Editing Lapse rate (section)

===Dry adiabatic lapse rate===
Thermodynamics defines an adiabatic process as:
:<math>P\, \mathrm{d}V = -\frac{V\, \mathrm{d}P}{\gamma}</math>

the [[first law of thermodynamics]] can be written as
:<math>m c_\text{v}\, \mathrm{d}T - \frac{V \,\mathrm{d}P}{\gamma} = 0</math>

Also, since the density <math>\rho = m/V</math> and <math>\gamma = c_\text{p}/c_\text{v}</math>, we can show that:
:<math>\rho c_\text{p} \,\mathrm{d}T - \mathrm{d}P = 0</math>

where <math>c_\text{p}</math> is the [[specific heat]] at constant pressure.

Assuming an atmosphere in [[hydrostatic equilibrium]]:<ref name="LL">Landau and Lifshitz, ''Fluid Mechanics'', Pergamon, 1979</ref>
:<math>\mathrm{d}P = -\rho g\, \mathrm{d}z</math>

where ''g'' is the [[standard gravity]]. Combining these two equations to eliminate the pressure, one arrives at the result for the ''dry adiabatic lapse rate'' (DALR),<ref>{{cite book|last1=Kittel|last2=Kroemer|title=Thermal Physics|publisher=W. H. Freeman|year=1980|chapter-url=https://books.google.com/books?id=c0R79nyOoNMC&pg=PA179|chapter=6|isbn=978-0-7167-1088-2|page=179}} problem 11</ref>
:<math>\Gamma_\text{d} = -\frac{\mathrm{d}T}{\mathrm{d}z} = \frac{g}{c_\text{p}} = 9.8\ ^{\circ}\text{C}/\text{km}</math>

The DALR (<math>\Gamma_\text{d}</math>) is the temperature gradient experienced in an ascending or descending packet of air that is not saturated with water vapor, i.e., with less than 100% relative humidity.