04/24/231

Basic Laws of Gases and Particulates

• Ideal gas law• Unit of concentration• Vapor pressure & partial pressure• Humidity & psychrometric chart• Viscosity• Aerosol size• Aerosol size distribution• Settling velocity• Brownian motion and diffusion

04/24/232

Ideal Gas Law

Other references:1. CRC Handbook of Chemistry & Physics2. Perry’s Chemical Engineers’ Handbook

TRnQPTRMWP

TRMWM

TRnVP

P: pressureV: volumen: moleR: Ideal gas law constantT: TemperatureM: massMW: molecular weight: densityQ: volume flow rate : molar flow raten

04/24/233

Ideal Gas Law Constant

82.057

8.314 8.314

8.314

What is the volume of 1 g-mole of air at 25 oC and 1 atm?

How many lb-moles are there for 380 ft3 of air at 60 oF and 14.7 psi?

Avogadro’s number: 6.0231023 molecules/mole

At 1 atm and 25 oC, 1 mole of air has a volume of 24.5 L

04/24/234

Unit of Concentration

Is 1 g/cm3 SO2 equal to 1 ppm SO2?

The annual standard of NO2 is 100 g/m3. What is the concentration in ppb?

Is “ppm” molar basis, volume basis or mass basis?

What’s the difference between “ACFM” and “SCFM”?

Section 7.1.2

04/24/235

Concentration on a “dry” basis• Water vapor is commonly present in a heated gas

stream, e.g., combustion of a hydrocarbon fuel. • Water vapor can condense as temperature cools down.

The amount varies and is very sensitive to temperature. • To prevent the variation, standards are written to correct

to "dry" conditions when expressing concentrations.

volume basis wet volume basis dryCO2 18% 18%*(100/88) = 20.5%

H2O 12%

O2 10% 10%*(100/88) = 11.4%

N2 60% 60%*(100/88) = 68.2%

Total = 100% (100-12)%*(100/88) = 100%

04/24/236

Vapor Pressure

The pressure required to maintain a vapor in equilibrium with the condensed vapor (liquid or solid) with a flat surface at a specified temperature

TCBATPv

)(log Pv in mmHg and T in oC (if Table 9.2 is used)

(Saturation) Vapor PressureTime to reach equilibrium

How does vapor pressure change if the temperature increases?

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What is the vapor pressure of water at 20 oC? If the measurement is conducted on Mars (the atmospheric pressure is about 0.006 atm), what will be the value?

04/24/239

Partial Pressure

)100( )(

SRHTPPSv

a Supersaturation: S > 1 (RH > 100%)

Saturation Ratio (or relative humidity for water)

The pressure that a gas (or vapor) in a mixture of gases would exert if it were to occupy the entire volume occupied by the mixture

Taa PyP ya: mole fraction of component “a” in the mixture in the gas phasePT: total pressure of the system

After a shower at dusk, the temperature starts to drop. How do PV and Pa change correspondingly?

1 mole of O2 @ 1 atm

4 moles of N2

How much is PO2?

04/24/2310

Humidity in Air/Water Mixture

• Psychometric Chart (Figure 1.3)– Dry bulb temperature– Wet bulb temperature: the temperature at

which a thermometer with a wet wick wrapped around the bulb stabilizes

http://www.usatoday.com/weather/wsling.htm

• The state of an air/water mixture is determined by pressure, temperature & humidity

Properties of TDB of 40 oC and TWB of 30 oC?

Why is TDB always higher than TWB?

04/24/2311http://howard.engr.siu.edu/staff1/tech/MET/ET401/LAB/psychro_carrier_si.jpg

04/24/2312

Viscosity• A measure of frictional force between fluid layers

moving at different velocities

At 20 oC, the viscosity () of air is 1.8110-5 Pa·s (N·s/m2).The temperature dependence (on absolute temperature) is:

74.0

1

212

TT

What is the viscosity of air at 100 oC?

(Valid between -70 to 500 oC)

04/24/2313

Characterizing an Aerosol Particle How do we characterize a particle?

• Size, Shape, Density, Composition (toxicity, corrosivity, reactivity), Phase (liquid, solid)

Coal fly ash particles Iron oxide particles from arc welding

Why should we care the aerosol size?

04/24/2314

Size Range of Aerosol Particles

Hinds, Aerosol Technology, 1999

04/24/2315

Aerosol Size DistributionHow do we characterize particle”S”?

• Concentration:– Number concentration by counting– Mass concentration by weight measurement

• Size• Spread Particle size distribution

Dis

tribu

tion

func

tion

04/24/2316

Type of Size DistributionEx. A system containing spherical particlesNumber Concentration: Mass Concentration:100 #/cc 1m & = 1.91g/cm3 10-10 g/cc 1m1 #/cc 10m 10-9 g/cc 10m

Do we have “more” 1 m or 10 m particles (i.e. are the majority 1 or 10 m)? How will it impact the PSD we see?

Number Distribution

Num

ber d

istri

butio

n fu

nctio

n

Mass Distribution

Mas

s di

strib

utio

n fu

nctio

n

04/24/2317

Settling Velocity

Microscopy, Settling velocity, Light scatteringHow do we determine the particle size?

FG=mg

t=0V(t)=0

FG=mg

t=V(t)=?

FG=mg

t>3V(t)=VTS

FD=3V(t)dp

FD=3VTSdp

In settling, an aerosol experiences gravitational force (FG) and drag force (FD)

When they are equal to each other, there is no more acceleration.

mgdVFF ppGD 3

18

2gdVV ppTSp

How to get a larger settling velocity?

04/24/2318

Brownian Motion & Diffusion

• The primary transport mechanism for small particles (< 0.1 m); Important when transport distance is small: e.g. filter, airway in human lung– Brownian motion: irregular wiggling motion of a

particle caused by random bombardment of gas molecules against the particle

– Diffusion: the net transport of the particles from a region of higher concentration to a region of lower concentration

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html

http://www.geocities.com/piratord/browni/Difus.html

p

c

dkTCD3

Stokes-Einstein Equation for Diffusion Coefficient How to get a

larger diffusivity?k = 1.38X10-23 J/K or 1.38X10-16 erg/K

04/24/2319

Quick Reflection