UNDERSTANDING WHAT HUMIDITY DOES AND WHY

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1 PRACTICAL GUIDE The following article was published in ASHRAE Journal, April Copyright 1999 American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc. It is presented for educational purposes only. This article may not be copied and/or distributed electronically or in paper form without permission of ASHRAE. UNDERSTANDING WHAT HUMIDITY DOES AND WHY By Kenneth M. Elovitz, P.E. Member ASHRAE P eople sometimes attribute effects to humidity without understanding the underlying physics. For example, we have all experienced hot, humid summer weather. Yet the outdoor air relative humidity on a hot, humid summer day (95 F db/78 F wb [35 C db/26 C wb]) is less than 50%. By contrast, the outdoor air relative humidity on a cold, dry winter day is typically around 80%. This article examines the difference between relative humidity, specific humidity, and vapor pressure. It goes on to explore how those measures influence phenomena loosely attributed to humidity. Measures of Humidity Different measures of humidity quantify different physical properties of the mixture of water vapor (moisture) and air. Understanding how moist air behaves requires understanding those measures of humidity. Relative humidity is the ratio of the amount of water vapor in the air to the amount of water vapor air can hold at that temperature. At 100% relative humidity, the dry bulb, wet bulb, and dew point temperatures are equal. At 100% relative humidity, the air is saturated, which means it cannot hold any more moisture. Raising the temperature without changing the amount of moisture in the air reduces the relative humidity. The relative humidity goes down because warmer air can hold more moisture than colder air. For example, a comfort cooling system might be designed to maintain 75 F (24 C)/55% RH at design load using 56 F (13 C) coil leaving air temperature. The system might have enough sensible capacity to cool the room to 70 F (21 C) at less than design load, or the system might be oversized. The coil leaving air temperature does not change, so the available dehumidification capacity does not change. The resulting room relative humidity at 70 F (21 C) will be 65%, possibly generating complaints that the relative humidity is too high. While room conditions should be analyzed in accordance with ASHRAE Standard , Thermal Environmental Conditions for Human Occupancy to evaluate comfort, if relative humidity itself is the problem, one practical solution might be to operate the system at the design temperature setpoint of 75 F (24 C). Achieving moderately low humidity at low room temperatures may require using a reheat system. Achieving low relative humidity at low temperatures usually requires specialized systems like desiccant dehumidification. Specific humidity is the amount of moisture in the air per unit mass of air. It is usually expressed as grains of water per pound of dry air (gr/lb) or pounds of water per pound of dry air (lbw/lbda, kgw/kgda). Specific humidity is proportional to the enthalpy or total energy content of the moist air mixture. Specific humidity changes when moisture is added or removed. Changing temperature does not change specific humidity unless the air is cooled below the dew point. Dew point is the temperature where moisture begins to condense out of the air. When air is cooled to its dew point, it reaches 100% relative humidity or saturation. Cooling the air any further causes water vapor in the air to change to the liquid phase. Liquid water molecules accumulate, droplets form, and moisture condenses out of the air. At the new conditions, the air contains less moisture, has lower specific humidity, and has a lower dew point temperature, but it is still at 100% relative humidity. Raising the temperature of air at its dew point reduces its relative humidity but does not change its water vapor content (specific humidity) so does not change its dew point. Vapor pressure is the pressure exerted by free molecules at the surface of a solid or liquid. Consider water in a closed vessel at 75 F (24 C). Water will evaporate until the partial pressure of the water in the vessel reaches 0.44 in. Hg (1.49 kpa), which 75 ASHRAE Journal April 1999

2 Practical Guide Figure 1a: Temperature and moisture gradient in a wall (condensation). is the vapor pressure of water at 75 F (24 C). For a given substance, vapor pressure is a function of temperature. As temperature increases, vapor pressure increases. When the vapor pressure reaches atmospheric pressure (29.92 in. Hg [100 kpa]), the liquid boils. For water at sea level, this condition occurs at 212 F (100 C). At 5,000 ft (1524 m) above sea level, atmospheric pressure is only in. Hg (84 kpa). That is why water boils at 202 F (94 C) in Denver. Vapor pressure is a measure of the affinity of a substance for itself. If a substance has low affinity for itself, it evaporates readily even at low temperature. The substance will have a high vapor pressure. For most HVAC processes, the vapor pressure of interest is for water in contact with itself. However, water in contact with other substances (e.g., wood, paper, salt) also has a vapor pressure. The vapor pressure of water in contact with those other substances may be different from the vapor pressure of water in contact with itself. Figure 1b: Temperature and moisture gradient in a wall (no condensation). Effects of Humidity Understanding how moisture affects materials and processes requires understanding whether those effects are a function of relative humidity, specific humidity, or vapor pressure. Much of the literature on effects of humidity covers a narrow temperature range. Those studies likely used relative humidity because it is easy to measure. At constant temperature, relative humidity varies directly with moisture content the lower the moisture content, the lower the relative humidity. Since the studies were conducted over a narrow temperature range, the data lend little insight into whether the operative factor is relative humidity, specific humidity, or vapor pressure. Engineers must identify the operative parameter before they can design HVAC/R systems that avoid or mitigate the effects of moisture in the air. Condensation Condensation is strictly a function of relative humidity. When air cools to a temperature below its dew point, moisture condenses out of the air. It is not necessary to cool the entire air mass to get condensation. Condensation occurs on the coldest surface in a room. A cold window might cool nearby air below its dew point and cause condensation while the rest of the room remains at normal temperature. Condensation causes a variety of problems. Condensation is a housekeeping problem if moisture puddles on the floor or if droplets stain the materials they contact. Condensation can damage wood, paper, and fabric, and it accelerates rusting of steel. It can also hurt products like frozen foods in a supermarket. No one wants to buy the package of ice cream coated with frost. Moreover, for water vapor in the air to form frost on the package of ice cream, it must give up its heat of vaporization (approximately 1000 Btu/lb [2326 kj/kg]) and its heat of fusion (approximately 144 Btu/lb [335 kj/ kg]). It gives up some of that heat to the air and some of it to the ice cream. The ice cream warms up a bit and can even begin to soften or melt if the freezer is not cold enough. HVAC/R designs generally try to avoid condensation in the conditioned space. For cooling applications, they accomplish that goal with dehumidifying coils that remove moisture from the supply air before it enters the conditioned space. Most comfort cooling systems are designed to control temperature, so they control 76 ASHRAE Journal April 1999

3 Museums & Renovation INDOOR TEMPERATURE 70 F (21.1 C) OUTDOOR TEMPERATURE 10 F ( 23.3 C) INDOOR MOISTURE 22.4 GR/LB OUTDOOR MOISTURE 1.3 GR/LB CUMULATIVE FRACTION OF SFCE. TEMP. CUMULATIVE MOISTURE SURFACE DEW POINT ITEM R-VALUE R-VALUE TEMP. DIFF. F ( C) PERMS REPS REPS DIFFERENCE GR/LB F ( C) Inside air film (17.1) nil ( 2) Paint nil (17.1) ( 3) ½ inch Wallboard (14.4) ( 3) 3½ inch Air space (8.4) ( 3) ¾ inch Polystyrene ( 13.8) ( 6) ½ inch Plywood ( 17.5) ( 20) Clapboards ( 22.3) ( 33) Outside air film ( 23.3) nil ( 33) Notes: (1) Perms are grains/hr per sq ft per in. Hg Pressure difference (3) SFCE. Temp. is on outside face of surface. (2) Reps are 1/perms (4) SFCE. Temp. = Indoor Temp. (Frac. of Temp. Diff. x Total Demp Diff.) Table 1: Stud wall dew point analysis. relative humidity and the risk of condensation only indirectly. However, matching both the sensible (temperature) and latent (dehumidification) capacities to the cooling loads is part of a successful design. Excessive winter humidification risks condensation on cold window and wall surfaces. Excess humidification is humidity above what the building envelope was designed to accommodate. Besides condensation, excess humidification can cause problems like peeling paint, either inside or outside. Moisture in the Building Structure Condensation problems are not limited to the occupied space. Condensation inside walls can be a serious problem. Any conditioned building has a temperature gradient between indoors and outdoors. The temperature difference across each element of the wall structure is proportional to the insulating value of that element. Buildings also have a moisture gradient between indoors and outdoors. The moisture difference across each element of the structure is proportional to the vapor diffusion resistance of the element. Figure 1 illustrates the temperature and vapor pressure gradients in a wood stud wall and shows how insulation placement affects performance. 1 While this example is for a modern house, the analysis applies to any structure, including historic buildings. The house had urea formaldehyde foam insulation that had shrunk away from the studs, leaving large areas effectively uninsulated. Moisture from the humidified house condensed on the back side of the sheathing, ruining it. The owner wanted to install insulated sheathing for energy conservation and to avoid another condensation problem. Table 1 is a dew point calculation for Figure 1a. Like the temperature gradient, the moisture gradient is proportional to the resistance of each element in the wall. Where the temperature gradient is expressed in degrees, the moisture gradient is expressed in vapor pressure (in. Hg or kpa) or specific humidity (grains/lb, lbw/lbda, or kgw/kgda). Since vapor permeance data are commonly tabulated in grains in the I-P system of units, it is easier to work in grains/lb than lb/lb. Although the units are different, the principle is similar to the more familiar temperature gradient calculation: Quantity Area Driving Force R-Value Btu/h ft 2 (m 2 ) F ( C) Permeance (perms) gr/h ft 2 (m 2 ) in. Hg (kpa) In Figure 1a, with the insulation inside the exterior sheathing, the surface of the sheathing falls below the dewpoint and damaging condensation can occur. The following calculation shows the basis for that conclusion: R-value of all components up to plywood: 5.89 Total R-value of assembly: 7.49 Temperature on inside surface of plywood: Inside R-value Temp. Ratio Temperature Difference 70 F 5.89 [70 F ( 10 F)] = 7.1 F ( 13.8 C) 7.49 Vapor diffusion resistance of components up to plywood: 0.88 Total vapor diffusion resistance of assembly: 2.71 Dew point calculation for surface of plywood Inside Rep Moisture Moisture Ratio Difference 22.4 gr/lb 0.88 ( ) gr/lb 2.71 = 15.5 gr/lb dew point = 20 F ( 6 C) Since the temperature on the plywood is lower than the dew point, moisture can condense. Figure 1b shows that installing the insulation outside the sheathing keeps the sheathing above the local dewpoint, avoiding con- April 1999 ASHRAE Journal 77

4 Practical Guide densation. Note that these conditions result in part from the fact that plywood sheathing is a moderately effective vapor retarder. 2 In hot, humid climates, the indoor temperature and dewpoint are below the outdoor temperature and dewpoint much of the year. In those situations, the vapor retarder is usually installed outside the insulation. 3 If a wall is not designed for the anticipated indoor/outdoor moisture gradient, or if the indoor humidity is higher than the building design contemplated, moisture can condense inside the wall. That moisture can eventually cause structural damage. New construction can include vapor retarders to accommodate indoor humidification. Depending on their construction, it might not be feasible to humidify existing buildings without risk of condensation and damage to the building structure. Mold and Fungus Growth Mold and fungus spores are difficult to eliminate from a building. The spores themselves are not much of a problem until they grow. To grow, mold spores need moisture and a food source. 4 Neither moisture nor food necessarily comes from the air. Rather, they both more often come from the substrate where the spores land and germinate. 5 Mold can grow inside air-handling units. In cooling systems, cooling coil condensate may be available as a moisture source. Although the relative humidity can be 95% or higher for months at a time, mold does not always grow in air-handling units. Mold will not grow even in high humidity environments unless it has food. When mold grows in air-handling units, the food source is accumulated dust and dirt. Keeping systems clean is the key to avoiding mold growth in air-handling units and ducts. Maintaining relative humidity below the oft-cited 60% level does not guarantee against mold growth. Mold can not only obtain food from a substrate, it can also obtain moisture from a substrate. Some substrates allow mold to germinate with fairly low moisture levels. Dirty surfaces and accumulated salts tend to deliquesce moisture out of the air. That moisture in the material promotes mold growth. Where moisture is unavoidable, as in a cooling system, the key to avoiding mold growth is to eliminate food sources. Materials that hold moisture can be sites for mold growth even in a room where the relative humidity is low. Like desiccants, some materials absorb moisture from the air even at low humidity. Other materials are slow to release moisture once they get wet. The literature suggests materials absorb moisture faster than they release it. 6 If these materials are organic, they are ideal substrates for mold growth. Maintaining relative humidity below 60% at temperatures in the normal human comfort range may reduce mold growth. However, low relative humidity is no guarantee. Selecting materials and treating surfaces so they do not absorb or hold moisture appears to be a more effective strategy against mold growth. Desiccants Desiccants are materials that absorb moisture. Commercial desiccants generally absorb several times their own weight in water. While desiccants are usually noted for their ability to absorb moisture, they also desorb moisture if the water vapor pressure of the ambient air is less than the vapor pressure of water in the desiccant. In that respect, desiccants can be a form of seasonal storage for latent cooling. Desiccants can be liquid or solid. Liquid desiccants ABsorb water vapor. Solid desiccants ADsorb water vapor. The difference is that the ABsorbed water goes into solution with the liquid desiccant. ADsorbed water attaches to the surface of solid desiccants. Solid desiccants have irregular surfaces with numerous pores that provide sites for water vapor molecules to attach. Liquid desiccants absorb water because they have a stronger attraction for water molecules than does water itself. Expressed scientifically, the vapor pressure of water in the desiccant is less than the vapor pressure of water in the air. The vapor pressure difference drives water molecules into the desiccant solution. The vapor pressure of water in the desiccant solution increases as the solution absorbs water and becomes more dilute. When the vapor pressure of water in the desiccant equals the vapor pressure of the ambient air, the desiccant stops absorbing water. 7 Solid desiccants have numerous small passages or capillaries that attract water. Water is attracted to the surface of the desiccant, collects into droplets, and condenses in the capillaries. As with liquid desiccants, water sitting on the surface of the desiccant has a lower vapor pressure than water in the ambient air. 8 Stated another way, the force attracting water vapor to the desiccant surface is greater than the force attracting water vapor into the air. Desiccants can achieve much lower specific humidity than mechanical refrigeration without over cooling the space or requiring a defrost cycle. As a practical matter, desiccant systems tend to be economical when the desired dew point is below about 40 F (4 C). Static Electricity Static electricity results when charges accumulate on a body. The problem occurs when those charges jump across an air gap on their way back to their source. People can pick up charges from walking across carpets. They carry those charges around with them until they get close to an object that has a conductive path back to the carpet. If the charges discharge through a computer or other electronic device, the discharge can scramble data or damage components. Indoor static electricity discharges are often associated with dry, winter weather. However, some of the biggest static electricity discharges in human experience occur during humid summer weather. They are thunderstorms. Even though people associate static electricity with low indoor humidity, broader observations show that static electricity discharges are not a function of relative humidity. The dielectric constant of a substance is a measure of its ability to hold a charge. The dielectric constant of air does not change very much with humidity. The reduction in static electricity discharges attributed to increasing humidity has little to do with moisture in the air. Rather, it is the influence of moisture on the electrical conductivity of materials. 9 Static electric charges can- 78 ASHRAE Journal April 1999

5 Museums & Renovation not accumulate on conductive materials. The electrical conductivity of most common materials increases in proportion to their moisture content. Materials such as plastics, rubber, and machine drive belts that do not readily absorb moisture can accumulate static charges at 100% relative humidity. 10 Previous editions of the ASHRAE Handbook implicitly recognize that increasing relative humidity does not necessarily eliminate static electricity. The 1983 and 1988 Handbooks state that under some conditions, and with certain materials, maximum electrostatic charging occurs at relative humidities of 25% to 35% or higher. 11 That statement disappeared from the same chapters in the 1992 and 1996 editions of the Handbook. Adding moisture to the air affects static electricity only indirectly. If the materials in the room absorb moisture from the air and increase their conductivity, the risk of static electricity discharge decreases. However, simply adding moisture is not reliable. NFPA , Health Care Facilities, calls for hospital operating rooms that utilize flammable anesthetics to be humidified to 50% relative humidity. Even with 50% relative humidity, the same standard calls for additional precautions against electrostatic discharge. 12 The need for additional precautions demonstrates that room air relative humidity does not necessarily have a cause and effect relationship with static electricity discharges. Controlling static electricity discharges seems to depend on surface conductivity, static dissipating clothing, conductive flooring, and grounding as opposed to humidifying the air. 13 Rust Atmospheric corrosion (rust) is uncontrolled oxidation of a metal. In the case of stainless steels, oxidation produces a thin, protective coating on the metal surface. That oxidation is part of what makes stainless steel stainless. Aluminum and copper also form protective oxide coatings. On the other hand, carbon steel forms a loose oxide that readily separates from the base metal. The loose oxide particles fall off as scale, exposing new base metal to oxidize. The process continues until the metal rusts away. Plain carbon steel reportedly remains uncorroded when exposed to air at a relative humidity less than about 30%. 14 The reference does not indicate whether 30% RH at 85 F (29 C) is any more aggressive to carbon steel than 30% RH at 25 F ( 4 C). The increase in corrosion with increasing humidity is attributed to an increase in the electrical conductivity of the environment contacting the metal surface. 15 All corrosion is electrolytic in nature, so the increase in conductivity almost certainly plays a part. However, moisture content does not affect the electrical conductivity of air. Any increase in conductivity associated with increased moisture can only be due to the interaction of water vapor with pollutants in the air. The ASM Metals Handbook describes the influence of surface condition on rust. Rust forms on surfaces with small pores at lower humidity than on surfaces with large pores. Small pores draw moisture out of the air by capillary condensation due to differences in vapor pressure. 16 Vapor pressure and capillary condensation make more sense Figure 2: Equilibrium moisture content of wood. Figure 3: Dimensional change of wood with change in moisture content. than relative humidity as a driving force for rusting. If the vapor pressure of water in the surrounding air is higher than the vapor pressure of water in small capillaries in the iron/iron oxide surface, the capillaries draw moisture out of the air. Moisture in the capillaries reacts with contaminants in the air or on the surface, increasing conductivity and resulting corrosion. Because rust tends to be irregular, more rust forms more capillaries, fostering even more rust. This analysis suggests that preventing corrosion appears to have more to do with surface finish and dew point than relative humidity environment. A smooth, polished surface provides few capillaries and few sites for capillary condensation. At high temperatures, low dew point results in a low relative humidity. However, as temperature goes down, relative humidity can increase without necessarily promoting rust if the vapor pressure of moisture in the air is below the vapor pressure required for capillary condensation. April 1999 ASHRAE Journal 79

6 Practical Guide Dimensional Changes Cellulosic materials like paper and wood readily take on and give up moisture from the air. Wood holds water in cell cavities and within its cell walls. Green wood can start out holding more moisture than the weight of the wood itself (more than 100% moisture content). When dried, wood first gives up water from cell cavities until the moisture content reaches about 30%. Further drying removes moisture from the cell walls. As the cell walls lose water, they shrink. The resulting stresses cause warping and checking. 17 After the water in the cell cavities is gone, the cell walls give up moisture only until the wood reaches an equilibrium moisture content. The equilibrium moisture content depends on species, temperature, and relative humidity. Relative humidity is the strongest of those three influences. Figure 2 shows how the equilibrium moisture content for wood varies with temperature and relative humidity. Changing moisture content makes the wood expand or shrink. Figure 3 shows the magnitude of these changes. Like wood, paper also shrinks and grows with changes in moisture content. A 1933 study by Weber and Snyder for the National Bureau of Standards showed the effects of changing moisture content on the physical properties of printing papers. 19 Figure 4 shows one of the findings from that study. Although the dimensional changes are small, they are enough to cause misalignment in multi-color printing processes. While the Weber and Snyder study confirms that relative humidity affects dimensions of wood and paper products, it is important to put these findings into perspective. First, the analysis relates to equilibrium moisture content. Depending on size, thickness and how it is stored, the article may take hours or days to reach a new equilibrium moisture content when the ambient temperature and humidity change. For these materials, temperature and humidity at any one moment or even over short periods are much less important than the long-term average over time. Second, unless a process requires extreme precision, fairly broad changes in temperature and relative humidity are required before the dimensional changes become significant. Figure 2 shows that a rather broad room temperature and humidity window of 59 F to 87 F (15 C to 30 C) and 25% to 50% relative humidity results in a 4 percentage point change in equilibrium moisture content of wood. Figure 3 shows that a 4 percentage point change in moisture results in less than 1% change in dimension. Figure 4: Influence of moisture content on dimensions of lithographic papers. Figure 5: Moisture isotherm of 194-year-old paper. Figure 5 shows the results of recent testing by the Smithsonian Center for Materials Research and Education on a page from an 1804 law book. The paper was allowed to reach equilibrium moisture content at various relative humidities at constant room temperature. The dimensional changes were then measured. Figure 4 and Figure 5 taken together relate room relative humidity to equilibrium moisture content for paper. In Figure 4, a 2 percentage point change in moisture content from 0.5% to 2.5% causes a dimensional change of 0.18% or a strain of Figure 5 shows that a rather extreme relative humidity change of 40 percentage points (20% to 60%) to achieve that dimensional change. As a result, unless extreme precision and dimensional stability are required, paper and wood can tolerate fairly broad changes in environmental conditions with minimal impact. 80 ASHRAE Journal April 1999

7 Museums & Renovation Summary and Conclusions Except for avoiding condensation, controlling indoor relative humidity does not necessarily protect materials. Relative humidity at best contributes indirectly to control of static electricity, and mold growth. The moisture content of the materials exerts a much greater influence and should be the parameter of interest for preserving books, papers and artwork. Other authors address the effects of moisture content on materials in greater detail. Stored materials can take weeks or months to reach their equilibrium moisture content. In a humidified environment, books and papers do not release moisture during the winter, so they start the mechanical cooling season loaded with moisture. If the environment is not humidified, stored books and papers give up moisture during the winter and go further into the cooling season before they have absorbed enough moisture to support mold growth. Also because hygroscopic materials take time to absorb and desorb moisture from the air, fairly wide variations in temperature and relative humidity over the course of a day or even a week most likely do not have a significant impact on the stored materials. On the other hand, the risk of condensation may make the building structure (including historic buildings) more sensitive to the effects of humidity than the stored materials. In northern climates, winter humidification adds moisture that can lead to condensation and increased mold growth. In hot, humid climates, over cooling can also result in condensation. Attempting to dehumidify without adequate vapor retarders will be expensive and ultimately unsuccessful. Using humidity wisely requires understanding the operative parameter: relative humidity, specific humidity, or dew point. Over cooling a room in the name of dehumidification raises relative humidity and may be counter productive for some materials. Allowing materials to absorb and desorb moisture slowly in response to seasonal climate changes may be a successful at maintaining long term stability in the materials and the buildings that house them. References 1. For a more detailed discussion of this topic, see 1997 ASHRAE, Handbook Fundamentals, p and Acker, William G., Water Vapor Migration and Condensation Control in Buildings, Heating/Piping/Air Conditioning, 70(6): The former term vapor barrier has fallen out of favor because barrier can imply an absolute block. Vapor retarders slow water vapor transfer just as thermal insulation slows, but does not eliminate, heat transfer. 3. For a thorough discussion of design for hot, humid climates, Using humidity wisely requires understanding the operative parameter: relative humidity, specific humidity, or dew point. see CH2M Hill, Preventing Indoor Air Quality Problems in Hot, Humid Climates: Design and Construction Guidelines, Orlando, Fla, See Technical Leaflet Protecting Books and Paper Against Mold, Northeast Document Conservation Center, Andover, Mass. 5. See Motylewski, Karen, Insect and Fungus Management Conference Notes citing Florian, Mary-Lou, Mold and its life cycles, pestnote.html, Nov Ibid ASHRAE, Handbook Fundamentals, Chapter Ibid. 9. NFPA , Guide for Fire and Explosion Investigations, section Ibid. 11. ASHRAE Handbook Equipment, p NFPA , Health Care Facilities Annex 2, Flammable anesthetizing locations, section : Reduction in Electrostatic Hazard. 13. Kassebaum, J. H. and R. A. Kocken, Controlling static electricity in hazardous (classified) locations, IEEE Transactions on Industry Applications, 33(1): United States Steel The Making, Shaping and Treating of Steel, 9th edition, p Ibid. 16. American Society for Metals, Handbook Vol. 13 Corrosion, p Hoadley, R.B., As dries the air, so shrinks the wood, Fine Woodworking, The Taunton Press, 39(2): Weber, C.G. and Snyder, L.W., Reactions of lithographic papers to variations in humidity and temperature, National Bureau of Standards Journal of Research, vol. 12, paper no. RP633, January Kenneth M. Elovitz, P.E., Member ASHRAE, is an engineering consultant and in-house counsel for Energy Economics, Inc., in Foxboro, Mass. Ken received a bachelor s degree in metallurgy and materials science from Lehigh University. He received a JD from Suffolk University Law School and has been admitted to practice in state and federal courts. He develops and edits these special supplements to ASHRAE Journal. = April 1999 ASHRAE Journal 81