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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: 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.
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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
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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 (m s ) 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 (Dalton’s Law) Thus the ideal gas law for dry air is P – e = d R d 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 Let’s derive! 1st law:
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Moist adiabatic processes on a thermodynamic chart. What to do? Let’s 1. substitute in p = RT 2. “parameterize” the Latent Heat Release:
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Moist adiabatic processes on a thermodynamic chart. This becomes equation (1) OK, let’s 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) w s / T 0 2) o = e 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 = d R d T + v R v T p = R T = R d T v where T v 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: T v = T + (w s / 6) where T is degrees C and w s 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!
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