pascal's Law.

Pascal's Law states that the pressure applied to an enclosed fluid is transmitted equally in all directions. In this case, the fluid is mercury.

Since the two manometers are identical and filled with mercury, we know that the pressure applied to the mercury in both manometers is the same, which is the pressure inside the closed pressurized box containing air (1,000 Torr).

Now, the height difference between the two levels of the mercury in the manometers is what we need to determine.

We can use the relationship between pressure, height (h), and density (ρ) for a liquid:

Pressure = density × gravitational acceleration × height

In this case, the density of mercury is given as 13.6 g/cm^3. However, we need to convert it to units of Torr.

1 g/cm^3 = 736 Torr (approximately)

Now, let's assume the height difference in the manometers as 'x' cm.

So, the pressure difference between the two manometers is:

Pressure difference = pressure of gas A - pressure of gas B
= (density of mercury × acceleration due to gravity × height of gas A) - (density of mercury × acceleration due to gravity × height of gas B)
= density of mercury × acceleration due to gravity × (height of gas A - height of gas B)

Since the density and acceleration due to gravity are constant, the pressure difference is directly proportional to the difference in the heights of the mercury levels in the manometers.

Now, converting the density of mercury to Torr:

13.6 g/cm^3 = 13.6 × 736 Torr = 10,049.6 Torr/cm

Therefore, the answer is:

A) 10 TORR.

The pressure difference between gases A and B in the manometers is 10 Torr.