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 4/23/2017

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 4/23/2017

Ideal Gas Law Constant 82.057 8.314 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 4/23/2017

Unit of Concentration Is 1 g/cm3 SO2 equal to 1 ppm SO2? Section 7.1.2 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”? 4/23/2017

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. volume basis wet volume basis dry CO2 18% 18%*(100/88) = 20.5% H2O 12% O2 10% 10%*(100/88) = 11.4% N2 60% 60%*(100/88) = 68.2% Total = 100% (100-12)%*(100/88) = 100% 4/23/2017

(Saturation) 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 (Saturation) Vapor Pressure Time to reach equilibrium How does vapor pressure change if the temperature increases? Pv in mmHg and T in oC (if Table 9.2 is used) 4/23/2017

4/23/2017

What is the vapor pressure of water at 20 oC 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? 4/23/2017

Partial Pressure ya: mole fraction of component “a” Saturation Ratio 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 1 mole of O2 @ 1 atm 4 moles of N2 How much is PO2? Supersaturation: S > 1 (RH > 100%) Saturation Ratio (or relative humidity for water) After a shower at dusk, the temperature starts to drop. How do PV and Pa change correspondingly? 4/23/2017

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? 4/23/2017

http://howard. engr. siu http://howard.engr.siu.edu/staff1/tech/MET/ET401/LAB/psychro_carrier_si.jpg 4/23/2017

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? 4/23/2017

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? 4/23/2017

Size Range of Aerosol Particles Hinds, Aerosol Technology, 1999 4/23/2017

Aerosol Size Distribution How do we characterize particle”S”? Concentration: Number concentration by counting Mass concentration by weight measurement Size Spread Particle size distribution Distribution function 4/23/2017

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 Mass Distribution Mass distribution function Number distribution function 4/23/2017

Settling Velocity How do we determine the particle size? Microscopy, Settling velocity, Light scattering How do we determine the particle size? In settling, an aerosol experiences gravitational force (FG) and drag force (FD) FG=mg t=0 V(t)=0 t= V(t)=? t>3 V(t)=VTS FD=3V(t)dp FD=3VTSdp When they are equal to each other, there is no more acceleration. How to get a larger settling velocity? 4/23/2017

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 How to get a larger diffusivity? Stokes-Einstein Equation for Diffusion Coefficient k = 1.38X10-23 J/K or 1.38X10-16 erg/K 4/23/2017

Quick Reflection 4/23/2017