
48 The Principles of Thermodynamics
Hence for an adiabatic atmosphere, temperature decreases linearly with height.
Using g= 9.8 m/s
2
along with the values of M and R given above, the rate of
decrease is 9.8 K/km. Actual rate is smaller than this.
If, on the other hand, we treat the atmosphere isothermally, we have P =
(RT/M)
ρ
and the hydrostatic equilibrium condition becomes
dP
dz
= −
gM
RT
PP(z)=P(z =0)e
−
gM
RT
z
(2.34)
In other words, the pressure (and hence the density) of an isothermal atmo-
sphere falls off exponentially with height. The scale of fall-off is determined by
the length scale L =
RT
gM
,whichcanbecalledtheheight of the atmosphere. Its
numerical value ...