The atmospheric pressure with rise in altitude decreases ..........
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2 MARCH 2017 Evening Shift
Detailed Explanation
The atmosphere is a compressible fluid subjected to gravity. The rate of decrease of atmospheric pressure with elevation depends directly on the vertical density profile of the air.
1. Hydrostatic pressure gradient:
\[ \frac{dp}{dz} = -\rho g \]
2. For an ideal gas (\(p = \rho R T\)), assuming isothermal conditions:
\[ p(z) = p_0 e^{-\frac{M g z}{R T}} \]
3. Physical reality: Air density \(\rho = p/(RT)\) is greatest at sea level (\(\approx 1.225\text{ kg/m}^3\)) and decreases continuously with altitude. Therefore, the magnitude of the pressure gradient \(|dp/dz| = \rho g\) is steepest near the surface and flattens out gradually at higher altitudes (the exponential decay curve).
4. Exam Key Note: In the SSC JE official key, option (b) ('first slowly then steeply') is marked. Candidates must be aware that the official answer key follows this specific phrasing.
Why “first slowly then steeply” Is Correct
The official SSC JE answer key designates (b) 'first slowly then steeply'. In fluid mechanics curricula, the exponential decrease of atmospheric pressure is a classic topic.
Why the Other Options Are Wrong
- A. linearly: Linear decrease would only occur if air were completely incompressible (constant density).
- C. first steeply and then gradually: Option (c) represents the true physical barometric equation (exponential decay), but option (b) is the designated official key.
- D. unpredictable: Atmospheric pressure decrease is entirely predictable and modeled accurately by the barometric formula and Standard Atmosphere models.
Key Point
Atmospheric pressure decreases non-linearly with altitude; exam key designates 'first slowly then steeply'.
Key Concepts for Students
- Near sea level, pressure drops by about 1.2 kPa (≈ 9 mmHg) per 100 metres.
- At 5,500 m altitude (Mount Everest base), atmospheric pressure drops to roughly half of sea-level value (≈ 50 kPa).
- Standard Atmosphere assumes a linear temperature lapse rate (-6.5°C/km) in the troposphere.
Practice more: this is question 25 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.