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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. Ideal Gas Law. P : pressure V : volume n : mole

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Basic laws of gases and particulates l.jpg
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. Perry’s 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?

Avogadro’s 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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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”?

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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(Saturation) Vapor Pressure

Time to reach equilibrium

How does vapor pressure change if the temperature increases?

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

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

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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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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

ya: mole fraction of component “a”

in the mixture in the gas phase

PT: total pressure of the system

4 moles of N2

1 mole of O2 @ 1 atm

Saturation Ratio

(or relative humidity for water)

How much is PO2?

Supersaturation: S > 1 (RH > 100%)

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

Partial Pressure

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Humidity in Air/Water Mixture would exert if it were to occupy the entire volume occupied by the 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?

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

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

At 20 oC, the viscosity () of air is 1.8110-5 Pa·s (N·s/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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Distribution function

Aerosol Size Distribution

How do we characterize particle”S”?

  • Concentration:

    • Number concentration by counting

    • Mass concentration by weight measurement

  • Size

  • Spread

  • Particle size distribution

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Mass Distribution

Mass distribution function

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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How do we determine the particle size?

Microscopy, Settling velocity, Light scattering

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






How to get a larger settling velocity?







Settling Velocity

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

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Stokes-Einstein Equation for

Diffusion Coefficient

How to get a larger diffusivity?

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

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

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Quick Reflection