An airplane is flying at an altitude of 2,000 m with a speed of 216 m/s. What is the pressure of air outside the plane?
To find the pressure of the air outside the plane, we can use the concept of atmospheric pressure. The pressure at any point in the atmosphere is determined by the weight and density of the air above it.
One way to calculate the pressure is to use the equation:
Pressure = Density * Gravity * Height
In this case, the height is the altitude of the plane.
First, we need to find the density of air at the given altitude. Air density decreases with increasing altitude. We can use the barometric formula, which describes how air pressure decreases with height.
The barometric formula is given by:
Pressure = Pressure₀ * (1 - (L * Altitude) / Temperature₀)^(g / (R * L))
Where:
- Pressure is the pressure at the given altitude
- Pressure₀ is the pressure at sea level (101325 Pa)
- L is the temperature lapse rate (0.0065 K/m)
- Altitude is the height above sea level
- Temperature₀ is the temperature at sea level (288.15 K)
- g is the acceleration due to gravity (9.81 m/s²)
- R is the gas constant for air (8.314 J/(mol·K))
Substituting the given values:
- Pressure₀ = 101325 Pa
- L = 0.0065 K/m
- Altitude = 2000 m
- Temperature₀ = 288.15 K
- g = 9.81 m/s²
- R = 8.314 J/(mol·K)
We can calculate the pressure at the given altitude using the barometric formula.