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
To find the difference between the pressures of gases A and B, we need to calculate the pressure difference between the two manometers.
Given:
Density of mercury = 13.6 g/cm^3
Air pressure in the closed box = 1000 Torr
Since the two manometers are filled with mercury, we can use the height difference between the two mercury columns to find the pressure difference.
Let's assume the height of the mercury column in manometer A is h1 and the height of the mercury column in manometer B is h2.
The pressure difference is given by the formula:
Pressure difference = density × gravity × (h2 - h1)
Since density and gravity are constants, we only need to calculate the height difference (h2 - h1).
As both manometers are identical, the height of the mercury columns in both manometers will be the same.
Therefore, the pressure difference will be 0 Torr.
Therefore, the answer is:
A) 10 Torr (as the pressure difference is 0 Torr)
To find the difference between the pressures of the two gases, you need to consider the difference in the height of the mercury columns in the two manometers.
Here's how you can solve the problem step by step:
1. Start by understanding the principles of using a manometer. A manometer measures the difference in pressure between two substances, in this case, gas A and gas B. The height difference of the mercury columns in each manometer corresponds to the difference in pressure between the gases.
2. Mercury is a dense liquid with a known density of 13.6 g/cm^3. This information will be used later to convert the height difference to a pressure difference.
3. Since both manometers are identical and filled with mercury, the pressure exerted by the mercury in each column will be equal. This means that the height difference of the mercury columns in the manometers will directly correspond to the pressure difference between the two gases.
4. Given that the air pressure in the closed box is 1,000 Torr, if gas A and gas B have different pressures, their manometers' mercury columns will differ in height.
5. Look at the options provided: 10 Torr, 30 Torr, 60 Torr, 90 Torr, and 120 Torr. These values represent the potential height differences of the mercury columns in the manometers.
6. Convert the height difference to pressure using the density of mercury. The pressure exerted by a column of mercury is proportional to its height and the density of the mercury. The formula for pressure is P = ρgh, where P is pressure, ρ is density, g is the acceleration due to gravity, and h is the height.
7. Plugging in the given density of mercury (13.6 g/cm^3), you can calculate the pressure difference corresponding to each option in the question.
For example, let's consider option A) 10 Torr.
Given that the density of mercury is 13.6 g/cm^3, convert this value to g/mm^3 (since the Torr unit corresponds to mmHg).
13.6 g/cm^3 = 13.6 g/mm^3.
Now, divide the pressure difference (10 Torr) by the density to obtain the height difference.
(10 Torr) / (13.6 g/mm^3) = 0.735 mm.
This means that if the pressure difference between the gases is 10 Torr, the height difference between the mercury columns would be 0.735 mm.
Repeat this calculation for options B, C, D, and E to see if any of them match the calculated height difference.
By going through the calculations for each option, you will find that the correct answer is option B) 30 Torr, as it yields the closest height difference to the calculated value.