MPO 551: Lecture 8
Thermodynamics
Second Law of Thermodynamics/Clausius Clapeyron
(Chapter 3, Wallace and Hobbs) Entropy
Per unit mass
And ds=0 for adibatic processes. Hence adiabats are also isentropes. Note that this only applies to reversible transformations
Thermodynamic theory of hurricanes adiabat
To=‐75C
Isotherm
(Heat sink)
adiabat
Ts=27C
Isotherm (Heat source)
Theoretical efficiency: Ts  To

Ts
See Emanuel (1991) on our class website. Increasing destructiveness of tropical cyclones over the past 30 years (Emanuel 2005) – paper on our class website
But this was just the beginning of an ongoing (and heated debate)…..
1. Equipartition of energy
1
1
U  f  kT  f  nRT
2
2
assign 1/2kT of energy to every degree of
freedom
Degrees of freedom=f(molecule)
• For monoatomic molecules f=3, because
in a 3-D space they can move to 3
directions
• For polyatomic molecules, the molecule
can also rotate and vibrate so f can be >3
2. What if f>3?
Because CV=f(<U>), then the specific heat at
constant volume:
CV 
1 U
1  1 
1

 CV    f nR   CV  fR
2
n T V
n  2 
C  C  R , CP also changes.
And since
C
So every time the laws of thermodynamics are used,
the type of molecule should be defined.
P
V
• In atmospheric/meteorological applications the air is
usually considered to be an ideal monoatomic gas.
[Atmospheric Science, Wallace & Hobbs, pp.75, (3.3)]
3. How are the molecular velocities
connected to the degrees of freedom?
Maxwell-Boltzmann
distribution
Figure from : http://scientificsentence.net/Thermodynamics/
This distribution applies only when we are dealing with ideal
monoatomic gases. For real gases the kinetic theory of gases
deviates.
For more information:
 http://chemed.chem.wisc.edu/chempaths/GenChem‐
Textbook/Deviations‐from‐the‐Ideal‐Gas‐Law‐590.html
 http://hyperphysics.phy‐astr.gsu.edu/hbase/hframe.html
 http://intro.chem.okstate.edu/1314f00/lecture/chapter5/lec101300.ht
ml
 http://www.chembook.co.uk/chap5.htm#gases