Questions: Atmospheric Pressure and Altitude

Question 1

At approximately what altitude does atmospheric pressure fall to roughly half its sea-level value (~50,700 Pa)?

• A. ~2 km
• B. ~5.5 km
• C. ~10 km
• D. ~20 km

Answer: (B)

Pressure halves approximately every 5.5 km in the lower atmosphere. At sea level pressure is ~101,325 Pa; at ~5.5 km it is ~50,700 Pa; at ~11 km it is ~25,350 Pa. This exponential decrease follows from the hydrostatic equation combined with the ideal gas law: because denser air near the surface supports more weight per unit distance, pressure drops faster near the surface than at altitude.

Question 2

At high altitude, breathing becomes difficult primarily because the percentage of oxygen in the air decreases below 21%.

• T. True
• F. False

Answer: False

This is a widespread misconception. The composition of dry air remains approximately 78% nitrogen and 21% oxygen up to about 80 km altitude — well above the range relevant to mountaineering or aviation. Difficulty breathing at altitude is caused by the lower total atmospheric pressure, which means the partial pressure of oxygen (21% of total pressure) is lower, so less O₂ enters the bloodstream with each breath. The fraction is unchanged; the absolute amount per breath is reduced.

Question 3

Explain why atmospheric pressure decreases faster near sea level than at high altitude, even though the pressure-altitude relationship is described as exponential.

Model answer: Near sea level, air density is high, so a thin layer of air has a large weight per unit area, causing pressure to drop steeply with even a small gain in altitude. At high altitude, the air is already thin (low density), so each additional kilometer of atmosphere contributes less weight. The hydrostatic equation (dP/dz = −ρg) shows that the pressure gradient is proportional to density — and density itself decreases with altitude — producing the characteristic exponential decay where the rate of decrease is always proportional to the current pressure.

This tests whether students understand that exponential decay means the rate of change is proportional to the current value. The misconception is to picture pressure decreasing at a constant rate. In reality, the hydrostatic equation and ideal gas law together yield P(z) = P₀·exp(−z/H) where H ≈ 8.5 km is the scale height, so each scale-height gain in altitude reduces pressure by the same factor (≈1/e), not by the same absolute amount.