Moist adiabatic processes on a thermodynamic chart.

1
Moist adiabatic processes on a thermodynamic
chart.

• Atms Sc 4310 / 7310
• Lab 3
• Anthony R. Lupo

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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..

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Moist adiabatic processes on a thermodynamic
chart.

• Mixing ratio
• Mv (mass of vapor)
• _______________
• Md (masss of dry air)
• Thermodynamics of dry air ? air without any form
  of water.
• Moist air ? dry air water vapor.

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Moist adiabatic processes on a thermodynamic
chart.

• Let Md mass of dry air (N2, O2 etc.)
• Then Mv (is the mass of water vapor)
• Note you may see Ml (liquid) or Mi (ice) in this
  class or in other classes.c

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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

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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)

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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 (ms) ? mixing ratio the
  air would have at the ambient temperature if it
  was saturated.

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Moist adiabatic processes on a thermodynamic
chart.

• Vapor pressure ? partial pressure of water
  (Daltons Law)
• Thus the ideal gas law for dry air is
• P e rd Rd T

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Moist adiabatic processes on a thermodynamic
chart.

• Relate mixing ratio (m) to vapor pressure (e) !
• Relative humidity

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Moist adiabatic processes on a thermodynamic
chart.

• Equivalent Potential Temperaure Moist adiabats
• Lets derive! ?
• 1st law

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Moist adiabatic processes on a thermodynamic
chart.

• What to do? Lets
• 1. substitute in pa RT
• 2. parameterize the Latent Heat Release

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Moist adiabatic processes on a thermodynamic
chart.

• This becomes equation (1)
• OK, lets leave this alone and look at

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Moist adiabatic processes on a thermodynamic
chart.

• Take natural log
• Take the derivative of this, and a little
  algebra to get equation (2)

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Moist adiabatic processes on a thermodynamic
chart.

• Hmm. The RHS of eq. (1) and (2) are the same,
  so
• Then apply the snake

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Moist adiabatic processes on a thermodynamic
chart.

• After integrating, a bit o algebra, and
  assuming
• 1) ws / T ? 0
• 2) qo qe
• we get moist potential temperature!

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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 rd Rd T rv Rv T
• p r R T r Rd Tv
• ? where Tv is the Virtual temperature.

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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!!

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Moist adiabatic processes on a thermodynamic
chart.

• Or, the shortcut (graphical) method
• Tv T (ws / 6)
• where T is degrees C and ws is g/kg

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Moist adiabatic processes on a thermodynamic
chart.

• Questions?
• Comments?
• Criticisms?

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Moist adiabatic processes on a thermodynamic
chart.

• The end!