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I recently went through the wikipedia page for Rain. It said that

There are four main mechanisms for cooling the air to its dew point: adiabatic cooling, conductive cooling,....

It proceeds as

Adiabatic cooling occurs when air rises and expands.

Why is this a adiabatic process?

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"Adiabatic" when it is not obvious (that is, when the process is not inside an insulator) means "so fast that it doesn't have time to exchange energy with the exterior". This is roughly what happens in the atmosphere, the airmass expansion happens in a time scale shorter than the mixture equilibrium.

As a side note, we use this approximation because it simplifies a lot the equations. For more realistic computations, we can use modified values of the adiabatic constant to take into account that the process is not purely adiabatic.

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It is an adiabatic process because the rising parcel of air is large and therefore has a small surface to volume ratio. As the parcel of air rises the pressure exerted on it by the surrounding air gets less and less. Therefore the parcel of air expands and cools adiabatically by pushing out against this atmospheric pressure. The energy it loses in this way is proportional to the volume of the air parcel.

Of course it also loses heat by conduction but the rate of heat energy lost by conduction is proportional to the surface area of the parcel of air.

The ratio of heat loss by conduction to heat loss by adiabatic cooling, equals the ratio of surface area to volume, which is very small for the large parcels of air which form clouds.

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