AOSC 620 Lecture 2 PHYSICS AND CHEMISTRY OF THE ATMOSPHERE I

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AOSC 620 Lecture 2PHYSICS AND CHEMISTRYOF THE
ATMOSPHERE I
Professor Russell Dickerson Room 2413, Computer
Space Sciences Building Phone(301)
405-5391 russ_at_atmos.umd.edu web site
www.meto.umd.edu/russ
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Experiment Room temperature
Last class TMean 23.3 /- 2.0C
(74/-3F) Measured with uncalibrated or no
thermometers.
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Raw Temp Data 1 Sept. 2009
20 20 21 21.1 22.2 22.8 22.8 23.4 24.6 25
25 25 25 25.6 26 23.3 C Mean 2.06 StDev
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Mean 23.3 /- 2.1C Median 23.4C
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Experiment Room temperature
Last class TMean 23.3 /- 2.0C (74F) Lets
repeat the experiment now that everybody has a
thermometer. Measure the current room
temperature. Do not discuss your results with
your colleagues. Write the temperature on a
piece of paper and hand it in.
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Lecture 2. Thermodynamics of Air, continued
water vapor.
Objective To find some useful relations among
air temperature, volume, and pressure. Review Ide
al Gas Law PV nRT Pa RT First Law of
Thermodynamics dq du dw W ? pda
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• Review (cont.)
• Definition of heat capacity
• cv du/dT ?u/?T
• cp cv R
• Reformulation of first law for unit mass of an
  ideal gas
• dq cvdT pda
• dq cpdT - adp

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• Review (cont.)
• For an isobaric process
• dq cpdT
• For an isothermal process
• dq - adp pda dw
• For an isosteric process
• dq cvdT du
• For an adiabatic process
• cvdT - pda and cpdT adp

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• Review (cont.)
• For an adiabatic process
• cvdT - pda and cpdT adp
• du dw
• (T/T0) (p/p0)K
• Where K R cp 0.286
• (T/?) (p/1000)K
• Define potential temperature
• ? T(1000/p)K
• Potential temperature, ?, is a conserved quantity
  in an adiabatic process.

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Review (cont.) The Second Law of Thermodynamics
is the definition of f as entropy. df dq/T ?
df 0 Entropy is a state variable. ?f
cpln(?/?0) In a dry adiabatic process potential
temperature doesnt change, thus entropy is
conserved.
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• Useful idea - a perfect or exact differential
• If z f(x,y), dz is a perfect differential if
• ?2f/?x?y ?2f/?y?x
• ? dz 0
• For example, v f(T,p)
• dv (?v/?p)T (?v/?T)p
• This is true for dU, dH, dG, but not dw or dq.

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Various Measures of Water Vapor Content

• Virtual temperature
• Dew point temperature
• Wet bulb temperature
• Equivalent temperature
• Isentropic Condensation Temperature

• Vapor pressure
• Vapor density absolute humidity
• Mixing ratio
• Specific humidity
• Relative humidity

• Potential temperature
• Wet-bulb potential temperature
• Equivalent potential temperature

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Virtual Temperature Tv or T
Temperature dry air would have if it had the
same density as a sample of moist air at the
same pressure.
Question should the virtual temperature be
higher or lower than the actual temperature?
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Consider a mixture of dry air and water vapor.
Let Md mass of dry air Mv mass of water
vapor md molecular weight of dry air mv
molecular weight of water.
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Daltons law P Spi
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Combine P and r to eliminate V
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Since P rRT
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Alternate derivation Since r proportional to Mwt
Where x H2O w/0.62 T T (29/(29-11H2O))
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Unsaturated Moist Air
Equation of state Pa RT
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Specific Heats for Moist Air
Let mv mass of water vapor md mass of
dry air To find the heat flow at constant volume
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For constant pressure
So Poissons equation becomes
(10.6w)/(10.9w) gt (1-0.2w) due to rounding
error.
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Water Vapor Pressure
Equation of state for water vapor ev rv Rv
T where ev is the partial pressure of water vapor