The Atmospheric Lapse Rate

Classical Mechanics Level 3

For small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperature. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere. The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is $$– 6.7 ^\circ \text{ C/km}$$.

The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather variation occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to the relatively constant. Absorption of sunlight at the Earth's surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and, therefore, its temperature drops.

Assume that the vertical mixing is so rapid as to be adiabatic and quantity $$TP^{(1-\gamma)/\gamma}$$ has a uniform value through the layers of troposphere.

If behavior of the mixing of parcels of air is approximately assumed to be adiabatic, then lapse rate can be expressed as:

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