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/m]) at this altitude, according to the standard atmospher
Why did the airplane bring a jacket? Because it was planning to chill at 30,000 feet! But fear not, I'll satisfy your curiosity.
According to the standard atmosphere model, at an altitude of 30,000 feet (or 9,144 meters), the air temperature is approximately -56.5 degrees Celsius or 216.65 Kelvin. As for the air pressure, it's around 11,165.7 Pascal (Pa). Finally, the air density at this altitude is approximately 0.3636 kilograms per cubic meter (kg/m³).
Now that you have the facts, you can impress your friends with some high-flying trivia!
According to the standard atmosphere model, the temperature, pressure, and density values at different altitudes can be calculated. At an altitude of 30,000 feet, the values are as follows:
1. Air Temperature:
The standard lapse rate is 1.98°C per 1,000 feet, or 6.49°C per 1,000 meters. At sea level, the standard temperature is 15°C or 288.15 K. To find the temperature at 30,000 feet, we calculate the change in temperature:
(30,000 feet / 1,000 feet) * 1.98°C = 59.4°C
Now, we add this change to the standard temperature:
Standard Temperature + Change in Temperature = 288.15 K + 59.4°C = 347.55 K
Therefore, the air temperature at an altitude of 30,000 feet is approximately 347.55 Kelvin.
2. Air Pressure:
The standard atmospheric pressure at sea level is 101,325 Pa. According to the standard atmosphere model, the pressure decreases with increasing altitude. The pressure is approximated using the equation:
Pressure = Standard Pressure * (1 - Lapse Rate * Altitude / Temperature)^ (Gravity / (Lapse Rate * Gas Constant))
Plugging in the values:
Lapse Rate = 1.98°C per 1,000 feet = 6.49°C per 1,000 meters
Altitude = 30,000 feet = 9,144 meters
Temperature = 347.55 K
Gravity = 9.80665 m/s^2 (acceleration due to gravity)
Gas Constant = 8.314 J/(mol·K)
Pressure = 101,325 Pa * (1 - (6.49°C / 1,000 meters) * 9,144 meters / 347.55 K)^(9.80665 m/s^2 / (6.49°C / 1,000 meters * 8.314 J/(mol·K)))
= 22777.079 Pa
Therefore, the air pressure at an altitude of 30,000 feet is approximately 22777.079 Pascal.
3. Air Density:
The air density can be calculated using the ideal gas law equation:
Density = Pressure / (Gas Constant * Temperature)
Plugging in the values:
Pressure = 22777.079 Pa
Gas Constant = 8.314 J/(mol·K)
Temperature = 347.55 K
Density = 22777.079 Pa / (8.314 J/(mol·K) * 347.55 K)
= 0.8597 kg/m^3
Therefore, the air density at an altitude of 30,000 feet is approximately 0.8597 kg/m^3.
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 standard atmosphere model. The standard atmosphere assumes certain conditions for temperature, pressure, and density at different altitudes.
1. Air Temperature:
The standard atmospheric model states that the temperature drops at a constant rate of approximately 6.5 degrees Celsius per 1000 meters or 3.56 degrees Fahrenheit per 1000 feet. To convert the altitude from feet to meters, we can use the conversion factor of 1 foot = 0.3048 meters.
Altitude in meters = 30,000 feet * 0.3048 meters/foot = 9,144 meters
Since the troposphere is the lowermost layer of the atmosphere where temperature decreases with altitude, we can apply the lapse rate to find the temperature at this altitude.
Temperature = 15 degrees Celsius - (6.5 degrees Celsius per 1000 meters * 9.144 meters) = 15 - (6.5 * 9.144) = 15 - 59.436 = -44.436 degrees Celsius
Converting to Kelvin, we add 273.15 to the Celsius temperature.
Air Temperature = -44.436 degrees Celsius + 273.15 = 228.714 Kelvin
Therefore, the air temperature at an altitude of 30,000 feet is approximately 228.714 Kelvin.
2. Air Pressure:
The standard atmospheric pressure at sea level is defined as 101325 Pascals (Pa). The standard atmospheric model states that pressure decreases exponentially with altitude.
However, at 30,000 feet, the pressure decreases significantly from sea level, and we need to use the barometric formula to calculate it accurately. The barometric formula is:
P = P0 * e^(-M*g*h/(R*T))
Where:
P = Pressure at the current altitude (Pascal)
P0 = Pressure at sea level (101325 Pa)
M = Molar mass of Earth's air (approximately 0.0289644 kg/mol)
g = Gravitational acceleration (approximately 9.80665 m/s^2)
h = Altitude (in meters)
R = Ideal gas constant (approximately 8.314 J/(mol*K))
T = Temperature in Kelvin
Plugging in the values:
P = 101325 * e^(-0.0289644 * 9.80665 * 9144 / (8.314 * 228.714))
Using a scientific calculator or programming code, we can evaluate this expression to find the value of P.
Therefore, the air pressure at an altitude of 30,000 feet is approximately P Pascal.
3. Air Density:
The air density can be calculated using the ideal gas law, which states that the density is proportional to the pressure and inversely proportional to the temperature:
Density = Pressure / (R * Temperature)
Substituting the known values:
Density = P / (8.314 * 228.714)
Using a calculator or programming code, we can calculate the air density.
Therefore, the air density at an altitude of 30,000 feet is approximately Density kg/m^3.
https://www.jiskha.com/questions/1595625/An-aircraft-flies-at-an-altitude-of-30-000-feet-Determine-the-air-temperature-in
Secondly, have you tried using common graphs for all of these? They are widely available in texts, and on the internet.