Thermodynamics of the Atmosphere
Atmosphere contains N2 + O2 + Ar + CO2 ± H2O
- well mixed in turbosphere
- ideal gas (unless saturated)
Ideal Gas
R*  8.31 Jmol-1K -1
*
R
8.31
Meterology p  RT
R

M 28.97 103
=287 Jkg -1K -1
R varies with gas
Physics
pV  NR*T
Hydrostatic Equation
for an Isothermal Atmosphere
Ideal Gas
p  RT
dp  weight of air column per unit area
p
p+dp
dz
=-  g dz
dp
g

dz
p
RT
p  z   p0e
z=0
gz

RT
Pressure
Scale Height
p  z   p0 exp   gz / RT 
 p0 exp  z / H 
H = RT/g
p0/e
is the (exponential) scale height
Decade scale height
H10= ln10 RT/g
p0/10
H
H10
Height
at 250 K
at 280 K
H10=16.8 km
H10=18.9 km
Scale height ~ thickness of troposphere
 thicker troposphere at low latitudes,
where air is warmer
Atmospheric pressure profile
Atmospheric layers
• Troposphere
– pressure drops from 1000 mbar to ~200 mbar,
contains 80% mass
– thickness 10 – 15 km
– temperature drops with height by ~6.5 ºC/km,
unstable as hot air rises!
– well mixed: molecules travel up and down in few days
– most weather in this layer, i.e. most heat transport
• Tropopause
– region of stable, isothermal air ~ 200 mbar
– division between troposphere and stratosphere
– top of “weather”
• Stratosphere
–
–
–
–
–
pressure from ~200 mb to ~1 mb, height 10 – 50 km
temperature increases with height (due to heating in ozone layer)
 stable air, isothermal strata with little mixing
stops weather extending upwards, so keeps water in atmosphere
temperature reaches maximum at Stratopause
• Mesosphere
– “middle atmosphere”, pressure 1 mb to 10-2 mb
– temperature drops to lowest values ~ -90ºC
– Mesopause is top of well mixed region, 99.9% of atmosphere below
• Thermosphere
– temperature increases rapidly (due to molecular dissociation)
– v.large KE/molecule, but few molecules!  Feels cold
– mean free path so large that no longer well mixed
1st law of thermodynamics
1
dq  c p dT  dp

dq=0 for adiabatic (fast) processes
dT
1 dp
g


dz c p dz
cp
dT g 9.81
 
~ 10 C km1
dz c p 1005
Dry Adiabatic Lapse Rate (DALR)
D  
Saturated Adiabatic Lapse Rate (SALR)
 S ~ 6 C km-1
SALR < DALR since latent heat is released by water vapour
Atmospheric
stability
Unstable if
 dT

 dz

  D

Conditionally
 dT 
S   
  D
stable if
 dz 
Stable if
 dT

 dz

  S
