Content Strategy Manager
Density of air, also known as ‘atmospheric density’ is the mass of air contained in a unit volume. The unit of air density is grams per cubic metre or kilograms per cubic metre. It can also be expressed as the density altitude.
- Density refers to the measure of mass.
- The density formula is d = m/v, where d = density, m = mass, and v = volume.
In simple terms, the density of atmosphere measures the number of atoms that are packed into a space. When the atoms are tightly packed the density of air can be called high but when it is less tightly packed it is called low density of air.
The value of density of air is approximately 1.225 kg/m3
Key Terms: Density of air, Density of dry air, Density of humid air, Standard density of air, Gravitation, Temperature, Volume, Mass
What is Density of Air?
[Click Here for Sample Questions]Density of air though is calculated on the basis of mass and volume. It can vary in different places as it depends on multiple factors. Air density can change with significant changes in the level of temperature, relative humidity, pressure, and altitude.
- The density of air is denoted by the greek letter ρ.
- It measures the mass of the air per unit volume.
- As the molecules of gases are free to move, the density of air can vary over a wide range.
- Thus air density at Earth’s surface would be different than at 50 kilometres above the earth.
- The air density at sea level and 0 humidity is 1.225 kg/m³, but it can go up to 0.122 kg/m³ depending on altitude.
Altitude and Density of Air
Read more:
What is the Value of the Density of Air?
[Click Here for Previous Year Questions]The value of density of air is 1.29 grams/litre i.e. 0.07967 pounds per cubic foot at 32 degrees Fahrenheit (0 degrees Celsius) at the average sea-level barometric pressure.
Average sea-level barometric pressure = 29.92 inches of mercury or 760 millimetres.
Density of Dry Air
Dry air consists of nitrogen (78%), oxygen (21%), and the remaining different gases such as argon, carbon dioxide, neon, or helium add to the left proportion (1%). However, this air ceases to be dry air when water vapor appears. Due to its instability of gases, air does not have a constant density. This change depends largely on air composition.
| The density of dry air is calculated using the ideal gas law as follows,
In this air density formula:
|
is the air density (kg/m3)Also read: Gravitational potential energy
Density of Humid Air
The density of the air reduces as a result of the addition of water. This happens due to the reason that the molar mass of water is less than the molar mass of dry air. The number of molecules is constant for a given volume of air for an ideal gas at a given temperature and pressure. The density of humid air is calculated by the air density formula as follows:
Where:
- Phumid is the density of the humid air
- Pd is the partial pressure of dry air
- Rd is the specific gas constant of dry air
- T is the temperature
- pv is the pressure of water vapour
- Rv is the specific gas constant for water vapour
- Md is the molar mass of dry air
- Mv is the molar mass of water vapour
- R is the universal gas constant
Also read: Earth Satellites
Calculation of Density of Air
[Click Here for Sample Questions]The weather parameters that are significant for the calculation of air density are given as follows:
- Air temperature
- Air pressure
- Relative humidity
The method of calculating air density is given as below:
- Calculate the saturation vapor pressure at a given temperature ‘T’ by using,
p1= 6.1078 * 10^ [(7.5 * T)/( T + 237.3)]
Where ‘T’ is measured in degrees celsius
- Find actual vapor pressure by the given formula:
pv= p1 * RH
- Where, pv= actual vapor pressure
- RH= relative humidity
- Find the pressure of dry air by:
pd= p - pv
- Where, pd= pressure of dry air
- p = total air pressure
- Then put the calculated values in the following formula:
ρ = [pd/(Rd * T)) + (pv / (Rv*T)]
Where, pd= pressure in dry air
- pv= water vapor pressure
- T= air temperature in Kelvins
- Rd = Specific gas constant for dry air= 287.058 J/(kg-K)
- Rv = Specific gas constant for water vapor= 461.495 J/(kg-K)
Also Read: Mass and Weight
Factors affecting the Density of Air
[Click Here for Previous Year Questions]The high-density altitude corresponds directly to reduced air density. There are three important factors that contribute to high-density altitude:
Altitude or Pressure
The higher the altitude is, the lower the pressure and hence the air becomes less dense. The different types of altitudes are Indicated Altitude, True Altitude, Absolute Altitude, Pressure Altitude, and Density Altitude.
- The pressure forces the molecules of air together, hence more mass is there in a given volume.
- As the altitude increases, there is a decrease in air pressure.
- The decrease in air density means that a person at high altitudes gets less oxygen while breathing.
Temperature
Temperature is another factor that affects air density. The warmer the air, the less dense it is.
- When the temperature rises above the standard temperature, the molecules move faster and spread on collision.
- Hence, the density of air in a particular location is decreased.
- The lower temperature and lower air pressure at high altitudes lead to lower air density.
Humidity
Humidity or the amount of moisture in the atmosphere changes the density of air. The more moisture there is in the air, the lower the density of air will be.
Table of Density of Air
[Click Here for Sample Questions]Air density at different temperatures, pressure and altitude is given below.
| Altitude [ft (m)] | Temperature [°F (°C)] | Pressure [psi (hPa)] | Air density [lb/cu ft (kg/m3)] |
|---|---|---|---|
| Sea level | 59 (15) | 14.7 (1013.25) | 0.077 (1.23) |
| 2000 (610) | 51.9 (11.1) | 13.7 (941.7) | 0.072 (1.16) |
| 4000 (1219) | 44.7 (7.1) | 12.7 (873.3) | 0.068 (1.09) |
| 6000 (1829) | 37.6 (3.1) | 11.7 (808.2) | 0.064 (1.02) |
| 8000 (2438) | 30.5 (-0.8) | 10.8 (746.2) | 0.06 (0.95) |
| 10000 (3048) | 23.3 (-4.8) | 10 (687.3) | 0.056 (0.9) |
| 12000 (3658) | 16.2 (-8.8) | 9.2 (631.6) | 0.052 (0.84) |
| 14000 (4267) | 9.1 (-12.8) | 8.4 (579) | 0.048 (0.77) |
| 16000 (4877) | 1.9 (-16.7) | 7.7 (530.9) | 0.045 (0.72) |
Standard Density of Air
[Click Here for Sample Questions]According to the International Standard Atmosphere (ISA) values - 15° C at sea level- the density of dry air is:
- In Metric units: 1.225 kg/m3
- In Imperial units: 0.0765 lb/ft3
Though pure water vapor cannot exist at STP, these density values for dry air can be used to calculate a theoretical value for water vapor density at STP.
| The following shows the list of several standard reference pressures:
|
Check Out:
Things to Remember
- Density is the measure of mass of air in a unit volume. It is denoted by ρ.
- The value of air density is 1.29 grams per litre at 32 degrees Fahrenheit at average sea-level barometric pressure.
- The dry air consists of Nitrogen (78%), Oxygen (21%) and other gases such as argon, carbon dioxide, neon or helium (1%).
- The density of air is mainly affected by three factors namely: Altitude, Temperature and Humidity.
- The standard air density is given by International Standard Atmosphere (ISA) at 15° C at sea level as:
- In Metric Units: 1.225 kg/m3
- In Imperial Units: 0.0765 lb/ft3
Sample Questions
Ques. Where is the air density considered to be the highest? (2 marks)
Ans. The factors that affect air density are altitude, temperature and humidity. Depending upon the height air density changes from high to low levels as we move up in the atmosphere i.e. when the altitude increases. Since at low altitudes the air pressure is found to be maximum it results in high air density. Therefore, the air density is considered to be the highest near the ground or at sea level.
Ques. Which instrument is used to measure atmospheric pressure? (2 marks)
Ans. The instrument used to measure the air pressure is a ‘Barometer’. Since the atmosphere consists of different layers of air that are pulled by the force of gravity, the barometer measures the pressure exerted by the layers of air towards any surface. The barometer consists of a glass tube that works by balancing the mercury present in it towards the air pressure present outside the glass tube. The mercury rises up in the tube when the air pressure increases and similarly goes down when the air pressure decreases. This helps in determining the air pressure with high accuracy.
Ques. What are the factors that affect air density in various regions? (3 marks)
Ans. There are three important factors that contribute to the changes in air density:
- Altitude: The higher the altitude, the less dense the air. For example: At airports in higher elevations, high temperatures sometimes have such an effect on density altitude that safe operations are impossible. Even when the aircraft is at a lower altitude, it becomes important to decrease the gross weight of the aircraft for safe operation.
- Temperature: The density of air decreases with a rise in the temperature. When the temperature of a particular place increases the air density in that particular area decreases but the density increases with an increase in the altitude
- Humidity: Humidity doesn't play a major role in the calculation of the density altitude since it is not a major part of the aircraft’s aerodynamics efficiency. In areas having high temperatures, the atmosphere can retain a high water vapor content.
Ques. What is ‘Standard air density’? (2 marks)
Ans: The air density that is calculated at standard temperature and standard pressure conditions is known as ‘Standard air density’. The value of standard air density is given by 1.225 kg/m3,
According to the International Standard Atmosphere (ISA) values- 15° C at sea level- the density of dry air is at:
- In Metric units: 1.225 kg/m3
- In Imperial units: 0.0765 lb/ft3
Ques. How is the air density calculated? (4 marks)
Ans. The methods for calculating air density is given as below:
- Calculate the saturation vapor pressure at ‘T’ by p1= 6.1078 * 10^ [ 7.5 * T / ( T + 237.3)]
- Find actual vapor pressure by: pv= p1 * RH
- Find the pressure of dry air by: pd= p - pv
- Then add the calculated values in the formula: ρ = (pd / (Rd * T)) + (pv / (Rv * T))
Ques. If the air density were uniform, then the height of the atmosphere above sea level to produce a normal atmospheric pressure of 1.0 * 105Pa is ( density of air is 1.3 kg/m3, g= 10 m/s2) (5 marks)
Ans. The pressure can be defined as the force per unit area. It is the force exerted per unit area. At higher altitudes, the pressure is found to be very low. As the altitude increases the air that presses against the body will be much smaller compared to the depths, hence the pressure of air will be less.
Given, Density of air, ρ= 1.3 kg/m3 and atmospheric pressure is, P= 1.0 * 105 Pa.
The pressure at any point is given by the expression,
P= ρgh
h= P/ρg
Where, ‘ρ’ is the density, ‘g’ is the acceleration due to gravity and ‘h’ is the height.
Substituting the respective values we get,
h= 1.0 * 105 Pa/ 1.3 kg/m3 * 10 m/s2
h= 7.69 * 103 m
h= 7.7 km
Thus, the height of the atmosphere above sea level is 7.7 km.
Ques. What is the value of the density of air? (4 marks)
Ans. The value of density of air is not constant. Its value varies with the different levels of altitude, temperature and humidity. Dry air has a density of 1.29 gram per litre at 0 degree Celsius (32 degrees Fahrenheit) at average sea level.
For instance,
- The density of air is around 1.225 kilogram per cubic meter at 15-degree celsius at sea level.
- Additionally, the IUPAC standard of temperature and pressure uses dry air density of 1.2754 kilogram per cubic meter.
- The density of dry air at 20- degree celsius and 101.325 kPa is 1.2041 kg/cubic meter.
- At 70 degree Fahrenheit and 14.696 psi, the density of dry air is about 0.74887 lmb/ft.
Ques. Define ‘density of air’? (2 marks)
Ans. The density of air also known as atmospheric pressure refers to the mass per unit volume of atmospheric gases. The density of air depends upon the atmospheric temperature, pressure and humidity. Normally, the units in which the density of air is measured is the Standard Temperature and Pressure.
The STP is one atmosphere of pressure at 0 degrees Celsius. Also, dry air is less dense than the cited value most of the time because of the water vapor contained by it making it denser.
Ques. What is relative humidity? (3 marks)
Ans. The relative humidity RH is defined as the ratio of the partial pressure of the ‘partial pressure of water vapor’ to the ‘equilibrium pressure of water vapor’ at a given temperature.
- Partial pressure is the pressure of one component of the air at the same volume and temperature as the whole.
- The equilibrium pressure of water vapor is the pressure exerted by a vapor that is in thermodynamic equilibrium with its liquid phase at a given temperature.
- Relative humidity RH ranges between 0% and 100%, where 0% means dry air, and 100% is the air that is completely saturated with water vapor.
Check Out:
Comments