1.2 Gas laws and basic atmospheric forces

The density (the mass of a unit of volume) of dry air is about 1.225 kg/m³ at mean sea level [msl] and decreases with altitude. The random molecular activity within a parcel of air exerts a force in all directions and is measured in terms of pressure energy per unit volume, or static pressure. This activity, i.e. the internal kinetic energy, is proportional to the absolute temperature. (Absolute temperature is expressed in kelvin units [K]. One K equals one degree Celsius and zero degrees in the Celsius scale is equivalent to 273 K.) There are several gas laws and equations that relate temperature, pressure, density and volume of a gas.

Boyle's law:
At a constant temperature the volume [V] of a given mass of gas is inversely proportional to the pressure [P] upon the gas; i.e. PV = constant.


The pressure law:
At a constant volume the pressure is directly proportional to temperature [T] in Kelvin units.


Charles' law:
At a constant pressure gases expand by about 1/273 of their volume, at 273 K, for each one K rise in temperature; i.e. the volume of a given mass of gas at constant pressure is directly proportional to the absolute temperature. If an amount of heat is taken up by a gas some of the heat is converted into internal energy and the balance is used in the work done in pushing back the environment as the gas expands.


The gas equation:
For one mole of gas, the preceding laws are combined in the gas equation PV = RT where R = the gas constant = 8.314 joules per Kelvin per mole. The constant for dry air is 2.87 when P is expressed in hectopascals [hPa]. Ordinary gases do not behave exactly in accordance with the gas laws because of molecular attraction and repulsion. The gas equation gives the behaviour of a parcel of air when temperature or pressure, or both, are altered; e.g. if temperature rises and pressure is constant, then volume must increase — consequently the density of the air decreases and the parcel becomes more buoyant. Conversely, if temperature falls and pressure is constant then volume must decrease, the air becomes denser and the parcel less buoyant. Warmed air is comparatively light and cooled air is comparatively heavy. (In meteorological terms a parcel is a mass of air small enough that the whole mass moves or behaves as a single object.)


The equation of state:
P = RrT / M where r = density and M = molecular weight. But for meteorological purposes M is ignored and the equation used is P = RrT. For example, if density remains constant and the temperature increases (decreases), then static pressure increases (decreases) or conversely, if density remains constant and the pressure increases (decreases) then temperature increases (decreases). Or, if pressure remains constant then an increase in temperature causes a decrease in density, and vice versa.


Dalton's law:
The total pressure of a mixture of gases or vapours is equal to the sum of the partial pressures of its components. The partial pressure is the pressure that each component would exert if it existed alone and occupied the same volume as the whole.


By restating the equation of state as: P = RrT , it can be seen that if density remains constant, pressure increases if temperature increases.

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