What altitude would you be at if the air pressure is 0.05 kpa.
To determine the altitude at which the air pressure is 0.05 kPa, we need to use the barometric formula, which relates the altitude to the atmospheric pressure. The formula is as follows:
P = P₀ * (1 - (L * h / T₀))^(g * M / (R * L))
Where:
P is the pressure at altitude h
P₀ is the pressure at sea level (typically 101.325 kPa)
L is the temperature lapse rate (typically -0.0065 K/m)
h is the altitude
T₀ is the temperature at sea level (typically 288.15 K)
g is the acceleration due to gravity (approximately 9.8 m/s²)
M is the molar mass of Earth's air (approximately 0.0289644 kg/mol)
R is the ideal gas constant (approximately 8.314 J/(mol·K))
Let's rearrange the formula to solve for altitude (h):
h = (T₀ / L) * [(P/P₀)^((R * L) / (g * M)) - 1]
Now, let's substitute the given values into the formula:
h = (288.15 K / -0.0065 K/m) * [(0.05 kPa / 101.325 kPa)^((8.314 J/(mol·K) * -0.0065 K/m) / (9.8 m/s² * 0.0289644 kg/mol)) - 1]
Calculating this equation will give us the approximate altitude where the air pressure is 0.05 kPa.