The Hydrostatic Equation and Adiabatic Processes

Abstract

In addition to obeying the Ideal Gas Law and principles of adiabatic motion, air moves vertically based on the principles described in the hydrostatic equation, which relates height differences in a static atmosphere to the vertical pressure change over those differences. In addition, the First Law of Thermodynamics—the postulate that energy can be neither created nor destroyed, but only changed from one form to another—applies by ensuring that air has some combination of gaining or losing internal energy and doing work (or having work done) on its surrounding environment as it moves vertically. These principles are important in modeling and predicting atmospheric motion. Specifically, if air is assumed to move adiabatically in its vertical motion and is not saturated, then these principles dictate that it will always cool by 0.9753 K (or approximately 1 C°) per 100 m. As will be shown in the subsequent chapters, this unsaturated adiabatic lapse rate becomes very important in determining whether an imaginary blob of air known as an air parcel will have a tendency to rise (and perhaps generate tall clouds) or sink.