An aircraft flies at an altitude of 30,000 feet. Determine the air temperature (in [K]), air pressure (in [Pa]) and air density (in [kg/m3]) at this altitude, according to the standard atmosphere.
T = 228.714
P = 30199.04
density = 0.4643
45 degree Celsius
So stuck on this question....
Well, at an altitude of 30,000 feet, the air temperature can get quite chilly. It's like the Earth's way of giving you the cold shoulder. According to the standard atmosphere, the air temperature at this altitude is approximately -49 degrees Celsius. Brrrrr, it's getting a bit chilly in here, isn't it?
Now, when it comes to air pressure, at 30,000 feet, things can get a bit light-headed. The air pressure in this region of the atmosphere is estimated to be around 3,156 Pascals. So, you might feel a bit light in the head, but just remember to keep your feet on the ground!
Finally, let's talk about air density. At an altitude of 30,000 feet, the air density is thinner than a thread of spider silk hanging on a windy day. It's around 0.364 kilograms per cubic meter. So, you'll be experiencing some pretty thin air up there, almost like a clown juggling feathers!
But hey, don't let these numbers bring you down! Just remember, even though the air might be cold, the pressure light, and the density thin, you've reached some great heights. So, keep soaring high like a jokester in the sky!
To determine the air temperature, air pressure, and air density at an altitude of 30,000 feet according to the standard atmosphere, we can use the International Standard Atmosphere (ISA) model. The ISA model provides a set of standard conditions for various altitudes.
1. Air temperature (T):
According to the ISA model, the lapse rate for temperatures above the troposphere is a constant -0.0065 Kelvin per meter. Since 30,000 feet is approximately 9,144 meters, we can calculate the temperature using the following equation:
T = T0 + (lapse rate * altitude)
Here, T0 is the standard temperature at sea level which is 288.15 Kelvin. Plugging in the values:
T = 288.15 + (-0.0065 * 9144) = 219.68 K
Therefore, the air temperature at an altitude of 30,000 feet is approximately 219.68 Kelvin.
2. Air pressure (P):
The pressure at different altitudes in the ISA model can be calculated using the following equation:
P = P0 * (1 + (lapse rate * altitude / T0))^(-g / (lapse rate * R))
Here, P0 is the standard pressure at sea level which is 101,325 Pascals. The lapse rate is -0.0065 Kelvin per meter. The acceleration due to gravity (g) is 9.80665 m/s^2, and the specific gas constant (R) is 287.05 J/(kg·K).
Plugging in the values:
P = 101325 * (1 + (-0.0065 * 9144 / 288.15))^(-9.80665 / (-0.0065 * 287.05)) = 10,042.22 Pa
Therefore, the air pressure at an altitude of 30,000 feet is approximately 10,042.22 Pascals.
3. Air density (ρ):
The air density can be calculated using the ideal gas law:
ρ = P / (R * T)
Here, P is the pressure calculated earlier, R is the specific gas constant, and T is the temperature calculated earlier. Plugging in the values:
ρ = 10,042.22 / (287.05 * 219.68) = 0.425 kg/m^3
Therefore, the air density at an altitude of 30,000 feet is approximately 0.425 kg/m3.
Keep in mind that the values obtained using the standard atmosphere model are approximate and represent average conditions. Actual atmospheric conditions can vary due to weather patterns and other factors.
Check if you are using these formulas for pressure and temperature. If so, go ahead and feed your calcxulator. If not, please post formulas you use.
https://en.wikipedia.org/wiki/Barometric_formula
You may post your answers for checking if you wish, but specify formulas you were using.