A volume of cool air rapidly descends from the top of a mountain. the air is a poor thermal conductor, but its temperature increases as its volume decreases, because of the increase in atmospheric pressure as it reaches the ground. what thermodynamic process takes place

These are all the characteristics of what is called the adiabatic process. This process occurs when there is no transfer of heat between the surroundings and the thermodynamic system. This is a key process for thermodynamics and it is of great importance for the first law of thermodynamics.