Height by pressure and density

Question

During a hike in the mountains, an air pressure of 107 kPa is first noted, after which it drops to 97 kPa after mounting a mountain peak. How many height meters were felled during the ascent? Assume that the average density of air is 1.2 kg / m3.

Answer 1

Set the difference in pressure equal to ρgh and solve for h. Recall that 1 Pa = 1 N/m².

Δp = ρgh

h = Δp / (ρg)

Δp = (107,000 - 97,000) N/m²

ρ = 1.2 kg/m³

g = 9.8 m/s²

Plug in the numbers. In these units, h will come out in meters.