Adiabatic processes on a
thermodynamic chart.
Atms Sc 4310 / 7310
Lab 2
Anthony R. Lupo
Adiabatic processes on a
thermodynamic chart.
 1st law of thermodynamics in the
form (imperfect form)
dq
dT
dP

Q
 cp

dt
dt
dt
dq
 source  sin k
dt
 is a statement of the Conservation of
energy (heat in = heat out)!
Adiabatic processes on a
thermodynamic chart.
 Left hand side (represents?):
 Diabatic heating, which includes
Latent Heat Release, Sensible
Heating, and Radiational Heating.
Adiabatic processes on a
thermodynamic chart.
 Right hand side:
 Term 1: Internal Energy (due to Temperature)
 Term 2: “pressure work” term or work done by
pressure by the environment on a parcel.
 (expansion – heat added to system diabatically
 contraction - heat removed diabatically)
Adiabatic processes on a
thermodynamic chart.
 Adiabatic process
 dq/dt = 0 (no work done)!!
 sources   sin ks
 Thus, the internal energy equals the
pressure work term. Also, now there are
no diabatics so;
dT
dp
cp

dt
dt
Adiabatic processes on a
thermodynamic chart.
 Expansion (lower pressure) cooling 
work done on air parcel and energy
lost to environment
 Contraction (higher pressure)
warming  work done by
environment and energy gained at
expense of environment
Adiabatic processes on a
thermodynamic chart.
 Constant Potential Temperature 
Adiabatic system or flow follows lines
of potential temperature.
 Why? Let’s derive relationship for
potential temperature
Adiabatic processes on a
thermodynamic chart.
 Derive…..start with 1st law
0  cp
dT
dP

dt
dt
invoke
T
 cp
To
" the
dT

dt
snake"
P
dP


dt
Po
then
  RT
P
so
T
1 dT
R

 T dt
cp
To
P
1 dP
 P dt
Po
Adiabatic processes on a
thermodynamic chart.
 And….
ln T
ln
T
To

R
P
ln P Po
cp
T
R
P

ln
To
cp
Po
call
To  
call
R
k 
cp
T
P


Po
 


Po 

 P 

Adiabatic processes on a
thermodynamic chart.
 Some adiabatic processes
 Adiabatic motion on the
thermodynamic diagram: no work
done, potential temperature is
constant.
 Use adiabatic motion as a first
estimate of maximum temperature
Adiabatic processes on a
thermodynamic chart.
 LCL – lifting condensation level (air lifted
adiabatically until saturation!)
 LFC – level of free convection: rising parcel
becomes warmer than environment, rises
under it’s own power, or due to bouyant
forces.
 CCL – convective condensation level: Raise
parcel along. Environmental sounding until
saturation (intersect mixrat. And sounding)
Adiabatic processes on a
thermodynamic chart.
 Convective temperature -- take
parcel down dry adiabatically to
surface, that’s the temp we must get
to to get convection.
 Equilibruim level – where
parcel becomes neutrally
bouyant again.
Adiabatic processes on a
thermodynamic chart.
Convective available potential energy:
 + value: parcels warmer than
environment which gains energy from
the air parcels
 - value: parcels cooler than environment
which must do work to lift parcels and
loses energy.
Adiabatic processes on a
thermodynamic chart.
 Other buoyancy related indicies:
 Lifted Index
 Showalter Index
 Energy Index
Adiabatic processes on a
thermodynamic chart.
 Questions?
 Comments?
 Criticisms?
Adiabatic processes on a
thermodynamic chart.
 The end!