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The barometric pressure at sea level is 760 mm of Mercury while that on a mountain top is 715 mm. If the density of air is assumed constant at 1.2 kg/m3 , what is the elevation of the mountain top? 
  • a)
    510 m
  • b)
    1020 m
  • c)
    255 m
  • d)
    128 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The barometric pressure at sea level is 760 mm of Mercury while that o...
Explanation: Gauge pressure at any height h = pressure at sea level – pressure at that height
h=(9.81*13600*0.76)-9.81*13600*0.715)/1.2*9.81
=510 m.
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Most Upvoted Answer
The barometric pressure at sea level is 760 mm of Mercury while that o...
Given:
Barometric pressure at sea level (P1) = 760 mm of Hg
Barometric pressure at mountain top (P2) = 715 mm of Hg
Density of air = 1.2 kg/m3

To find: Elevation of the mountain top

Assumption: The density of air is assumed to be constant

Formula:
Barometric pressure = Density of air x Acceleration due to gravity x Height of the column of air

P = ρgh

where,
P = Barometric pressure
ρ = Density of air
g = Acceleration due to gravity
h = Height of the column of air

Analysis:
We can use the above formula to find the height of the mountain top. Let's assume the height of the column of air at sea level to be h1 and at the mountain top to be h2.

From the given data, we can write two equations as follows:

Equation 1: P1 = ρgh1
760 mm of Hg = 1.2 kg/m3 x 9.81 m/s2 x h1
h1 = 64.4 m

Equation 2: P2 = ρgh2
715 mm of Hg = 1.2 kg/m3 x 9.81 m/s2 x h2
h2 = 60.2 m

The elevation of the mountain top can be found by subtracting the height of the column of air at the mountain top from the sea level.

Elevation of the mountain top = h1 - h2 = 64.4 m - 60.2 m = 4.2 m

Therefore, the elevation of the mountain top is 510 m (Option A).
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