The pressure exerted by a column of liquid is equal to the product of the height of the column times the gravitational constant times the density of the liquid, P = ghd. How high a column of water (d = 1.0 g/mL) would be supported by a pressure that supports a 713 mm column of mercury (d = 13.6 g/mL)? A) 1.2 × 10⁴mm B) 9.7 × 10³mm C) 14 mm D) 713 mm E) 52 mm

Question

Quizplus · Accepted Answer

First, we need to find the pressure that supports the 713 mm column of mercury. Using the formula given in the problem, we have:
P = ghd
P = (9.8 m/s^2) (0.713 m) (13.6 × 10^3 kg/m^3)
P = 9.7 × 10^4 Pa

Now, we can use this pressure to find the height of the water column using the same formula:
P = ghd
h = P/(gd)
h = (9.7 × 10^4 Pa)/[(9.8 m/s^2) (1.0 × 10^3 kg/m^3)]
h = 9.7 × 10^3 m
h = 9.7 × 10^6 mm
h ≈ 9.7 × 10^6 ≈ 1 × 10^7 mm
Therefore, the height of the water column that would be supported by the given pressure is 9.7 × 10^6 mm, which is closest to answer choice B (9.7 × 10^13 mm).

The Pressure Exerted by a Column of Liquid Is Equal