Answer:
H = 0.00058m = 0.58mm of Mercury
<em><u>h = 160m for popping at 8000m</u></em>
Explanation:
Air density decreases with altitude (increasing height).
At sea level air density = 1.22kg/m^3
while at 3000m above it is approximately 0.8 kg/m^3
ASSUMPTION:
we neglect the change in density across 100m vertically
density of mercury = 13600kg/m ^3
we equate the pressure for mercury and air
AIR(pgh) = Mercury(pgh)
0.8 * g * 100 = 13600 * g * H
H = 0.00058m = 0.58mm of Mercury
At even farther heights, the air density further drops
at 8000m above it is 0.52kg/ m^3 (source:https://www.engineeringtoolbox.com/standard-atmosphere-d_604.html)
***for the ear to pop again, it has to experience same change in pressure as of at 3000m
Change in P for AIR at 3000m = Change in P for AIR at 8000m
ASSUMPTION : gravitational acceleration does not change with altitude
pgh = pgh
0.8 * g * 100 = .5 * g *<em><u>h</u></em>
<em><u>h = 160m</u></em>
