Nitrogen at 300 K

Plate 14 speaks for itself: “The air in this room averages 1,700 km/h.”

The Physics

Molecules in a gas have a Maxwell–Boltzmann spread of speeds. For N₂ at 300 K the most probable, mean and rms speeds are all around 400–500 m/s; the mean, 476 m/s, is about 1 700 km/h.

v_p = √(2 k_B T / m)

• v_p: most probable speed, m s⁻¹
• k_B: Boltzmann constant, J K⁻¹
• T: temperature, K
• m: molecular mass (N₂: 4.65×10⁻²⁶ kg), kg
• ⟨v⟩: mean speed √(8k_BT/πm), m s⁻¹
• v_rms: root-mean-square speed √(3k_BT/m), m s⁻¹

N₂, T = 300 K: v_p ≈ 422, ⟨v⟩ ≈ 476, v_rms ≈ 517 m/s. Maxwell, 1860.

Honest caveat: The molecules move fast but random; the air as a whole stays still.

Sources

• J. C. Maxwell, Phil. Mag. 19, 19 (1860).

On the poster

Plate 014, “Nitrogen at 300 K”: the pixel-art plate with its slogan “The air in this room averages 1,700 km/h.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.