Final answer:
The geopotential height of an atmosphere with an adiabatic lapse rate can be used to calculate atmospheric pressure at different altitudes using the barometric formula and considering the decrease in air density with height.
Step-by-step explanation:
Estimating Atmospheric Pressure at Different Altitudes
The geopotential height is a concept used in atmospheric sciences to compare the potential energy of a unit mass (air parcel) at various heights within the Earth's atmosphere. The adiabatic lapse rate is the rate at which the temperature of the atmosphere decreases with an increase in altitude, when the air is rising and cooling at a rate determined by the adiabatic process, which is around 6.5 K/km for dry air under normal atmospheric conditions. Given the surface pressure Πo = 1.013 × 105 Pa, and temperature T = 293 K, to estimate the pressure at a higher altitude like 3.0 km, we would use the concept of the lapse rate and the barometric formula which describes how the atmospheric pressure (p) decreases with height (h).
Geopotential height is necessary to consider because Earth's gravity varies with latitude and altitude, which affects the pressure levels. To calculate the pressure at 3.0 km based on the provided lapse rate of 6.5 K/km and the known surface pressure, one would follow the steps of calculating the temperature at the new height, then applying the barometric formula, which takes into account the changes in temperature and hence density of air with height.
Furthermore, when the lapse rate is known, other atmospheric conditions such as the air density can also be deduced. Air density decreases with altitude, as evidenced by a slope derived from data points at different altitudes, which indicates that air density decreases by about 0.1 kilograms/cubic meter for each additional 1,000 meters of altitude.