How does the atmospheric pressure (AP) vary with respect to the altitude?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 05/06/2024 (09am-11am)
Detailed Explanation
Atmospheric pressure at any height is created by the weight of the air column resting above that elevation. As altitude increases, the height of the remaining overlying atmosphere diminishes and the air becomes less dense.
From the hydrostatic equation for a compressible atmosphere:
\[ \frac{dp}{dz} = -\rho g \]
Since density \(\rho > 0\) and gravity \(g > 0\), the vertical pressure gradient is always negative: pressure monotonically decreases with height \(z\).
Why “AP decreases with increase in altitude” Is Correct
As elevation increases, less air remains overhead to exert downward gravitational force. Consequently, atmospheric pressure decreases continuously with increasing altitude.
Why the Other Options Are Wrong
- A. AP either increases or decreases depending only on temperature: Atmospheric pressure always decreases with altitude; temperature variations alter the lapse rate but do not reverse this decrease.
- C. AP increases with increase in altitude: Pressure never increases with altitude because the weight of the overlying air column strictly decreases.
- D. It remains constant at all heights: Atmospheric pressure varies significantly with elevation, dropping to roughly half its sea-level value at 5.5 km.
Key Point
Atmospheric pressure decreases monotonically with altitude due to reduced weight of the air column overhead.
Key Concepts for Students
- Hydrostatic equation: dp/dz = -ρg.
- In the troposphere, standard temperature drops with altitude at approximately 6.5°C/km.
- Barometric formula models exponential decrease in pressure for an isothermal atmosphere: p = p₀ exp(-gz/RT).
Practice more: this is question 8 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.