Basic Laws.pptx
Transcript of 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 -
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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