temperature - How is pressure related to air density? - Aviation Stack Exchange
Density and pressure have an integral relationship. The density (r) of an object depends on temperature and pressure. You may be aware that the density of water is approximately 1, kg/m3 and the density of air is At pressures at or near atmospheric air behaves quite close to an “ideal gas” so that at a constant temperature the density is proportional to the pressure. Any time you specify a relation between any two of pressure, density or temperature you must hold the third constant or specify its behavior.
Given the mixture of gases found in air the average molecular weight of air is around Water is made up of two hydrogen and one oxygen atoms H2O. Hydrogen is the lightest element and has a molecular weight of one.
Water is a very light molecule and much lighter than the average weight of the molecules found in air.
Density of air - Wikipedia
Moist Air In the real world the air always contains some moisture. The addition of water vapour to a mass of air makes it less dense. Whilst this may appear a bit odd at first this occurs because the molecular mass of water 18 is less than the molecular mass of air The density of humid air can be calculated as the sum of the densities of the two gases, dry air and water vapour in proportion with their partial pressures.
Calculating Water Vapour Pressure The amount of water vapour that a parcel of air can hold varies with temperature. The warmer the air the more moisture that it can hold. Air is said to be saturated when the temperature and dew point of the parcel are equal. There are a number of algorithms available for calculating vapour pressure but we shall use a polynomial developed by Herman Wobus.
How to Calculate Air Density
Imagine a box full of bouncing balls, if these balls start moving faster the balls will hit the walls of the box harder, imparting more force on the box. Pressure is merely force per area, so if the force increases but the box stays the same size, the pressure has increased.
Air density can decrease with temperature if pressure is also decreasing. If pressure is constant, this cannot happen they would be inversely related. Any time you specify a relation between any two of pressure, density or temperature you must hold the third constant or specify its behavior. For example, hot air rises, but why then is it cold on top of a mountain. The answer is that hot air is less dense than the cold air surrounding it for a constant pressure, and being less dense it rises.
With a mountain, the pressure is decreasing, and we likewise find in the atmosphere that temperature decreases with decreasing pressure. On a hot day what tends to happen is that the surface, which is being warmed by the sun, heats the lowest level of the atmosphere, reducing its density it is at the same pressure as its surroundings and its T rises.
This will eventually drive convection and mix this warmer air vertically.The relationship between the density and the temperature and pressure
Given enough time, this will reduce the mass in the column of air and therefore reduce the pressure at the surface. These are called "heat lows" and you can see them forming in the desert areas and they play roles in sea breeze formation and the monsoons.
To address the expanded question: The point in the FAA written is best understood by forgetting that we fly at constant altitudes -- we don't. In level flight we fly on constant pressure surfaces which we then translate to an altitude.
Density of air
In any given column of atmosphere, if it is warmer than standard a given pressure surface will be higher and when colder than standard the pressure surface will be lower.
To illustrate, let's consider you are flying at ft or roughly mb. Everywhere on this pressure surface will indicate ft on our altimeter for its current setting. If we go somewhere hot, this pressure surface rises, and so we climb though we think we are level with this pressure surface but because the pressure has not changed, we still indicate ft. However, we are higher than ft in reality.
This follows into your next question. Aneroid wafers detect pressure changes and your altimeter displays an altitude not corrected for temperature.