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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
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
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

ideal gas law constant





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

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”?

Unit of Concentration

Section 7.1.2

concentration on a dry basis
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.
vapor pressure

(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)


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?

partial pressure

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
humidity in air water mixture
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?

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


  • 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?

characterizing an aerosol particle
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?

size range of aerosol particles
Size Range of Aerosol Particles

Hinds, Aerosol Technology, 1999

aerosol size distribution

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
type of size distribution

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

settling velocity

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)

brownian motion diffusion

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