Basic Laws of Gases and Particulates

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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
P pressure V volume n mole R Ideal gas law
constant T Temperature M mass MW molecular
weight ? density Q volume flow rate molar
flow rate
Other references 1. CRC Handbook of Chemistry
Physics 2. Perrys Chemical Engineers Handbook
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Ideal Gas Law Constant
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?
Avogadros number 6.023?1023 molecules/mole At
1 atm and 25 oC, 1 mole of air has a volume of
24.5 L
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Unit of Concentration
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 correct to "dry" conditions when expressing
  concentrations.

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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

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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
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Humidity in Air/Water Mixture

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

• 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

Why is TDB always higher than TWB?
http//www.usatoday.com/weather/wsling.htm
Properties of TDB of 40 oC and TWB of 30 oC?
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http//howard.engr.siu.edu/staff1/tech/MET/ET401/L
AB/psychro_carrier_si.jpg
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Viscosity

• A measure of frictional force between fluid
  layers moving at different velocities

At 20 oC, the viscosity (?) of air is 1.81?10-5
Pas (Ns/m2). The temperature dependence (on
absolute temperature) is
(Valid between -70 to 500 oC)
What is the viscosity of air at 100 oC?
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Characterizing an Aerosol Particle
How do we characterize a particle?
Coal fly ash particles
Iron oxide particles from arc welding

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

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
• Spread
• Particle size distribution

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Type of Size Distribution

• Ex. A system containing spherical particles
• Number Concentration Mass
  Concentration
• 100 /cc 1?m ? 1.91g/cm3 10-10 g/cc 1?m
• 1 /cc 10?m
  10-9 g/cc 10?m

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
Number distribution function
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Settling Velocity
In settling, an aerosol experiences gravitational
force (FG) and drag force (FD)
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Brownian Motion Diffusion
http//galileo.phys.virginia.edu/classes/109N/more
_stuff/Applets/brownian/brownian.html
http//www.geocities.com/piratord/browni/Difus.htm
l

• The primary transport mechanism for small
  particles (lt 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

k 1.38X10-23 J/K or 1.38X10-16 erg/K
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Quick Reflection