1. Moist adiabatic processes on a thermodynamic chart. Atms Sc 4310 / 7310 Lab 3 Anthony R. Lupo

2. Moist adiabatic processes on a thermodynamic chart.  Last time we examined dry adiabatic processes   Now examine moist processes (saturation!)   moist adiabats are lines of moist potential temperature, read; Bluestein, pp 201 – 211..

3. Moist adiabatic processes on a thermodynamic chart.  Mixing ratio: M v (mass of vapor) _______________ M d (masss of dry air)  Thermodynamics of dry air  air without any form of water.  Moist air  dry air + water vapor.

4. Moist adiabatic processes on a thermodynamic chart.  Let: Md = mass of dry air (N 2, O 2 etc.)  Then: M v (is the mass of water vapor)  Note: you may see M l (liquid) or M i (ice) in this class or in other classes.c

5. Moist adiabatic processes on a thermodynamic chart.  The mixing ratio (m) (r)  general definition:  m = Mass of trace substance / mass of fluid  so, using water vapor  m,  but ml or mi can also be defined

6. Moist adiabatic processes on a thermodynamic chart.  The specific humidity  (q) = Mv / Md + Mv  Recall “fun fact” from Atms. 50   Water vapor constitutes near 0 to up to 4%, water vapor (usually about 1%)

7. Moist adiabatic processes on a thermodynamic chart.  Thus, for most situations: “m” roughly equals “q”  Mixing ratio (m)  of air is the actual mixing ratio (and is associated with the dewpoint)  Saturated mixing ratio (m s )  mixing ratio the air would have at the ambient temperature if it was saturated.

8. Moist adiabatic processes on a thermodynamic chart.  Vapor pressure  partial pressure of water (Dalton’s Law)  Thus the ideal gas law for dry air is  P – e =  d R d T

9. Moist adiabatic processes on a thermodynamic chart.  Relate mixing ratio (m) to vapor pressure (e) !  Relative humidity:

10. Moist adiabatic processes on a thermodynamic chart.  Equivalent Potential Temperaure: Moist adiabats  Let’s derive!  1st law:

11. Moist adiabatic processes on a thermodynamic chart.  What to do? Let’s  1. substitute in p = RT  2. “parameterize” the Latent Heat Release:

12. Moist adiabatic processes on a thermodynamic chart.  This becomes equation (1)  OK, let’s leave this alone and look at:

13. Moist adiabatic processes on a thermodynamic chart.  Take natural log:  Take the derivative of this, and “a little” algebra to get equation (2):

14. Moist adiabatic processes on a thermodynamic chart.  Hmm…. The RHS of eq. (1) and (2) are the same, so:  Then apply “the snake”

15. Moist adiabatic processes on a thermodynamic chart.  After integrating, a bit o’ algebra, and assuming:  1) w s / T  0  2)  o =  e  we get moist potential temperature!

16. Moist adiabatic processes on a thermodynamic chart.  Virtual temperature  When air is inherently moist, if we could take into account the effect of moisture and get a temperature the air would have if it were dry:  p =  d R d T +  v R v T  p =  R T =  R d T v   where T v is the Virtual temperature.

17. Moist adiabatic processes on a thermodynamic chart.  We can calculate using “brute force”  Tv = (1 + 0.609m)T  where T = Kelvins and m is kg / kg or a unitless number!!

18. Moist adiabatic processes on a thermodynamic chart.  Or, the shortcut (graphical) method:  T v = T + (w s / 6)  where T is degrees C and w s is g/kg

19. Moist adiabatic processes on a thermodynamic chart.  Questions?  Comments?  Criticisms?

20. Moist adiabatic processes on a thermodynamic chart.  The end!