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------------------------------------------------ The atmospheric pressures at the top and the bottom of a mountain are read by a barometer to be 93.8 kPa and 100.5 kPa, respectively. If the average density of air is 1.25 kg/m³, what is the height of the mountain (in meters)?

The atmospheric pressures at the top and the bottom of a mountain are read by a barometer to be 93.8 and 100.5 kPa. If the average density of air is 1.25 kg/m3, The height of the mountain is approximately 546.31 meters.

To find the height of the mountain using the given atmospheric pressures at the top and bottom, we can use the hydrostatic pressure formula:
ΔP = ρgh
Where ΔP is the difference in atmospheric pressure, ρ is the average air density, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height of the mountain.
First, calculate the difference in atmospheric pressure:
ΔP = P_bottom - P_top = 100.5 kPa - 93.8 kPa = 6.7 kPa
Convert kPa to Pa:
ΔP = 6.7 kPa × 1000 = 6700 Pa
Now, rearrange the formula to find the height of the mountain:
h = ΔP / (ρg)
Plug in the given values:
h = 6700 Pa / (1.25 kg/m³ × 9.81 m/s²) ≈ 546.31 meters
The height of the mountain is approximately 546.31 meters.

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