Basic Laws.pptx

7/27/2019 Basic Laws.pptx

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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


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Ideal Gas Law

Other references:

1. CRC Handbook of Chemistry & Physics

2. Perrys Chemical Engineers Handbook

TRnQP

TRMWP

TRMW

MTRnVP

P: pressure

V: volumen: mole

R: Ideal gas law constant

T: Temperature

M: mass

MW: molecular weight: density

Q: volume flow rate

: molar flow raten


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Ideal Gas Law Constant

82.057

8.3148.314

8.314

What is the volume of 1 g-moleof 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?

Avogadros number:

6.0231023 molecules/mole

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


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Unit of Concentration

Is 1 g/cm3

SO2 equal to 1 ppm SO2?

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

Is ppm molar basis, volume basis or mass basis?

Whats the difference between ACFM and SCFM?

Section 7.1.2


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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 correctto "dry" conditions when expressing concentrations.

volume basis wet volume basis dry

CO2 18% 18%*(100/88) = 20.5%

H2

O 12%

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

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

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


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Vapor Pressure

The pressure required to maintain a vaporin equilibrium

with the condensed vapor (liquid or solid) with a flatsurface at a specified temperature

TC

BATPv )(log Pv in mmHg and Tin 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?


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Partial Pressure

)100()( SRHTPP

Sv

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 ain the mixture in the gas phase

PT: 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

?


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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 wickwrapped 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 40oC and TWB of 30

oC?

Why is TDB

always higher than TWB

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


11/198/18/201311http://howard.engr.siu.edu/staff1/tech/MET/ET401/LAB/psychro_carrier_si.jpg


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Viscosity

A measure of frictional force between fluid layersmoving at different velocities

At 20 oC, the viscosity () of air is 1.8110-5 Pas (Ns/m2).

The temperature dependence (on absolute temperature) is:

74.0

1

212

T

T

What is the viscosity of air at 100 oC?

(Valid between -70 to 500 oC)


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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?


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Size Range of Aerosol Particles

Hinds, Aerosol Technology, 1999


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Aerosol Size Distribution

How do we characterize particleS?

Concentration: Number concentration by counting

Mass concentration by weight measurement

Size

SpreadParticle size distribution

dp

(m)

0 10 20 30 40 50

q(dp)ProbabilityDensityFunction

0.00

0.02

0.04

0.06

0.08

0.10

Distributionfunction


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0 10 20 30 40 50

q(dp)ProbabilityDensityFunction

0.00

0.02

0.04

0.06

0.08

0.10

Type of Size Distribution

Ex. A system containing spherical particles

Number Concentration: Mass Concentration:100 #/cc 1m & = 1.91g/cm3 10-10 g/cc 1m

1 #/cc 10m 10-9 g/cc 10m

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

dp (m)

0 10 20 30 40 50

Massfraction/m

0.00

0.01

0.02

0.03

0.04

Number Distribution

Numberdistribution

function

Mass Distribution

Massdistributionfu

nction


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Settling Velocity

Microscopy, Settling velocity, Light scattering

How do we determine the particle size?

FG=mg

t=0

V(t)=0

FG=mg

t=

V(t)=?

FG=mg

t>3

V(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

pp

TSp

How to get a larger

settling velocity?


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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 aparticle 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 lowerconcentration

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

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

p

c

d

kTCD

3

Stokes-Einstein Equation for

Diffusion CoefficientHow to get a

larger diffusivity?k= 1.38X10-23 J/K or 1.38X10-16 erg/K
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.htmlhttp://www.geocities.com/piratord/browni/Difus.htmlhttp://www.geocities.com/piratord/browni/Difus.htmlhttp://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html


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Quick Reflection

Documents

Basic Laws.pptx