Question

Question • (a) Given that the empty space above the mercury column in barometer Q is a vacuum, state the atmospheric pressure as measured by this barometer in pascals if the density of mercury in the tube F is 14x10³ kg/m3. Take gravity to be 10N/kg (b) What is the pressure at point E? Give your answer in mm Hg and show essential working on how you arrive at your answer. (c) If barometer P is brought up to the mountains, gh what do you expect to happen to the column of vacuum in P? Give a reason for your answer​

Answer 1

Step-by-step explanation:

(a) The atmospheric pressure as measured by the barometer Q can be calculated using the formula:

P = ρgh

where P is the pressure, ρ is the density of mercury, g is the acceleration due to gravity, and h is the height of the mercury column in the tube F. Since the space above the mercury column is a vacuum, there is no pressure exerted on the top of the column. Therefore, the pressure measured by the barometer is equal to the atmospheric pressure, which is given by:

P = ρgh = (14 × 10³ kg/m³) × (0.76 m) × (10 N/kg) = 106,240 Pa

Therefore, the atmospheric pressure as measured by the barometer Q is 106,240 Pa.

(b) The pressure at point E can be calculated using the formula:

P = ρgh

where P is the pressure, ρ is the density of mercury, g is the acceleration due to gravity, and h is the height of the mercury column above point E. From the diagram, we can see that the height of the mercury column above point E is 0.86 m. Therefore, the pressure at point E is:

P = ρgh = (14 × 10³ kg/m³) × (0.86 m) × (9.81 N/kg) = 120,965 Pa

To convert this pressure to mm Hg, we can use the conversion factor:

1 Pa = 0.0075 mm Hg

Therefore, the pressure at point E is:

P = (120,965 Pa) × (0.0075 mm Hg/Pa) ≈ 907 mm Hg

(c) When barometer P is brought up to the mountains, the atmospheric pressure decreases. As a result, the height of the mercury column in the tube will also decrease. This is because the pressure difference between the top and bottom of the column is proportional to the height of the column, according to the formula P = ρgh. As the atmospheric pressure decreases, the pressure at the top of the column decreases, and the column of mercury will fall until the pressure difference between the top and bottom of the column is equal to the new atmospheric pressure. Therefore, we expect the column of vacuum in P to decrease in height as the barometer is brought up to the mountains.