Variation of Atmospheric Pressure

Atmospheric pressure decreases with altitude because air is pulled toward Earth's surface by gravity. As you move higher, there is less air above you exerting downward force, resulting in lower pressure. The gravitational force per unit area diminishes with distance from the surface, causing this exponential decline in pressure with increasing height.

The barometric formula describes how atmospheric pressure varies with height. It is derived by combining the ideal gas law with the relationship between pressure and height, then integrating from sea level. The resulting exponential equation shows that pressure decreases exponentially as altitude increases, providing a mathematical model for atmospheric pressure variation.

Pressure scale height is a characteristic length, approximately 8,800 meters, that describes how quickly atmospheric pressure changes with altitude. It represents the height at which pressure drops by a factor of 1/e (about 37% of its initial value). This scale height is fundamental to understanding atmospheric structure and predicting pressure at any given altitude above sea level.

The ideal gas law connects pressure, density, temperature, and molecular mass of air. By expressing density from the ideal gas law and substituting it into the pressure-height relationship, we can derive how pressure changes with altitude. Assuming constant temperature and gravity, this relationship yields the barometric formula describing exponential pressure decay.

The barometric formula assumes that air temperature remains constant with height and that gravitational acceleration is constant. It also assumes the ideal gas law accurately describes atmospheric behavior. These simplifications allow integration of the pressure-height differential equation to obtain the exponential relationship between pressure and altitude.

Atmospheric pressure drops by a factor of 1/e (approximately 0.368 or 37%) for every 8,800 meters above sea level. This means that at 8,800 meters, the pressure is about 37% of its sea level value. This exponential decay pattern continues consistently, making pressure scale height a reliable predictor of pressure changes in the atmosphere.

Air density decreases with altitude because pressure decreases and fewer air molecules occupy a given volume. From the ideal gas law, density is directly proportional to pressure at constant temperature. As pressure drops exponentially with height, so does air density, creating the exponential pressure variation described by the barometric formula.