The Thinning Sky

Plate 91 speaks for itself: “At Everest, a third of the air remains.”

The Physics

Air pressure falls with height as the weight of the air above shrinks. The International Standard Atmosphere puts the summit of Everest at about 31 kPa, under a third of sea level.

p = p₀ (1 − L h / T₀)^(g M / R L)

• p: pressure at height h, Pa
• p₀: sea-level pressure 101 325 Pa
• L: lapse rate 0.0065 K m⁻¹
• h: altitude, m
• T₀: sea-level temperature 288.15 K
• g: 9.80665 m s⁻²
• M: molar mass of air 0.0289644 kg mol⁻¹
• R: gas constant 8.314 J mol⁻¹ K⁻¹

At 8849 m the ISA gives ≈ 31.4 kPa. That is a model value; real pressure varies.

Honest caveat: Measured summit pressure is usually somewhat higher, about 33–34 kPa, because the tropical air column is warmer.

Sources

• ISO 2533:1975, Standard Atmosphere.
• J. B. West, J. Appl. Physiol. 86, 1062 (1999).

On the poster

Plate 091, “The Thinning Sky”: the pixel-art plate with its slogan “At Everest, a third of the air remains.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.