Basic Laws of Gases and Particulates

1. 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

2. 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

3. 82.057 8.314 8.314 8.314 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

4. 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

5. 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.

6. (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)

8. 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?

9. 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

10. 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?

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

12. 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 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?

13. 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?

14. Size Range of Aerosol Particles Hinds, Aerosol Technology, 1999

15. 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

16. 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

17. How do we determine the particle size? Microscopy, Settling velocity, Light scattering When they are equal to each other, there is no more acceleration. FD=3VTSdp FD=3V(t)dp FG=mg FG=mg FG=mg How to get a larger settling velocity? t>3 V(t)=VTS t= V(t)=? t=0 V(t)=0 Settling Velocity In settling, an aerosol experiences gravitational force (FG) and drag force (FD)

18. Stokes-Einstein Equation for Diffusion Coefficient How to get a larger diffusivity? Brownian Motion & Diffusion http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html http://www.geocities.com/piratord/browni/Difus.html • 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

19. Quick Reflection