As encouraged to do by Prof. kstra, the following exercises investigate what the atmospheric properties were like at the altitude Mr. Baumgartner went to (38,969 m).
Whilst practising, the following picture of the standard temperature profile may be of help.
What is, according to the standard atmosphere, the temperature (in Kelvin) at 38,969 metres altitude?
What is, according to the standard atmosphere, the air pressure (in Pascal) at 38,969 metres altitude?
What is, according to the standard atmosphere, the air density (in kilograms per cubic metre) at 38,969 metres altitude?
To find the temperature, air pressure, and air density at an altitude of 38,969 meters according to the standard atmosphere, we can follow these steps:
Step 1: Determine the temperature at the given altitude.
The standard atmosphere provides a standard temperature profile. To find the temperature at 38,969 meters, we need to reference this profile. Unfortunately, you have mentioned a picture of the profile but have not provided it. Therefore, without the specific details of the profile, it is not possible to determine the temperature accurately. The standard temperature at this altitude can vary depending on the specific model used.
Step 2: Calculate the air pressure at the given altitude.
Similarly, without knowledge of the standard pressure profile, it is not possible to determine the air pressure accurately. The standard pressure at 38,969 meters also varies depending on the specific standard atmosphere model used.
Step 3: Determine the air density at the given altitude.
The air density can be calculated using the ideal gas law equation. The equation is as follows:
Density = Pressure / (Specific Gas Constant × Temperature)
Unfortunately, since we don't have the temperature or pressure values, we cannot find the air density at 38,969 meters altitude accurately.
In summary, without the specific details of the standard temperature and pressure profiles, we cannot provide the exact temperature, air pressure, or air density at an altitude of 38,969 meters according to the standard atmosphere.
Well, let's see what the standard atmosphere has to say about Mr. Baumgartner's lofty altitude of 38,969 meters.
According to the standard atmosphere, the temperature at that altitude is approximately -70.66 degrees Celsius, which is equal to 202.49 Kelvin. Brrr, it's a bit chilly up there!
Now, let's talk about air pressure. At 38,969 meters, the air pressure according to the standard atmosphere is around 257.98 Pascal. That's considerably lower than what we experience at sea level.
Lastly, let's calculate the air density. According to the standard atmosphere, at 38,969 meters the air density is roughly 0.041 kilograms per cubic meter. That's pretty thin air up there!
So, to summarize:
- The temperature is approximately 202.49 Kelvin.
- The air pressure is around 257.98 Pascal.
- The air density is roughly 0.041 kilograms per cubic meter.
Hope that brings some "altitude" to your day!
To find the temperature, air pressure, and air density at a specific altitude according to the standard atmosphere, we can use the mathematical model provided by the International Standard Atmosphere (ISA).
The standard atmosphere is a representation of the average vertical distribution of atmospheric properties such as temperature, pressure, and density. It serves as a reference for comparison and calculations.
To find the temperature at 38,969 meters altitude, we need to use the temperature lapse rate provided in the standard temperature profile. The standard temperature profile states that the temperature decreases at a rate of approximately 6.5 degrees Celsius per kilometer of altitude up to the tropopause, which is around 11 kilometers.
In this case, 38,969 meters is equal to 38.969 kilometers. So, the temperature decrease can be calculated as:
Temperature decrease = 6.5 * 38.969 = 253.0485 degrees Celsius
To convert the temperature to Kelvin, we need to add 273.15 to the Celsius value:
Temperature (Kelvin) = 253.0485 + 273.15 = 526.1985 Kelvin
Therefore, according to the standard atmosphere, the temperature at 38,969 meters altitude is approximately 526.2 Kelvin.
To find the air pressure at this altitude, we can use the barometric formula, which takes into account the altitude and the sea-level pressure. However, since the sea-level pressure is not mentioned in the question, we cannot calculate the exact air pressure without that information. The air pressure decreases exponentially with increasing altitude, and the specific altitude-pressure relationship depends on local conditions and other variables.
Similarly, to find the air density at 38,969 meters altitude, we would need additional information such as the sea-level density or additional equations that describe the relationship between altitude and density.
Without more information, we cannot calculate the exact air pressure or air density at 38,969 meters altitude according to the standard atmosphere.
The standard atmospheric model is an idealized representation of the Earth's atmosphere. It divides the atmosphere into five distinct layers based on temperature: troposphere, stratosphere, mesosphere, thermosphere, and exosphere.
1. Temperature at 38,969 meters altitude:
The altitude of 38,969 meters falls within the second layer of the atmosphere called the stratosphere, which begins at around 18,000 meters and ends at about 50,000 meters (18 to 50 km). In this layer, the temperature generally increases with altitude.
According to the U.S. Standard Atmosphere 1976 model, the temperature in the stratosphere can be calculated using the following formula:
T = T₀ + a(H - H₀)
where
T is the temperature at the given altitude (in Kelvin),
T₀ is the reference temperature at the beginning of the layer, H₀ is the reference altitude at the beginning of the layer, H is the given altitude, and a is the temperature lapse rate.
For the stratosphere (H₀ = 20000 m, T₀ = 216.65 K, a = 0.001 K/m):
T = 216.65 + 0.001*(38969-20000) = 216.65 + 0.001*18969 = 216.65 + 18.969 = 235.619 K
So the temperature at 38,969 meters altitude is approximately 235.619 K.
2. Air pressure at 38,969 meters altitude:
To calculate the air pressure at 38,969 meters altitude, we can use the following equation from the U.S. Standard Atmosphere 1976 model:
P = P₀ * (1 + a*(H-H₀)/T₀)^(-g*M/(R*a))
where
P is the air pressure at the given altitude (in Pascal),
P₀ is the reference air pressure at the beginning of the layer, g is the acceleration due to gravity (9.80665 m/s²), M is the molar mass of the air (0.028964 kg/mol), R is the ideal gas constant (8.31432 J/mol*K), and other terms are as defined before.
For the stratosphere (P₀ = 5.4749 x 10⁴ Pa):
P = 5.4749 x 10⁴ * (1 + 0.001*(38969-20000)/216.65)^(-9.80665*0.028964/(8.31432*0.001)) ≈ 3022.57 Pa
So the air pressure at 38,969 meters altitude is approximately 3022.57 Pa.
3. Air density at 38,969 meters altitude:
To calculate the air density at 38,969 meters altitude, we can use the equation:
ρ = P*M/(R*T)
where
ρ is the air density at the given altitude (in kg/m³) and other terms are as defined before.
For the stratosphere:
ρ = 3022.57*0.028964/(8.31432*235.619) ≈ 0.03526 kg/m³
So the air density at 38,969 meters altitude is approximately 0.03526 kg/m³.