The air pressure at a given altitude can be estimated using the International Standard Atmosphere (ISA) model. At 38,969 meters, which is approximately the altitude of the stratosphere, the air pressure decreases significantly compared to sea level.
Using the barometric formula, the pressure \( P \) at altitude \( h \) can be approximated using the standard atmospheric conditions and is given by:
\[ P = P_0 \cdot \left(1 - \frac{L \cdot h}{T_0}\right)^{\frac{g_0 \cdot M}{R \cdot L}} \]
Where:
- \( P_0 \) = pressure at sea level (approximately 101325 Pa)
- \( L \) = temperature lapse rate (approximately 0.0065 K/m for the troposphere)
- \( T_0 \) = sea level standard temperature (approximately 288.15 K)
- \( g_0 \) = acceleration due to gravity (approximately 9.80665 m/s²)
- \( M \) = molar mass of Earth's air (approximately 0.029 kg/mol)
- \( R \) = ideal gas constant (approximately 8.314 J/(mol·K))
However, at high altitudes like 38,969 meters, temperature and lapse rate change. Generally, the value for air pressure at this altitude can be approximated using standard references.
From ISA tables, the pressure at 38,969 meters is about 0.0002336 atm. To convert this to Pascals:
\[ P \approx 0.0002336 \times 101325 \approx 23.6 , \text{Pa} \]
So the air pressure at an altitude of 38,969 meters is approximately 23.6 Pascals.