Ch 9. Thermodynamics of Aerosols. CONTENTS 9.1 Thermodynamics Principles 9.2 Aerosol Liquid Water...

Ch 9. Thermodynamics of Aerosols

CONTENTS9.1 Thermodynamics Principles

9.2 Aerosol Liquid Water Content

9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect

9.4 Thermodynamics of Atmospheric Aerosol Systems

CONTENTS• 9.1 Thermodynamics Principles

• 9.1.1 Internal Energy and Chemical Potential

• 9.1.2 The Gibbs Free Energy• 9.1.3 Conditions for Chemical Equilibr

ium• 9.1.4 Chemical Potentials of Ideal Ga

ses and Ideal Gas Mixtures• 9.1.5 Chemical Potential of Solutions• 9.1.6 The Equilibrium Constant

Chemical Potential

藉由熱力學觀念討論 Gas-Phase 、 Aqueous Phase 、 Solid Phase 三相平衡SOLID=LIQUID

Chemical Potential =f(T, P, ni)ni:the moles of species i

9.1 Thermodynamics Principles

•9.1.3 Conditions for Chemical Equilibrium

自發性反應趨向減少 Gibbs free energy 之方向進行

0G

CONTENTS• 9.2 Aerosol Liquid Water Content

• 9.2.1 Chemical Potential of Water in Atmospheric Particles

• 9.2.2 Temperature Dependence of the DRH

• 9.2.3 Deliquescence of Multicomponent Aerosols

• 9.2.4 Crystallization of Single and Multicomponent Salts

DRH(deliquescence relative humidity)

Low RH aerosol solid

Deliquescence ：當 RH 開始增加至 DRH 時，氣膠內特定組成會開始吸收水分，藉以維持其其熱力學平衡關係，因而變為水相。每一物種之DRH並不相同。Crystallization ：當 RH 下降時，其水分會揮發形成結晶，但此 RH 與 DRH 並不相同。例如 (NH4)2SO4 , fig 9.4



DRH 、 Deliquescence 、 Crystallization ：與 G 相關

Deliquescence and Crystallization

Deliquescence當 RH<DRH, ， Solid 之 Gibbs free energy 較低，因而致使 (NH4)2SO4以 Solid 存在

當 RH>DRH ， Liquid 之 Gibbs free energy 較低，因而致使 (NH4)2SO4以 Liquid 存在

當 RH=DRH ，兩者之 Gibbs free energy 相同，因而致使 Solid 會開始吸收水分Gibbs free energy 變化圖

Crystallization當 RH 下降至 DRH 時，水分並不會在此時揮發。

RH 持續下降，使氣膠成為超飽和溶液。帶其達到臨界超飽和 (Critical Supersaturation) 後，即發生再結晶現象

Gibbs free energy 變化圖

9.2.1 Chemical Potential of Water in Atmospheric Particles

Water Vapor (atmosphere): the order of grams per m3 of air.

H2O concentration in the aerosol is less than 1 mg/m3 of air

氣膠相內水之濃度變化並不會影響大氣中水蒸氣之濃度氣膠熱力學模式計算時，可將 ambient RH 視為一常數

9.2.1 Chemical Potential of Water in Atmospheric ParticlesWater Activity

Pw: the water vapor pressure(in atm)

w: the water activity in solution

純水平衡 w=1 ， pw=pw0(T, saturation

vapor pressure)

(9.61) 、 (9.62) 可得

)(2)(2 aqg OHOH

)(22 )( aqOHgOH

)61.9(lnln *0

22 wOHwOH RTpRT

)62.9(ln 00*

22 wOHOH pRT

1000

RH

p

p

w

ww

9.2.1 Chemical Potential of Water in Atmospheric ParticlesWater Activity

由於 Pw/Pw0 即為相對濕度 (0~1) 之定義

大氣氣膠中之水活性 (w) 即為相對濕度 (RH)

單一鹽類於 DRH ， H2O 於氣相與氣膠相平衡

ws: the water activity of the saturated solution of the salt at T (It can be calculated from thermodynamic arguments )

1000

RH

p

p

w

ww

ws

DRH 100

9.2.2 Temperature Dependence of the DRH

單一鹽類之 DRH 會隨溫度改變 (推導 )、 (應用 )

n: the solubility of S in water(moles of solute/mole of water) (A 、 B 、 C)

Hs: the enthalpy of solution of the salt(data)

)()(2

)(2)(2

aqsaq

aqg

nSnSOH

OHOH

298

298ln

298

11exp298 TC

TB

TA

R

HDRHTDRH s

The solubility of S in water

The enthalpy of solution of the salt

DRH 理論值與量測值比較

(NH4)2SO4 之 DRH 變化較小，即接近常數

NaNO3 之 DRH 變化較大

DRH 理論值與量測值比較( 續 )

混合鹽類 (Mixed-Salt) 之 DRH會下降

Temperature Dependence of the DRH

bnSnSOH

aOHOH

aqsaq

aqg

)()(2

)(2)(2 )(

vs HHnH

)67.9(lnln

222 RT

Hn

RT

H

dT

pd

RT

H

dT

pd svww

)68.9(ln

2

0

RT

H

dT

pd vw

(a) 式：水之冷凝熱 (-Hv) 即為水之蒸發熱 (Hv) 之負值

(b) 式：鹽類之溶解熱 (Hs)

The overall enthalpy change

溶液中水蒸氣於此溫度之變化 =>Clausius-Clapeyron equation

純水時之飽和蒸汽壓：溫度T0wp

298

298ln

298

11exp298 TC

TB

TA

R

HDRHTDRH s

0

000

ln11

ln TTCT

TB

TTA

R

H

TDRH

TDRH s

2

100/ln

RT

Hn

dT

DRHd s

結合 (9.67) 、 (9.68)

代入 DRH 關係式

2

0/ln

RT

Hn

dT

ppd sww

Temperature Dependence of the DRH( 續 )

代入 n=A+BT+CT2 ，積分範圍 T0~T

T0=298 K

9.2.3 Deliquescence of Multicomponent Aerosols

多成分氣膠 (Multicomponent Aerosols)之吸水行為與單一鹽類相同。 KCl-NaCl之 deliquescence growth 、 evaporation 、crystallization 如 fig 9.7 。

Hydroscopic growth and evaporation of a mixed-salt particle

Initial66% mass KCl 34% mass NaCl

混合鹽類之 DRH 較低

DRH

Mixed-salt 72.7%

KCl 84.2%

NaCl 75.3%

推導雙電解質造成之 DRH 改變Gibbs-Duhem equation ：用於計算單一電解質加入單一溶質水溶液中之 DRH 改變於溫度 T 、壓力 p ，包含雙電解質 (1,2) 、水(w)

n1、 n2、 nw： the numbers of moles of electrolytes of 1, 2, and water

1、 2、 w： chemical potential


0dndndn ww2211


初時假設 electrolyte 1 與固相鹽類 1 平衡，此時並不包含 electrolyte 2 。加入 electrolyte 2 ， electrolyte 1 之化學潛能尚未改變，即 d1=0 。 electrolyte 2 和 H2O 之化學潛能 0dlnndlnn ww22

0dlnn

1000dlnm w

w22

1000

mM

n

n 2w

w

2 m2: the molality of electrolyte 2

Mw: the molecular weight of water

推導雙電解質造成之 DRH 改變


積分 m’2=0~m2

Wexler and Seinfeld(1991)

由上式可知加入 electrolyte 2 後， water activity會減少，因而降低 DRH

得知 ( 實例， NH4NO3 and NH4Cl)

1.DRH 時之水活性最小 (m2=0 ，左右兩項相等 )2. 混合鹽類之 DRH 恆小於單一鹽類之 DRH

2m

0

'2'

2

'22

'22

'2w

w

2w dmdm

md

m

m

1000

M-

0

mln

0mm 2w2w 0

dm

d

2

2

推導雙電解質造成之 DRH 改變


NH4NO3 and NH4Cl

303 K DRH

NH4Cl(only) 77.4%

NH4NO3(only) 61.8%

兩電解質混合後，潮解點相對濕度會降低，最低達 51% 。

1

23

4 56

7


NH4NO3 and NH4Cl

1

23

4 5 6

7

Solid Aqueous

1 - NO3-,NH4

+,Cl-

2 NH4Cl NO3-,NH4

+,Cl-

3 - NO3-,NH4

+,Cl-

4 NH4Cl NO3-,NH4

+,Cl-

5 - NO3-,NH4

+,Cl-

6 NH4NO3 NO3-,NH4

+,Cl-

7 NH4ClNH4NO3， RH<DRH*(51%)

不同 RH 時，氣膠內組成變化


氣膠內組成變化 (RH)

氣膠內組成： 40%NH4NO3 、 60%NH4Cl

RH ： 40%~90%(increase)

No evaporation and condensationRH xNH4NO3 xNH4Cl

51%* 0.811 0.189

60% 0.73 0.27

70% 0.42 0.58

71% - -

Eutonic point: 最低 DRH 之相對組成點

如表 9.4

DRH*

(Mutual deliquescence points)


多於三物種之相轉換圖 ( 如圖 9.9)• Solid:(NH4)2SO4 、 NH4HSO4 、 ((NH4)3H(SO4)2) 、 NH4N

O3 (Solid lines 區分各主導 solid ，為 phase boundary ，線上為共存。 Label : DRH)• Aqueous:H+ 、 NH4

+ 、 HSO4- 、 SO4

2- 、 NO3-

(Dashed lines 說明反應發生方向 )• Total Hydrogen= total moles of protons and bisulfate ions• Total Sulfate=total moles of sulfate and bisulfate ions• Dotted line 乃指反應發生方向 (path lines) ，乃指低於 DRH 之 RH(solid) 減少時之進行方向。如： 1 mole (NH4)2SO4 形成必須消耗 2 moles NH4

+ 、 1mole SO42- ，因而 X 、

Y 會改變。


X(Ammomia)

Y(Sulfate) DRH Solid

1 1 80% (NH2)4SO4

1 0.3 68% (NH2)4SO4·2NH4NO3

9.2.4 Crystallization of Single and Multicomponent Salts

1. 再結晶過程會有延遲現象。2. 多種鹽類組成之粒狀物會顯示多個再結晶點，如圖 9.7 。 KCl-NaCl 之組成有兩階段蒸發過程： KCl(65%) 、 NaCl(62%)3.Spann and Richardson(1985) ：氣膠組成介於 NH4HSO4和 (NH4)2SO4組成， crystallization RH:10%~40% ，於大氣中氣膠並不會呈現固體

CONTENTS• 9.3 Equilibrium Vapor Pressure Over a

Curved Surface: The Kelvin Effect• Aerosol : curved interface(not flat)• The effect of curvature ：在此之前所討論之物種蒸汽壓皆於一平面上，此一節將討論物種 A 於氣膠粒狀物表面上之蒸汽壓，其受曲面之影響

• Gibbs free energy•藉由形成單一液滴之 Gibbs free energy變化，引入表面張力相 (Derived)

G=Gdroplet-Gpure vapor (Result)

G for the formation of a single dropSpecies A 、 radius Rp 、 n molecules

NT: total number of vapor initially

After the drop forms: vapor, N1=NT-n

gl 、 gv:the G of a molecules (Liquid and Vapor)

: surface tension

Rp: the radius of curvature

n:the number of molecules in the drop

(gl-gv) (9-13)

at T, dni=0

dg=vdp or dg=(vl-vv)dp

vv>>vl ， dg=-vvdp

vv=kT/p

waterpuredrpolet GGG

vTplv gNRnggNG 21 4

24)( pvl RggnG

l

p

v

Rn

3

4 3

2

3

4)(3

4pvl

l

p Rggv

RG

A

A

p

pvl p

dpkTgg

0

0ln

A

Avl p

pkTgg

2

3

4ln3

4p

ll

p RSv

kT

v

RG

k

iiidnVdpSdTdG

1

Gibbs free change for formation of a droplet

Bulk free energy

Surface tension

The behavior of G as a function of Rp

S<1 Both terms are positive G increase with RpS>1 Small Rp:Surface tension term dominatesLarge Rp:Bulk free energy dominates

0Rp

G


The Kelvin effect(Derived)

液滴曲面對平衡蒸汽壓之影響於一外凸液面，要拉住一分子之其他液體分子數目比於一平面之液體數目為少，因而可知，與一液滴達到平衡之蒸汽分子所產生之氣壓要比平面液體之蒸汽壓高。

RpRT

Mpp

lAA

2exp0


The Kelvin effectGmaximum G* at Rp=Rp*

the equilibrium at this point is metastable S:Saturation ratio(pA/pA

0) :surface tension

orM:the molecular weight of the substance

l:the liquid-phase density

RpRT

Mpp

lAA

2exp0

2

3

4ln3

4p

ll

p RSv

kT

v

RG

0Rp

G

SkT

vR lp ln

2*

kTRp

vpp lAA

2exp0

The Kelvin Effect

Table 9.5 為水與有機物之表面張力。 298 K 時，五種有機物之分子量 (M/) 為水之 3~6 倍，但其表面張力皆為水之 1/3倍。


RpRT

Mpp

lAA

2exp0

The Kelvin EffectFig 9.12 為 H2O 、 DOP(typical organic compound) 於不同粒徑時，受 Kelvin effect 影響之大小


H2O ：於 0.1 m 時，增加2.1% ；於 0.01 m 時增加 23% ，可知約 50 nm 時， Kelvin effect 影響顯著。

較高分子量有機物，如 DOP ： <200 nm 時，則需加以考量

成長區

蒸發區

RpRT

Mpp

lAA

2exp0

CONTENTS• 9.4 Thermodynamics of Atmospheric

Aerosol Systems

• 9.4.1 The H2SO4-H2O system• 9.4.2 The Sulfuric Acid-Ammonia-

Water System• 9.4.3 The Ammonia-Nitric Acid-Water

System• 9.4.4 The Ammonia-Nitric Acid-

Sulfuric Acid-Water System• 9.4.5 Other Inorganic Aerosol

Species

9.4.1 The H2SO4-H2O systemH2SO4-hydroscopic, extremely low RH


Dp/Dp0:particle growth factor

Dpoln(pH2SO4/p0H2SO4):Kelvin effect parameter

How to use fig 9.13(1 m H2SO4-H2O droplet)

9.4.1 The H2SO4-H2O system

RH 50%(negligible Kelvin effect)

90%(negligible Kelvin effect)

H2SO4 Conc. 42.5% 18%

Density() 1.32 1.1

B. P. 115 C 100 C

Surface tension() 76 dyn/cm 73 dyn/cm

Normality 11 N 4 N

Mass concentration(xH2SO4) 0.55 g/cm3 of solution 0.2 g/cm3 of solution

Particle growth factor(Dp/Dp0) 1.48 2.12

pure H2SO4 1/1.48=0.68 m 2.12/1.48=1.43 m

Kelvin effect parameter 11.310-4 m 9.210-4 m

ln(pH2SO4/p0H2SO4) 11.310-4/0.68=16.6210-4 9.210-4/1.43= 6.410-4

(pH2SO4/p0H2SO4) 1.0017 1.0006

9.4.1 The H2SO4-H2O systemThe saturation vapor pressure of pure sulfuric acid, p0

H2SO4

p0H2SO4=1.31.010-8 atm(1310 ppb) at 296 K (T dependenc

e)

H2SO4 蒸汽壓於表面之變化，為 H2SO4-H2O 混合物內組成、溫度之函數RH>50% ， [H2SO4]<40% by mass ， xH2SO4<0.1(T=20 C) ， H2

SO4 equilibrium vapor pressure<10-12 mmHg 。[H2SO4]gas<[SO4

2-]aerosol

9.4.1 The H2SO4-H2O systemThe effect on the composition of atmospheric H2SO4-H2O droplets.

Particle size>1 m， negligible Kelvin effect

For smaller particles the H2SO4 mole fraction in the droplet is highly dependent on particle size.

The water concentration increases as the RH increase.

9.4.1 The H2SO4-H2O systemThe composition of atmospheric H2SO4-H2O droplets

The vapor pressure of H2SO4(g) is zero over atmospheric particles

The whole systembisulfate dissociation reaction

Keq(298 K)=1.0110-2(mol/kg)

The molar ratio of HSO4- to SO4

2-

The ratio is proportional to [H+]

[H+],pH,[HSO4-]

4)(42 HSOHSOH g

)(42)(42 aqg SOHSOH

244 SOHHSO

44

24

24

2

,2 /1001.1HSOHSO

SOHSOH

m

mmkgmol

H

HSO

SOH

SO

HSO mm

m

4

24

24

4

2

,99

9.4.2 The Sulfuric Acid-Ammonia-Water SystemT, RH, NH3, H2SO4, determine the aerosol composition

30%, 298 K, 10 g/m3 H2SO4


[NH3]/[H2SO4]

<0.5 H2SO4 dominate

0.5~1.25 NH4HSO4 dominate

1.25~1.5 (NH4)3H(SO4)2 dominate

2 (NH4)2SO4 dominate

>2 NH3, it does not change the aerosol composition

0.5 1 1.25 2[NH3],[H2SO4],H2O , total mass

9.4.2 The Sulfuric Acid-Ammonia-Water System75%, 298 K, 10 g/m3 H2SO4


[NH3]/[H2SO4]

<0.5 H2SO4 dominate

0.5~1. 5 HSO4- dominate

High NH3 SO42- dominate

DRHNH4HSO4 40%

DRH(NH4)3H(SO4)2 69%

DRH(NH4)2SO4 80%

Molar ratio=2, form (NH4)2SO4, loss water

Liquid phaseSolid Phase


9.4.2 The Sulfuric Acid-Ammonia-Water SystemNH3/H2SO4

molar ratio<0.5

Exist primarily as H2SO4 solution

0.5< NH3/H2SO4 molar ratio<1.5

Consist mainly as HSO4-

NH3/H2SO4 molar ratio=2

Consist mainly as (NH4)2SO4

NH3/H2SO4 molar ratio>2

Ammonia also exist in the gas phase

9.4.3 The Ammonia-Nitric Acid-Water System

NH3(g)+HNO3(g)NH4NO3(s)

Condition:high NH3、 high HNO3、 lowSO42-

2 Cases for NH4NO3

Ambient RH<DRHSolid Ambient RH>DRHLiquid




Ambient RH<DRHSolid

Equilibrium condition (chemical potential of ideal gases and solids)

Kp(ppb2): estimated by van’t Hoff equation, shown as fig9.19, it is sensitive to T change

6954.17.723

ln T

DRH

T(K) DRH

298 61.8%

288 67%

3433 NONHHNONH 33

3334

00*

exp HNONHpHNONHNONH ppTK

RT

298ln1.6

242206.84ln

T

TKp


Lower TLower KpLower equilibrium values of the NH3 and HNO3 gas-phase concentrations

Lower T shift the equilibrium of the system toward the aerosol phase, increasing the aerosol mass of NH4NO3(fig 9.20)



NH3(g)+HNO3(g)NH4++NO3

-(9.92)

Ambient RH>DRHLiquid(8~26 M)

Strongly non-idealneed activity coefficient

Equilibrium condition

Estimate K(T)Need “m”Need aerosol water content

Fig 9.21 depicts the results of such a computation.(The product of the mixing ratios of ammonia and nitric acid over solution as a function of RH)

3433 NONHHNONH

33

34344333

00

expNHHNO

NONHNONHNHNOHNONH

pp

mm

RT

3434

2

NONHNONH

33

3434

2

92.9NHHNO

NONHNONH

pp

mmK

TTTK

298298ln151.111

2987.64exp104 17

92.9


Water activity=RH

One needs to relate the tendency of the aerosol components to absorb moisture(RH)

W: the mass of aerosol water(kg of water/m3 of air)

Ci:the aqueous-phase concentration of electrolyte i (moles/m3 of air)

mi,o(aw):the molality(mol/kg) of a single-component aqueous solution of electrolyte i (water activity, aw=RH/100)查表計算

Aerosol water content

(ZSR relationship, Zdanovskii-Stokes-Robinson relationship)

i w

aoi

miC

W,



-(9.92)Y=1no (NH4)2SO4, 隨 RH 增加，濃度乘積快速減少，可知主要以 aerosol phase 為主。 Water 會使 NH4NO3 溶解，並使其在 aerosol phase 量增加。

33 NHHNOpK



-(9.92)

Input RH, T, [TN], [TA], 可知 gas phase-aerosol phase 平衡組成[TN]=[HNO3(g)]+[NO3

-]

[TA]=[NH3(g)]+[NH4+]

Kp/(RT)2[TN][TA]: no NH4NO3

[TN][TA]Kp/(RT)2: NH4NO3 formation

Equilibrium Kp/(RT)2=[NH3(g)]e[HNO3

(g)]e[NH4NO3]e=0.5([TA]+[TN]-[([TA]+[TN])2-4([TA][TN]-Kp/(RT)2)]0.5

[NH3(g)]=[TA]-[NH3NO3]e

[HNO3(g)]=[TN]-[NH3NO3]e92.9

2

3434

K

mmK NONHNONH

p

9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System

Gas Phase: NH3,HNO3,H2SO4,H2O

Solid Phase:NH4HSO4, (NH4)2SO4, NH4NO3, (NH4)SO4·2NH4NO3, (NH4)2SO4 ·3NH4NO3,(NH4)3H(SO4)2

Aqueous Phase:NH4+,H+,HSO4

-,SO42-,NO3

-,H2O

Two observations 1.Sulfuric acid possesses an extremely low vapor pressure( 僅在 aeros

ol) 2.(NH4)2SO4 solid or aqueous is the preferred form of sulfate

Two regime

Fig 9.23


Ammonia SO42- form NH4NO3

Poor [TA]<2[TS] HSO4- No

Rich [TA]>2[TS] SO42- Yes

9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System


Low [NH3] : SO42- and HSO4

-

As NH3 increase: NH4NO3 become important

Aerosol water content : nonlinear( 與其電解質組成變化有關 )

nonlinear

Low NH3 High NH3


9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water Systemsulfatereplacement by nitrate(HNO3 and NH3 react)

sulfateNO3- , and NH4

+, water, total mass

The reduction of the mass is nonlinear

減少 20 g SO42-/m3(from 30 to 10 g/m3)

Dry aerosol mass 減少 12.9 g/m3

只會增加 10 g NO3-/m3

僅會減少 2.9 g NH4+/m3

9.4.5 Other Inorganic Aerosol Species

加入其他物種 (Cl-、 Na+) 之熱力學計算NaCl(s)+HNO3(g)NaNO3(s)+HCl(g)

2NaCl(s)+H2SO4(s) Na2SO4(s)+2HCl(g)

NaCl(s)+H2SO4(s) NaHSO4(s)+HCl(g)


Suppose a solution contains 6 moles H+/m3, 6 moles Na+/m3, 7 moles Cl-/m3, 5 moles NO3

-/m3

The 4 ions can combine in many ways to form electrolytes: HNO3, HCl, NaNO3, NaCl.

Mass-balance

CH+,m=CHNO3,m+CHCl,m CNa+,m=CNaNO3,m+CNaCl,m

CCl+,m=CHCl,m+CNaCl,m CNO3-,m=CHNO3,m+CNaNO3,m

Result

Y0,k,Y1,k,Y2,k: polynomial coefficients(table)


Case CHCl,m CHNO3,m CNaCl,m CNaNO3,m

1 6 0 1 5

2 4 2 3 3

3 1 5 6 0

mHCl

mHCl

mHNO

mHNO

mNaNO

mNaNO

mHCl

mNaCl

ww m

C

m

C

m

C

m

C

mC

,

,

,

,

,

,

,

,

3

3

3

31000

3,3

2,2,1,0, wkwkwkkak aYaYaYYm


RPM input: TOTSO4, TOTNH3, TOTNO3

1. 分配 : Temp, gas phase and aerosol phase

TOTSO4 皆為 aqueous phase

2. Composition

1. SO42->2NH4

+: all NH4+(NH4)2SO4 、 H2SO4 、 HNO3

2. 2NH4+>SO4

2-: (NH4)2SO4 、 NH4NO3 、 HNO3

3. Aerosol water content

依個別計算所得之物種莫爾濃度 (in air) 配合大氣相對溼度，計算其相對吸水量，相加後即得氣膠含水量。

i wio

i

am

MW 3

,32

,2,1,00 )( wiwiwiiwi aYaYaYYam

Y’s 為 polynomial coefficients( 如表 )

計算含水率之重要參數 (298.15 K)

(NH4)2SO4

37% R.H.; 29.0 m

HNO3

0% R.H.; 22.6 m

H+/HSO4-

0% R.H.; 30.4 m

NH4NO3

62% R.H.; 28 m

(NH4)2SO4

37% R.H.; 29.0 m

2H+/SO42-

0% R.H.; 30.4 mY

0

1.1065495×102 2.306844303×101 3.0391387536×101 3.983916445×103 1.1065495×102 3.0391387536×101

Y

1

-3.6759197×102 -3.563608869×101 -1.8995055929×102 1.153123266×104 -3.6759197×102 -1.8995058929×102

Y

2

5.0462934×102 -6.210577919×101 9.7428231047×102 -2.13956707×105 5.0462934×102 9.7428231047×102

Y

3

-3.1543839×102 5.510176187×102 -3.1680155761×103 7.926990533×105 -3.1543839×102 -3.1680155761×103

Y

4

6.770824×101 -1.460055286×103 6.1400925314×103 -1.407853405×106 6.770824×101 6.1400925314×103

Y

5

1.894467542×103 -6.9116348199×103 1.351250086×106 -6.9116348119×103

Y

6

-1.220611402×103 4.1631475226×103 -6.770046794×106 4.1631475226×103

Y

7

3.098597737×102 -1.0383424491×103 1.393507324×105 -1.0383424491×103

3,3

2,2,1,00 )( wiwiwiiwi aYaYaYYam

Ch 9. Thermodynamics of Aerosols. CONTENTS 9.1 Thermodynamics Principles 9.2 Aerosol Liquid Water...

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Transcript of Ch 9. Thermodynamics of Aerosols. CONTENTS 9.1 Thermodynamics Principles 9.2 Aerosol Liquid Water...