Mercury is 13.6 times as dense as liquid water. What would be the reading of a water-filled barometer at normal atmospheric pressure, 760. mmHg? A)1.03 × 10 ³ torr B)1.03 × 10 ³Pa C)1.03 × 10 ³mm height of water column D)1.03 × 10 ³cm height of water column E)13.6 atm

Question

Quizplus · Accepted Answer

The height of a water barometer column is directly proportional to atmospheric pressure. Therefore, the reading of the barometer is determined by the height of the water column, which is given by the equation:
P = hρg
where P is the atmospheric pressure, h is the height of the water column, ρ is the density of water, and g is the acceleration due to gravity.

Since mercury is 13.6 times as dense as water, its density is:
ρ_hg = 13.6ρ_water

Substituting the given data, we have:
P = hρ_waterg
P = (h/13.6)ρ_hgg

At normal atmospheric pressure, P = 760 mmHg (or torr). Substituting this value, we get:
760 mmHg = (h/13.6)×(13.6 g/cm³)×(981 cm/s²)
h = (760×13.6)/(981) cm
h ≈ 104 cm

Therefore, the height of the water column in the barometer would be approximately 104 cm, which is equivalent to 1.03×10¹³ mm. The best choice is option D, 1.03×10¹³ cm height of water column.

Mercury Is 13