Rate Temperature and Altitude

The origin of the lapse rate can be understood on the basis of fundamental thermodynamics. That is, under the assumptions of a dry air parcel rising adia-batically in the atmosphere, the temperature is expected to fall about 10 degrees per kilometer increase in altitude. This drop in temperature is defined as a positive lapse rate. 

This relationship for the variation of pressure with altitude can be converted into that between temperature and altitude as shown in Eq. (N) below for a parcel of dry air that rises without heat exchange occurring between it and the surrounding air this is known as an adiabatic process. 

The work done by an expanding gas is defined as dw = -PdV. From the ideal gas law, 

Combining Eqs. (D) and (M), one obtains the temperature-altitude profile, or lapse rate, for a dry adiabatic gas  

In reality, measured lapse rates are 6-7°C per km. This is due to the fact that atmospheric air is not dry but contains significant amounts of water vapor that also cools as the air parcel rises. When it reaches saturation, it condenses and releases its heat of vaporization, which warms the air somewhat, resulting in a less steep drop in temperature with altitude than expected for a dry air parcel. 

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