CHAPTER 1. PSYCHROMETRICS
Psychrometrics uses thermodynamic and transport prop erties to analyze conditions and processes involving moist air. This chapter discusses perfect gas relations and their use in common heating, cooling, and humidity control problems. Formulas developed by Herrmann et al. (2009) may be used where greater precision is required.
Herrmann et al. (2009), Hyland and Wexler (1983a, 1983b), and Nelson and Sauer (2002) developed formulas for thermodynamic properties of moist air and water modeled as real gases. However, perfect gas relations can be substituted in most air-conditioning problems. Kuehn et al. (1998) showed that errors are less than 0.7% in calculating humidity ratio, enthalpy, and specific volume of saturated air at standard atmospheric pressure for a temperature range of –50 to 50°C. Furthermore, these errors decrease with decreasing pressure.
Herrmann et al. (2020) prepared formulas for transport properties of moist air.
1. COMPOSITION OF DRY AND MOIST AIR
Atmospheric air contains many gaseous components as well as water vapor and miscellaneous contaminants (e.g., smoke, pollen, and gaseous pollutants not normally present in free air far from pollution sources).
Dry air is atmospheric air with all water vapor and contaminants removed. Its composition is relatively constant, but small variations in the amounts of individual components occur with time, geographic location, and altitude. Harrison (1965) lists the approximate percentage composition of dry air by volume as: nitrogen, 78.084; oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524; methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; and minor components such as krypton, xenon, and ozone, 0.0002. Harrison (1965) and Hyland and Wexler (1983a) used a value 0.0314 (circa 1955) for carbon dioxide. Carbon dioxide reached 0.0379 in 2005, is currently increasing by 0.00019 percent per year and is projected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling and Whorf 2005a, 2005b). Increases in carbon dioxide are offset by decreases in oxygen; consequently, the oxygen percentage in 2036 is projected to be 20.9352. Using the projected changes, the mole mass for dry air for at least the first half of the 21st century is 28.966 kgda/kmol, based on the carbon-12 scale. The gas constant for dry air using the Mohr and Taylor (2005) value for the universal gas constant is
Moist air is a binary (two-component) mixture of dry air and water vapor. The amount of water vapor varies from zero (dry air) to a maximum that depends on temperature and pressure. Saturation is a state of neutral equilibrium between moist air and the condensed water phase (liquid or solid); unless otherwise stated, it assumes a flat interface surface between moist air and the condensed phase. Saturation conditions change when the interface radius is very small (e.g., with ultrafine water droplets). According to the Industrial Formulation IAPWS-IF97 (R7-97 2012), the mole mass of water is 18.015 257 kgw/kmol. The gas constant for water is
2. U.S. STANDARD ATMOSPHERE
The temperature and barometric pressure of atmospheric air vary considerably with altitude as well as with local geographic and weather conditions. The standard atmosphere gives a standard of reference for estimating properties at various altitudes. At sea level, standard temperature is 15°C; standard barometric pressure is 101.325 kPa. Temperature is assumed to decrease linearly with increasing altitude throughout the troposphere (lower atmosphere), and to be constant in the lower reaches of the stratosphere. The lower atmosphere is assumed to consist of dry air that behaves as a perfect gas. Gravity is also assumed constant at the standard value, 9.806 65 m/s2. Table 1 summarizes property data for altitudes to 10 000 m.
Pressure values in Table 1 may be calculated from
The equation for temperature as a function of altitude is
where
| Z = altitude, m |
| p = barometric pressure, kPa |
| t = temperature, °C |
Equations (3) and (4) are accurate from –5000 m to 11 000 m. For higher altitudes, comprehensive tables of barometric pressure and other physical properties of the standard atmosphere, in both SI and I-P units, can be found in NASA (1976).
3. THERMODYNAMIC PROPERTIES OF MOIST AIR
Table 2, calculated using ASHRAE’s (2023) LibHuAirProp software (based on ASHRAE RP-1485; Herrmann et al. 2009, 2020), shows values of thermodynamic properties of saturated moist air and dry air at 101.325 kPa and temperatures from –60 to 90°C.
The following properties are shown in Table 2:
| t = Celsius temperature, °C, based on the ITS-90 and expressed relative to absolute temperature T in Kelvin, by the following relation: |
| Ws = humidity ratio at saturation, kgw/kgda; gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given temperature and pressure (standard atmospheric pressure). At given values of temperature and pressure, humidity ratio W can have any value from zero to Ws. |
| vda = specific volume of dry air, m3/kgda. |
| vs = specific volume of moist air at saturation, m3/kgda. |
| hda = specific enthalpy of dry air, kJ/kgda. In Table 2, hda is assigned a value of 0 at 0°C and standard atmospheric pressure. |
| hs = specific enthalpy of moist air at saturation, kJ/kgda. |
| cp,da = specific heat capacity of dry air, kJ/(kg· K) |
| cp,s = specific heat capacity of moist air at saturation, kJ/(kg· K) |
| sda = specific entropy of dry air, kJ/(kgda · K). In Table 2, sda is assigned a value of 0 at 0°C and standard atmospheric pressure. |
| ss = specific entropy of moist air at saturation, kJ/(kgda · K). |
4. THERMODYNAMIC PROPERTIES OF WATER AT SATURATION
Table 3 shows thermodynamic properties of water at saturation for temperatures from –60 to 150°C, calculated using ASHRAE’s (2023) LibHuAirProp software of Herrmann et al. (2009, 2020), based on IAPWS formulations described in IAPWS R7-97 (2012), R10-06 (2009), and R14-08 (2011). The internal energy and entropy of saturated liquid water are both assigned the value zero at the triple point, 0.01°C. Between the triple-point and critical-point temperatures of water, both saturated liquid and saturated vapor may coexist in equilibrium; below the triple-point temperature, both saturated ice and saturated vapor may coexist in equilibrium.
The following properties are shown in Table 3:
| t = Celsius temperature, °C, based on ITS-90 and expressed relative to absolute temperature T in Kelvin by the following relation: |
| pws = saturation pressure of water (solid, liquid, or vapor), kPa |
| vi = specific volume of saturated solid (ice), m3/kg |
| vf = specific volume of saturated liquid (water), m3/kg |
| vg = specific volume of saturated vapor (steam), m3/kg |
| hi = specific enthalpy of saturated solid (ice), kJ/kg |
| hf = specific enthalpy of saturated liquid (water), kJ/kg |
| hg = specific enthalpy of saturated vapor (steam), kJ/kg |
| cp,i = specific heat capacity of saturated solid (ice), kJ/(kg·K) |
| cp,f = specific heat capacity of saturated liquid (water), kJ/(kg·K) |
| cp,g = specific heat capacity of saturated vapor (steam), kJ/(kg·K) |
| si = specific entropy of saturated solid (ice), kJ/(kg·K) |
| sf = specific entropy of saturated liquid (water), kJ/(kg·K) |
| sg = specific entropy of saturated vapor (steam), kJ/(kg·K) |
The saturation pressure over liquid water for the temperature range of 0°C ≤ t < 373.946°C (critical temperature) is given by the IAPWS Industrial Formulation IAPWS-IF97 (R7-97, 2012):
where
| A = θ2 + n1θ + n2 |
| B = n3θ2 + n4θ + n5 |
| C = n6θ2 + n7θ + n8 |
with
and the coefficients
| n1 = 0.116 705 214 527 67 E+04 |
| n2 = –0.724 213 167 032 06 E+06 |
| n3 = –0.170 738 469 400 92 E+02 |
| n4 = 0.120 208 247 024 70 E+05 |
| n5 = –0.323 255 503 223 33 E+07 |
| n6 = 0.149 151 086 135 30 E+02 |
| n7 = –0.482 326 573 615 91 E+04 |
| n8 = 0.405 113 405 420 57 E+06 |
| n9 = –0.238 555 575 678 49 E+00 |
| n10 = 0.650 175 348 447 98 E+03 |
Equation (5) fits exactly to Equation (39).
The saturation (sublimation) pressure over ice for the temperature range of –223.15°C ≤ t < 0°C is given by IAPWS 2008 Formulation (R14-08, 2011):
where
with the coefficients and exponents
| a1 = –0.212 144 006 E+02 |
| a2 = 0.273 203 819 E+02 |
| a3 = –0.610 598 130 E+01 |
| b1 =0.333 333 333 E–02 |
| b2 =0.120 666 667 E+01 |
| b3 = 0.170 333 333 E+01 |
In both Equations (5) and (6),
| pws = saturation pressure, kPa |
| T = absolute temperature, T = (t / °C + 273.15) K |
The vapor pressure ps of water in saturated moist air at total pressures, which approximately correspond to the barometric pressure, differs negligibly from the saturation vapor pressure pws of pure water at the same temperature (e.g., 0.5% at 100 kPa and 0.8% at 200 kPa total pressures) (e.g., 0.5% at 100 kPa and 0.8% at 200 kPa total pressure). Consequently, ps can be used in place of pws at atmospheric pressure p:
where xws is the mole fraction of water vapor in saturated moist air at temperature t and pressure p, and p is the total barometric pressure of moist air.
Humidity ratio W (or mixing ratio) of a given moist air sample is defined as the ratio of the mass of water vapor to the mass of dry air in the sample:
W equals the mole fraction ratio xw/xda multiplied by the ratio of mole masses (18.015 257/28.966 = 0.621 945):
Specific humidity γ is the ratio of the mass of water vapor to total mass of the moist air sample:
In terms of the humidity ratio,
Absolute humidity (alternatively, water vapor density) dv is the ratio of the mass of water vapor to total volume of the sample:
Density ρ of a moist air mixture is the ratio of total mass to total volume:
where v is the moist air specific volume, m3/kgda, as defined by Equation (25).
Humidity Parameters Involving Saturation
The following definitions of humidity parameters involve the concept of moist air saturation:
Saturation humidity ratio Ws(t, p) is the humidity ratio of moist air saturated with respect to water (or ice) at the same temperature t and pressure p.
Saturated water vapor pressure enhancement factor was introduced by Goff and Gratch in 1943, significantly broadened by Wexler and Hyland in 1983, and recently updated by Herrmann et. al. in 2009. The enhancement factor is a function of temperature and total pressure. It represents the increase of the actual water vapor saturation pressure in moist air from the saturation pressure of pure water with no air present at specified temperature and elevated pressure.
where f is the water vapor pressure enhancement factor, ps is the corrected saturation water vapor pressure, and pws is the saturation vapor pressure of pure water.
This factor accounts for the nonideal behavior of the water vapor-air mixture in the saturated state. The nonideal behavior arises from: (a) the increase in vapor pressure because of the interaction between different molecular species in the gaseous phase of the mixture (the major contribution); (b) the increase in vapor pressure because of the superimposed pressure of the air on the condensed phase (the Poynting effect); and (c) the decrease in vapor pressure due to the solution of air in the water condensed phase with which the gas mixture is in equilibrium (the Raoult or Henry’s law effect). (This is a negligible decrease.). Figure 1 illustrates the effects of both pressure and temperature on the enhancement factor.
Relative humidity ϕ is the ratio of the actual water vapor partial pressure pw in moist air at the total pressure p and dew-point temperature td to the saturation water vapor partial pressure at the total pressure p and dry-bulb temperature t:
Note that Equations (13) and (23) have been revised so that they cover both the normal range of relative humidity where pws(t) < p and the extended range (e.g., atmospheric pressure drying kilns) where pws(t) ≥ p. The definitions in earlier editions applied only to the normal range.
Dew-point temperature td is the temperature of moist air saturated at pressure p, with the same humidity ratio W as that of the given sample of moist air. It is defined as the solution td(p, W) of the following equation:
Thermodynamic wet-bulb temperature t* is the temperature at which water (liquid or solid), by evaporating into moist air at dry-bulb temperature t and humidity ratio W, can bring air to saturation adiabatically at the same temperature t* while total pressure p is constant. This parameter is considered separately in the section on Thermodynamic Wet-Bulb and Dew-Point Temperature.
6. PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR
When moist air is considered a mixture of independent perfect gases (i.e., dry air and water vapor), each is assumed to obey the perfect gas equation of state as follows:
where
| pda = partial pressure of dry air |
| pw = partial pressure of water vapor |
| V = total mixture volume |
| nda = number of moles of dry air |
| nw = number of moles of water vapor |
| R = universal gas constant, 8314.472 J/(kmol · K) |
| T = absolute temperature, K |
The mixture also obeys the perfect gas equation:
or
where p = pda + pw is the total mixture pressure and n = nda + nw is the total number of moles in the mixture. From Equations (15) to (18), the mole fractions of dry air and water vapor are, respectively,
and
From Equations (8), (19), and (20), the humidity ratio W is
The saturation humidity ratio Ws is
The term pws represents the saturation pressure of water vapor in the absence of air at the given temperature t. This pressure pws is a function only of temperature and differs slightly from the vapor pressure of water in saturated moist air.
The relative humidity ϕ is defined in Equation (13). Using the second equality and eliminating the enhancement factors, which are not applicable using the perfect gas assumption, gives
Substituting Equation (22) for Ws into Equation (14),
where μ is degree of saturation W/Ws, dimensionless.
Both ϕ and μ are zero for dry air and unity for saturated moist air. At intermediate states, their values differ, substantially at higher temperatures.
The specific volume v of a moist air mixture is expressed in terms of a unit mass of dry air:
where V is the total volume of the mixture, mda is the mass of dry air, nda is the number of moles of dry air, and the value 28.966 kgda/kmol is the molar mass of dry air. By Equations (15) and (25), with the relation p = pda + pw,
Using Equations (8) and (19) with the relation 1 = xda + xw,
In Equations (26) and (27), v is specific volume, R is the universal molar gas constant, Rda is the specific gas constant of dry air, T is absolute temperature, p is total pressure, pw is partial pressure of water vapor, and W is humidity ratio.
In specific units, Equation (27) may be expressed as
where
| v = specific volume, m3/kgda |
| t = dry-bulb temperature, °C |
| W = humidity ratio, kgw/kgda |
| p = total pressure, kPa |
The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components. Therefore, the specific enthalpy of moist air can be written as follows:
where hda is the specific enthalpy for dry air in kJ/kgda and hg is the specific enthalpy for saturated water vapor in kJ/kgw at the mixture’s temperature. As an approximation,
where t is the dry-bulb temperature in °C. The moist air specific enthalpy in kJ/kgda then becomes
7. THERMODYNAMIC WET-BULB AND DEW-POINT TEMPERATURE
For any state of moist air, a temperature t* exists at which liquid (or solid) water evaporates into the air to bring it to saturation at exactly this same temperature and total pressure (Harrison 1965). During adiabatic saturation, saturated air is expelled at a temperature equal to that of the injected water. In this constant-pressure process,
-
Humidity ratio increases from initial value W to Ws*, corresponding to saturation at temperature t*
-
Enthalpy increases from initial value h to hs*, corresponding to saturation at temperature t*
-
Mass of water added per unit mass of dry air is (Ws* – W), which adds energy to the moist air of amount (Ws* – W)hw*, where hw* denotes specific enthalpy in kJ/kgw of water added at temperature t*
Therefore, if the process is strictly adiabatic, conservation of enthalpy at constant total pressure requires that
Ws*, hw*, and hs* are functions only of temperature t* for a fixed value of pressure. The value of t* that satisfies Equation (33) for given values of h, W, and p is the thermodynamic wet-bulb temperature.
A psychrometer consists of two thermometers; one thermometer’s bulb is covered by a wick that has been thoroughly wetted with water. When the wet bulb is placed in an airstream, water evaporates from the wick, eventually reaching an equilibrium temperature called the wet-bulb temperature. This process is not one of adiabatic saturation, which defines the thermodynamic wet-bulb temperature, but one of simultaneous heat and mass transfer from the wet bulb. The fundamental mechanism of this process is described by the Lewis relation [Equation (40) in Chapter 6]. The thermodynamic wet-bulb temperature can be approximated by the measured wet-bulb temperature. Refer to ANSI/ASHRAE Standard 41.6-2014 for information on measurement of wet-bulb temperature. Measured wet-bulb temperature is not exactly equal to the adiabatic saturation temperature (or, thermodynamic wet-bulb temperature) according to ASHRAE RP-1460 (Brenner et al. 2010) because:
-
Radiative heat exchange occurs between wick (psychrometer) and environment.
-
Temperature of water being added to wick is not equal to the thermodynamic wet-bulb temperature of air.
-
Velocity of air flowing over the wick may not be sufficiently fast enough to prevent moisture in that airstream affecting the process of water evaporating from the wick into the airstream.
For more information see Greenspan and Wexler (1968) and Simões-Moreira (1999).
As defined, thermodynamic wet-bulb temperature is a unique property of a given moist air sample independent of measurement techniques.
Equation (33) is exact because it defines the thermodynamic wet-bulb temperature t*. Substituting the approximate perfect gas relation [Equation (32)] for h, the corresponding expression for hs*, and the approximate relation for saturated liquid water
into Equation (33), and solving for the humidity ratio,
where t and t* are in °C. Below freezing, the corresponding equations are
A wet/ice-bulb thermometer is imprecise when determining moisture content at 0°C.
The dew-point temperature td of moist air with humidity ratio W and pressure p was defined as the solution td(p, W) of Ws(p, td). For perfect gases, this reduces to
where pw is the water vapor partial pressure for the moist air sample and pws(td) is the saturation vapor pressure at temperature td. The saturation vapor pressure is obtained from Table 3 or by using Equation (5) or (6).
The dew-point temperature above and equal 0°C can be calculated from the water vapor partial pressure by the IAPWS-IF97 saturation temperature equation:
where
with
where
and the coefficients:
| n1 = 0.116 705 214 527 67 E+04 |
| n2 = –0.724 213 167 032 06 E+06 |
| n3 = –0.170 738 469 400 92 E+02 |
| n4 = 0.120 208 247 024 70 E+05 |
| n5 = –0.323 255 503 223 33 E+07 |
| n6 = 0.149 151 086 135 30 E+02 |
| n7 = –0.482 326 573 615 91 E+04 |
| n8 = 0.405 113 405 420 57 E+06 |
| n9 = –0.238 555 575 678 49 E+00 |
| n10 = 0.650 175 348 447 98 E+03 |
Equation (39) is valid for the water vapor partial pressures 0.6112 ≤ pw < 1000 kPa. It fits exactly to Equation (5). The dew-point temperature td of moist air at total pressures that approximately correspond to the barometric pressure differs negligibly from the saturation temperature of pure water at the same pressure pw (e.g., 0.03% at 100 kPa and 0.05% at 200 kPa total pressures).
The dew-point temperature below 0°C is obtained from Table 3 or iteratively by using the Equation (6). Alternatively, it can be calculated directly from the equation:
where
with the coefficients and exponents:
| d0 = 0.212 573 393 068 044 4 E+03 |
| d1 = –0.111 182 915 832 924 7 E+02 |
| d2 = 0.101 399 557 485 811 1E+00 |
| d3 = 0.212 958 716 178 593 0 E–05 |
| e0 = 0.1 E+01 |
| e1 = –0.868 954 548 461 757 7 E–01 |
| e2 =0.229 516 184 515 270 4 E–02 |
| e3 = –0.174 889 589 777 246 0 E–04 |
Equation (40) is valid for the water vapor partial pressures 1.93·10–43 ≤ pw ≤ 0.06112 kPa.
In both Equations (39) and (40),
| pw = water vapor partial pressure, kPa |
| Td = absolute dew-point temperature, Td = (td/°C + 273.15) K |
8. NUMERICAL CALCULATION OF MOIST AIR PROPERTIES
The following are outlines, citing equations and tables already presented, for calculating moist air properties using perfect gas relations. These relations are accurate enough for most engineering calculations in air-conditioning practice, and are readily adapted to either hand or computer calculating methods. For more details, refer to Tables 15 through 18 in Chapter 1 of Olivieri (1996). Graphical procedures are discussed in the section on Psychrometric Charts.
SITUATION 1.
Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p
SITUATION 2.
Given: Dry-bulb temperature t, Dew-point temperature td, Pressure p
SITUATION 3.
Given: Dry-bulb temperature t, Relative humidity ϕ, Pressure p
Moist Air Property Tables for Standard Pressure
Table 2 shows thermodynamic properties for standard atmospheric pressure at temperatures from –60 to 90°C calculated using the ASHRAE RP-1485 (Herrmann et al. 2009) research project numerical model. Properties of intermediate moist air states can be calculated using the degree of saturation μ:
These equations are accurate to about 350°C. At higher temperatures, errors can be significant.
A psychrometric chart graphically represents the thermodynamic properties of moist air.
The choice of coordinates for a psychrometric chart is arbitrary. A chart with coordinates of enthalpy and humidity ratio provides convenient graphical solutions of many moist air problems with a minimum of thermodynamic approximations. ASHRAE developed five such psychrometric charts. Chart 1 is shown as Figure 2; the others may be obtained through ASHRAE.
Charts 1, 2, 3 and 4 are for sea-level pressure (101.325 kPa). Chart 5 is for 750 m altitude (92.634 kPa), Chart 6 is for 1500 m altitude (84.54 kPa), and Chart 7 is for 2250 m altitude (77.058 kPa). All charts use oblique-angle coordinates of enthalpy and humidity ratio, and are consistent with the data of Table 2 and the properties computation methods of Hyland and Wexler (1983a) and ASHRAE research project RP-1485. Palmatier (1963) describes the geometry of chart construction applying specifically to Charts 1 and 4.
The dry-bulb temperature ranges covered by the charts are
|
Charts 1, 5, 6, 7
|
Normal temperature
|
0 to 50°C
|
|
Chart 2
|
Low temperature
|
–40 to 10°C
|
|
Chart 3
|
High temperature
|
10 to 120°C
|
|
Chart 4
|
Very high temperature
|
100 to 200°C
|
Psychrometric properties or charts for other barometric pressures can be derived by interpolation. Sufficiently exact values for most purposes can be derived by methods described in the section on Perfect Gas Relationships for Dry and Moist Air. Constructing charts for altitude conditions has been discussed by Haines (1961), Karig (1946), and Rohsenow (1946).
Comparison of charts 1 and 6 by overlay reveals the following:
-
The dry-bulb (db) lines coincide.
-
Wet-bulb (wb) lines for a given temperature originate at the intersections of the corresponding dry-bulb line and the two saturation curves, and they have the same slope.
-
Humidity ratio W and enthalpy h for a given dry- and wet-bulb temperature increase with altitude, but there is little change in relative humidity (rh).
-
Volume v changes rapidly; for a given dry-bulb temperature and humidity ratio, it is practically inversely proportional to barometric pressure.
The following table compares properties at sea level (chart 1) and 1500 m (chart 6):
|
Chart No.
|
db
|
wb
|
h
|
W
|
rh
|
v
|
|
1
|
40
|
30
|
99.5
|
23.0
|
49
|
0.920
|
|
6
|
40
|
30
|
114.1
|
28.6
|
50
|
1.111
|
Figure 2 shows humidity ratio lines (horizontal) for the range from 0 (dry air) to 30 grams moisture per kilogram dry air. Enthalpy lines are oblique lines across the chart precisely parallel to each other.
Dry-bulb temperature lines are straight, not precisely parallel to each other, and inclined slightly from the vertical position. Thermodynamic wet-bulb temperature lines are oblique and in a slightly different direction from enthalpy lines. They are straight but are not precisely parallel to each other.
Relative humidity lines are shown in intervals of 10%. The saturation curve is the line of 100% rh, whereas the horizontal line for W = 0 (dry air) is the line for 0% rh.
Specific volume lines are straight but are not precisely parallel to each other.
A narrow region above the saturation curve has been developed for fog conditions of moist air. This two-phase region represents a mechanical mixture of saturated moist air and liquid water, with the two components in thermal equilibrium. Isothermal lines in the fog region coincide with extensions of thermodynamic wet-bulb temperature lines. If required, the fog region can be further expanded by extending humidity ratio, enthalpy, and thermodynamic wet-bulb temperature lines.
The protractor to the left of the chart shows two scales: one for sensible/total heat ratio, and one for the ratio of enthalpy difference to humidity ratio difference. The protractor is used to establish the direction of a condition line on the psychrometric chart.
Example 1 shows use of the ASHRAE psychrometric chart to determine moist air properties.
Example 1.
Moist air exists at 40°C dry-bulb temperature, 20°C thermodynamic wet-bulb temperature, and 101.325 kPa pressure. Determine the humidity ratio, enthalpy, dew-point temperature, relative humidity, and specific volume.
Solution: Locate state point on chart 1 (Figure 2) at the intersection of 40°C dry-bulb temperature and 20°C thermodynamic wet-bulb temperature lines. Read humidity ratio W = 6.5 gw/kgda.
The enthalpy can be found by using two triangles to draw a line parallel to the nearest enthalpy line (60 kJ/kgda) through the state point to the nearest edge scale. Read h = 56.7 kJ/kgda.
Dew-point temperature can be read at the intersection of W = 6.5 gw/kgda with the saturation curve. Thus, td = 7°C.
Relative humidity ϕ can be estimated directly. Thus, ϕ = 14%.
Specific volume can be found by linear interpolation between the volume lines for 0.88 and 0.90 m3/kgda. Thus, v = 0.896 m3/kgda.
10. TYPICAL AIR-CONDITIONING PROCESSES
The ASHRAE psychrometric chart can be used to solve numerous process problems with moist air. Its use is best explained through illustrative examples. In each of the following examples, the process takes place at a constant total pressure of 101.325 kPa.
Moist Air Sensible Heating or Cooling
Adding heat alone to or removing heat alone from moist air is represented by a horizontal line on the ASHRAE chart, because the humidity ratio remains unchanged.
Figure 3 shows a device that adds heat to a stream of moist air. For steady-flow conditions, the required rate of heat addition is
Example 2.
Moist air, saturated at 2°C, enters a heating coil at a rate of 10 m3/s. Air leaves the coil at 40°C. Find the required rate of heat addition.
Solution: Figure 4 schematically shows the solution. State 1 is located on the saturation curve at 2°C. Thus, h1 = 13.0 kJ/kgda, W1 = 4.38 gw/kgda, and v1 = 0.785 m3/kgda. State 2 is located at the intersection of t = 40°C and W2 = W1 = 4.38 gwT/kgda. Thus, h2 = 51.5 kJ/kgda. The mass flow of dry air is
From Equation (41),
Moist Air Cooling and Dehumidification
Moisture condensation occurs when moist air is cooled to a temperature below its initial dew point. Figure 5 shows a schematic cooling coil where moist air is assumed to be uniformly processed. Although water can be removed at various temperatures ranging from the initial dew point to the final saturation temperature, it is assumed that condensed water is cooled to the final air temperature t2 before it drains from the system.
For the system in Figure 4, the steady-flow energy and material balance equations are
Thus,
Example 3.
Moist air at 30°C dry-bulb temperature and 50% rh enters a cooling coil at 5 m3/s and is processed to a final saturation condition at 10°C. Find the kW of refrigeration required.
Solution: Figure 6 shows the schematic solution. State 1 is located at the intersection of t = 30°C and ϕ = 50%. Thus, h1 = 64.3 kJ/kgda, W1 = 13.3 gw/kgda, and v1 = 0.877 m3/kgda. State 2 is located on the saturation curve at 10°C. Thus, h2 = 29.5 kJ/kgda and W2 = 7.66 gw/kgda. From Table 3, hw2 = 42.02 kJ/kgw. The mass flow of dry air is
From Equation (45),
Adiabatic Mixing of Two Moist Airstreams
A common process in air-conditioning systems is the adiabatic mixing of two moist airstreams. Figure 7 schematically shows the problem. Adiabatic mixing is governed by three equations:
Eliminating 
gives
according to which, on the ASHRAE chart, the state point of the resulting mixture lies on the straight line connecting the state points of the two streams being mixed, and divides the line into two segments, in the same ratio as the masses of dry air in the two streams.
Example 4.
A stream of 2 m3/s of outdoor air at 4°C dry-bulb temperature and 2°C thermodynamic wet-bulb temperature is adiabatically mixed with 6.25 m3/s of recirculated air at 25°C dry-bulb temperature and 50% rh. Find the dry-bulb temperature and thermodynamic wet-bulb temperature of the resulting mixture.
Solution: Figure 8 shows the schematic solution. States 1 and 2 are located on the ASHRAE chart: v1 = 0.789 m3/kgda, and v2 = 0.858 m3/kgda. Therefore,
According to Equation (44),
Consequently, the length of line segment 1-3 is 0.742 times the length of entire line 1-2. Using a ruler, state 3 is located, and the values t3 = 19.5°C and t3* = 14.6°C found.
Adiabatic Mixing of Water Injected into Moist Air
Steam or liquid water can be injected into a moist airstream to raise its humidity, as shown in Figure 9. If mixing is adiabatic, the following equations apply:
Therefore,
according to which, on the ASHRAE chart, the final state point of the moist air lies on a straight line in the direction fixed by the specific enthalpy of the injected water, drawn through the initial state point of the moist air.
Example 5.
Moist air at 20°C dry-bulb and 8°C thermodynamic wet-bulb temperature is to be processed to a final dew-point temperature of 13°C by adiabatic injection of saturated steam at 110°C. The rate of dry airflow 
is 2 kgda/s. Find the final dry-bulb temperature of the moist air and the rate of steam flow .
Solution: Figure 10 shows the schematic solution. By Table 3, the enthalpy of the steam hg = 2691.07 kJ/kgw. Therefore, according to Equation (47), the condition line on the ASHRAE chart connecting states 1 and 2 must have a direction:
The condition line can be drawn with the Δh/ΔW protractor. First, establish the reference line on the protractor by connecting the origin with the value Δh/ΔW = 2.691 kJ/gw. Draw a second line parallel to the reference line and through the initial state point of the moist air. This second line is the condition line. State 2 is established at the intersection of the condition line with the horizontal line extended from the saturation curve at 13°C (td2 = 13°C). Thus, t2 = 21°C.
Values of W2 and W1 can be read from the chart. The required steam flow is
Space Heat Absorption and Moist Air Moisture Gains
Air conditioning required for a space is usually determined by (1) the quantity of moist air to be supplied, and (2) the supply air condition necessary to remove given amounts of energy and water from the space at the exhaust condition specified.
Figure 11 shows a space with incident rates of energy and moisture gains. The quantity qs denotes the net sum of all rates of heat gain in the space, arising from transfers through boundaries and from sources within the space. This heat gain involves energy addition alone and does not include energy contributions from water (or water vapor) addition. It is usually called the sensible heat gain. The quantity 
denotes the net sum of all rates of moisture gain on the space arising from transfers through boundaries and from sources within the space. Each kilogram of water vapor added to the space adds an amount of energy equal to its specific enthalpy.
Assuming steady-state conditions, governing equations are
or
The left side of Equation (48) represents the total rate of energy addition to the space from all sources. By Equations (48) and (49),
according to which, on the ASHRAE chart and for a given state of withdrawn air, all possible states (conditions) for supply air must lie on a straight line drawn through the state point of withdrawn air, with its direction specified by the numerical value of 
. This line is the condition line for the given problem.
Example 6.
Moist air is withdrawn from a room at 25°C dry-bulb temperature and 19°C thermodynamic wet-bulb temperature. The sensible rate of heat gain for the space is 9 kW. A rate of moisture gain of 0.0015 kgw/s occurs from the space occupants. This moisture is assumed as saturated water vapor at 30°C. Moist air is introduced into the room at a dry-bulb temperature of 15°C. Find the required thermodynamic wet-bulb temperature and volume flow rate of the supply air.
Solution: Figure 12 shows the schematic solution. State 2 is located on the ASHRAE chart. From Table 3, the specific enthalpy of the added water vapor is hg = 2555.58 kJ/kgw. From Equation (50),
With the Δh/ΔW protractor, establish a reference line of direction Δh/ΔW = 8.555 kJ/gw. Parallel to this reference line, draw a straight line on the chart through state 2. The intersection of this line with the 15°C dry-bulb temperature line is state 1. Thus, t1* = 14.0°C.
An alternative (and approximately correct) procedure in establishing the condition line is to use the protractor’s sensible/total heat ratio scale instead of the Δh/ΔW scale. The quantity ΔHs/ΔHt is the ratio of rate of sensible heat gain for the space to rate of total energy gain for the space. Therefore,
Note that ΔHs/ΔHt = 0.701 on the protractor coincides closely with Δh/ΔW = 8.555 kJ/gw.
The flow of dry air can be calculated from either Equation (48) or (49). From Equation (48),
At state 1, v1 = 0.829 m3/kgda.
Therefore, supply volume = 
= 0.873 × 0.829 = 0.724 m3/s.
11. TRANSPORT PROPERTIES OF MOIST AIR
For certain scientific and experimental work, particularly in the heat transfer field, many other moist air properties are important. Generally classified as transport properties, these include diffusion coefficient, viscosity, thermal conductivity, and thermal diffusion factor.
Table 4 shows diffusion coefficients calculated by Mason and Monchick (1965). Table 5, calculated using ASHRAE LibHuAirProp Software (ASHRAE 2023) based on ASHRAE RP-1767 (Herrmann et al. 2018, 2020), shows values of density, viscosity, kinematic viscosity, thermal conductivity, and Prandtl number of saturated moist air and dry air at the pressure 101.325 kPa and temperatures from –60°C to 90°C.
The following properties are shown in Table 5:
| t = Celsius temperature, °C, based on the ITS-90 and expressed relative to absolute temperature T in Kelvin by the following relation: |
| Ws = humidity ratio at saturation, kgw/kgda; gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given temperature and pressure (standard atmospheric pressure). At given values of temperature and pressure, humidity ratio W can have any value from zero to Ws |
| ρda = density of dry air, kg/m3 |
| ρs = density of moist air at saturation, kg/m3 |
| ηda = viscosity of dry air, μPa·s |
| ηs = viscosity of moist air at saturation, μPa·s |
| νda = kinematic viscosity of dry air, 10−6 m2/s |
| νs = kinematic viscosity of moist air at saturation, 10−6 m2/s |
| λda = thermal conductivity of dry air, W/(m·K) |
| λs = thermal conductivity of moist air at saturation, W/(m·K) |
| Prda = Prandtl number of dry air |
| Prs = Prandtl number of moist air at saturation |
In addition, Figures 13 and 14 summarize viscosity and thermal conductivity at atmospheric pressure in diagrams.
12. TRANSPORT PROPERTIES OF WATER AT SATURATION
Table 6 shows transport properties of water at saturation for temperatures from 0 to 150°C, calculated using ASHRAE LibHuAirProp Software (ASHRAE 2021) based on IAPWS formulations described in the releases IAPWS R7-97 2012, R12-08 2008, and R15-11 2011.
The following properties are shown in Table 6:
| t = Celsius temperature, °C, based on the ITS-90 and expressed relative to absolute temperature T in Kelvin by the following relation: |
| pws = saturation pressure of water (liquid or vapor), kPa |
| ρf = density of saturated liquid water, kg/m3 |
| ρg = density of saturated water vapor, kg/m3 |
| ηf = viscosity of saturated liquid water, μPa·s. |
| ηg = viscosity of saturated water vapor, μPa·s. |
| νf = kinematic viscosity of saturated liquid water, 10−6 m2/s. |
| νg = kinematic viscosity of saturated water vapor, 10−6 m2/s. |
| λf = thermal conductivity of saturated liquid water, W/(m·K). |
| λg = thermal conductivity of saturated water vapor, W/(m·K). |
| Prf = Prandtl number of saturated liquid water. |
| Prg = Prandtl number of saturated water vapor. |
| a1 to a3 = constants in Equation (6) |
| b1 to b3 = exponents in Equation (6) |
| d0 to d3 = constants in Equation (40) |
| dv = absolute humidity of moist air, mass of water per unit volume of mixture, kgw/m3 |
| e0 to e3 = exponents in Equation (40) |
| f = saturated water vapor pressure enhancement factor |
| h = specific enthalpy of moist air, kJ/kgda |
| Hs = rate of sensible heat gain for space, kW |
| hs* = specific enthalpy of saturated moist air at thermodynamic wet-bulb temperature, kJ/kgda |
| Ht = rate of total energy gain for space, kW |
| hw* = specific enthalpy of condensed water (liquid or solid) at thermodynamic wet-bulb temperature and a pressure of 101.325 kPa, kJ/kgw |
| mda = mass of dry air in moist air sample, kgda |
 = mass flow of dry air, per unit time, kgda/s |
| mw = mass of water vapor in moist air sample, kgw |
 = mass flow of water (any phase), per unit time, kgw/s |
| n = nda + nw, total number of moles in moist air sample |
| n1 to n10 = constants in Equations (5) and (39) |
| nda = number of moles of dry air |
| nw = number of moles of water vapor |
| p = total pressure of moist air, kPa |
| pda = partial pressure of dry air, kPa |
| ps = vapor pressure of water in moist air at saturation, kPa. Differs from saturation pressure of pure water pws at elevated total pressures. |
| pw = partial pressure of water vapor in moist air, kPa |
| pws = pressure of saturated pure water, kPa |
| Pr = Prandtl number |
| qs = rate of addition (or withdrawal) of sensible heat, kW |
| R = universal gas constant, 8314.472 J/(kmol·K) |
| Rda = specific gas constant for dry air, kJ/(kgda · K) |
| Rw = specific gas constant for water, kJ/(kgw · K) |
| s = specific entropy, kJ/(kgda · K) or kJ/(kgw · K) |
| T = absolute temperature, K |
| t = dry-bulb temperature of moist air, °C |
| td = dew-point temperature of moist air, °C |
| t* = thermodynamic wet-bulb temperature of moist air, °C |
| V = total volume of moist air sample, m3 |
| v = specific volume, m3/kgda or m3/kgw |
| W = humidity ratio of moist air, kgw/kgda or gw/kgda |
| Ws* = humidity ratio of moist air at saturation at thermodynamic wet-bulb temperature, kgw/kgda or gw/kgda |
| xda = mole fraction of dry air, moles of dry air per mole of mixture |
| xw = mole fraction of water, moles of water per mole of mixture |
| xws = mole fraction of water vapor under saturated conditions, moles of vapor per mole of saturated mixture |
| Z = altitude, m |
Greek
| γ = specific humidity of moist air, mass of water per unit mass of mixture |
| η = viscosity, μPa · s |
| λ = thermal conductivity, W/(m · K) |
| ν = kinematic viscosity, 10–6 m2/s |
| ρ = moist air density, kg/m3 |
| ϕ = relative humidity, dimensionless |
Subscripts
| da = dry air |
| f = saturated liquid water |
| g = saturated water vapor |
| i = saturated ice |
| s = saturated moist air |
| t = total |
| w = water in any phase |
ASHRAE members can access ASHRAE Journal articles and ASHRAE research project final reports at technologyportal.ashrae.org. Articles and reports are also available for purchase by nonmembers in the online ASHRAE Bookstore at www.ashrae.org/bookstore.
Gatley, D.P. 2013. Understanding psychrometrics, 3rd ed. ASHRAE.
Gatley, D.P., S. Herrmann, and H.-J. Kretzschmar. 2008. A twenty-first century molar mass for dry air. HVAC&R Research (now Science and Technology for the Built Environment) 14:655-662.
Greenspan, L., and A. Wexler. 1968. An adiabatic saturation psychrometer. Journal of Research of the National Bureau of Standards, Section C: Engineering and Instrumentation 72C(1):33-47.
Haines, R.W. 1961. How to construct high altitude psychrometric charts. Heating, Piping, and Air Conditioning 33(10):144-146.
Harrison, L.P. 1965. Fundamental concepts and definitions relating to humidity. In Humidity and moisture measurement and control in science and industry, vol. 3. A. Wexler and W.A. Wildhack, eds. Reinhold, New York.
Herrmann, S., H.-J. Kretzschmar, and D.P. Gatley. 2009. Thermodynamic properties of real moist air, dry air, steam, water, and ice. HVAC&R Research (now Science and Technology for the Built Environment) 15(5): 961-986.
Herrmann, S., H.-J. Kretzschmar, V.C. Aute, D.P. Gatley, and E. Vogel. 2021. Transport properties of real moist air, dry air, steam, and water. Science and Technology for the Built Environment 27(4):393-401.
Hyland, R.W., and A. Wexler. 1983a. Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures to 5 MPa. ASHRAE Transactions 89(2A):520-535.
Hyland, R.W., and A. Wexler. 1983b. Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K. ASHRAE Transactions 89(2A):500-519.
IAPWS. 2018. R6-95, Revised release on the IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
IAPWS. 2012. R7-97, Revised release on the IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
IAPWS. 2009. R10-06, Revised release on the equation of state 2006 for H2O ice Ih. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
IAPWS. 2008. R12-08, Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
IAPWS. 2011. R14-08, Revised release on the pressure along the melting and sublimation curves of ordinary water substance. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
IAPWS. 2011. R15-11, Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance. International Association for the Properties of Water and Steam. (Available at www.iapws.org).
Keeling, C.D., and T.P. Whorf. 2005a. Atmospheric carbon dioxide record from Mauna Loa. Scripps Institution of Oceanography—CO2 Research Group. gml.noaa.gov/ccgg/trends/mlo.html.
Keeling, C.D., and T.P. Whorf. 2005b. Atmospheric CO2 records from sites in the SIO air sampling network. In Trends: A compendium of data on global change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy.
Kuehn, T.H., J.W. Ramsey, and J.L. Threlkeld. 1998. Thermal environmental engineering, 3rd ed. Prentice-Hall, Upper Saddle River, NJ.
Mason, E.A., and L. Monchick. 1965. Survey of the equation of state and transport properties of moist gases. In Humidity and moisture measurement and control in science and industry, vol. 3. A. Wexler and W.A. Wildhack, eds. Reinhold, New York.
Mohr, P.J., and P.N. Taylor. 2005. CODATA recommended values of the fundamental physical constants: 2002. Reviews of Modern Physics 77:1-107.
NASA. 1976. U.S. Standard atmosphere, 1976. National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and the United States Air Force. Available from National Geophysical Data Center, Boulder, CO.
Nelson, H.F., and H.J. Sauer, Jr. 2002. Formulation of high-temperature properties for moist air. International Journal of HVAC&R Research 8(3):311-334.
Olivieri, J. 1996. Psychrometrics—Theory and practice. ASHRAE.
Palmatier, E.P. 1963. Construction of the normal temperature. ASHRAE psychrometric chart. ASHRAE Transactions 69:7-12.
Rohsenow, W.M. 1946. Psychrometric determination of absolute humidity at elevated pressures. Refrigerating Engineering 51(5):423.
Simões-Moreira, J.R. 1999. A thermodynamic formulation of the psychrometer constant. Measurement Science and Technology 10(4):302-311.
Brenner, J.P., G.F. Nellis, and D.T. Reindl. 2010. Design specifications for wet-bulb aspirator apparatus. ASHRAE Research Project RP-1460, Final Report.
Gatley, D.P. 2016. A proposed full range relative humidity definition. ASHRAE Journal 58(3):24-29.
Herrmann, S., H.-J. Kretzschmar, V.C. Aute, D.P. Gatley, and E. Vogel. 2018. Transport properties of real moist air, dry air, steam, and water. ASHRAE Research Project RP-1767, Final Report.
Herrmann, S., H.-J. Kretzschmar, and D.P. Gatley. 2020. Thermodynamic properties of real moist air, dry air, steam, water, and ice. ASHRAE Research Project RP-1485, Final Report.
Lemmon, E.W., R.T. Jacobsen, S.G. Penoncello, and D.G. Friend. 2000. Thermodynamic properties of air and mixture of nitrogen, argon, and oxygen from 60 to 2000 K at pressures to 2000 MPa. Journal of Physical and Chemical Reference Data 29:331-385.
NIST. 1990. Guidelines for realizing the international temperature scale of 1990 (ITS-90). NIST Technical Note 1265. National Institute of Technology and Standards, Gaithersburg, MD.
Wexler, A., R. Hyland, and R. Stewart. 1983. Thermodynamic properties of dry air, moist air and water and SI psychrometric charts. ASHRAE Research Projects RP-216 and RP-257, Final Report.