What is Adiabatic Lapse Rate?

When a parcel of air ascends, the pressure exerted on it by the surrounding atmosphere decreases, so allowing the parcel to expand. In order to do so it requires energy which is derived from the parcel itself, and its temperature therefore decreases. Since air is a poor conductor, it is assumed that no energy is exchanged between the air parcel and the surrounding atmosphere. This process, in which no heat enters or leaves the system, is termed adiabatic from the Greek word meaning “impassable”.
when an air parcel descends, the reverse process occurs and its temperature increases. The rate at which the temperature of the parcel changes with height is termed the Adiabatic Lapse Rate.
Cloud formation is mainly the result of air ascending and cooling adiabatically.

Wet And Dry Air
Any parcel or sample of air that is fully saturated is called wet air or saturated air.
Any parcel or sample of air that is not fully saturated is called dry air.

Dry Adiabatic Lapse Rate (D.A.L.R.),
For a dry air parcel, in which the air is unsaturated, the rate is 9.8°C/km (usually rounded up to 10°C/km). This is the Dry Adiabatic Lapse Rate (D.A.L.R.), which is applicable whether the air parcel is ascending or descending.

Saturated Adiabatic Lapse Rate (S.A.L.R.)
The temperature of a saturated parcel of air, which is made to rise, falls at a rate of approximately 5°C/km of ascent i.e. the adiabatic lapse rate of a saturated parcel of air, or Saturated Adiabatic Lapse Rate (SALR), is about 5°C/km.
SALR is less than DALR because, as the saturated air is cooled its capacity to hold water vapour decreases and the excess moisture condenses into water droplets. This condensation releases latent heat that warms up the parcel of air. The temperature of the rising parcel of saturated air therefore, falls only by about 5°C/km instead of 10°C/km. SALR  is slightly variable – less at the equator and more at the poles.
When we require an average value of the adiabatic lapse rate of any parcel of rising air, and we so not know its exact moisture content, an average value of 6.5°C/km would give reasonably approximate results.