Druk en volume in een adiabatisch proces

Consider a volume of air molecules rising in the atmosphere. As the pressure decreases with altitude, the air molecules try to maintain the same pressure by increasing their volume under an adiabatic process.

The internal energy change is written in terms of molar heat capacity and rearranged.

Using the ideal gas law, differentiating it, and rearranging the terms gives an expression for temperature change.

Equating the temperature change equations obtained from the first law of thermodynamics and the ideal gas law and rearranging gives an equation in terms of the molar heat capacity.

Divide throughout by pV and use the relation between molar heat capacities. The equation can be further simplified using their ratio.

Upon integration and using a general mathematical expression for logarithms, the condition for an ideal gas to undergo an adiabatic process is obtained in terms of pressure and volume.

Similarly, the conditions for adiabatic processes in terms of temperature-volume and pressure-temperature can be written.

So, when air expands, the temperature drops as given by the temperature-volume condition, condensing to form clouds.