Effect of temperature and pressure on density

What is density: Density is  mass per unit volume expressed usually in kilogram per meter cube (kg/m³ ). Imagine you have a box of size 1meter x 1meter x 1meter. If you put air inside it, it can hold uptill the entire space is filled up. That is the maximum capacity it can hold. Our atmosphere is also like that. At sea level at 15°C it is 1.225 kg/m³

Effect of pressure and temperature as height increases:

1. As you climb up the atmospheric pressure above you reduces i.e. if at ground level you have 1010 mb or 29.92in of pressure then at 1000 ft above it will be less i.e. the amount of air above you and hence the pressure exerted will be less. Other way to understand is if you apply pressure then molecules are closely packed and hence more dense. Reverse when you remove pressure.
2. Secondly the temperature reduces as you climb higher e.g. at ground it may be 15degree Celsius but at 1000ft height it will be less say 10 degree Celsius. 
3. Density reduces as height increases (at sea level 100%, at 20000 ft 50%). Scientifically it has been put into this formula.

where ρ is the air density, p is absolute pressure, R_specific is the specific gas constant for dry air, and T is absolute temperature

As you can see from the above formula, density reduces as pressure reduces, which means that as per point 1 above, since height increases, pressure reduces and hence density reduces. So far so good. We have established the relationship. 

Now to point number 2, as temperature reduces as height increases density increases (inversely proportional). But that's contradicting or cancelling pt number 1. However that is true but density reduction due to pressure is more than density increase due to temperature decrease, resulting in net decrease in density. 

Effect of water vapor to density: Introduction of water vapor in atmosphere i.e. making the air humid. Humidity reduces density. Why? Cause water has less molecular mass than air and hence when water is added to atmosphere it displaces air in the given cubic meter volume but results in lowering of density.


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