Psychrometrics
"Psychrometrics is the study of the physical and thermal properties of air and water vapor mixtures (Henderson et al., 1993)." Atmospheric air contains water vapor, pollutants, and gases, such as nitrogen, oxygen, carbon dioxide, etc. Dry air is referred to as air devoid of water vapor and pollutants. The mixture of dry air and water vapor, called moist air, is the basis for psychrometric analysis. A solid understanding of the physical and thermal properties of moist air is the foundation for conceptual and design analyses of industrial drying, heating and cooling processes.
For engineering purposes, moist air can be considered as a mixture of perfect gases and the ideal gas law may be applied. For a given number of moles of moist air,
Dry air
Water vapor 
where Pair and PH2O are the partial pressures of dry air and water vapor, respectively. The terms nair and nH2O correspond to the number of moles of these components in the mixture. The mixture obeys the ideal gas law and these two equations may be combined.
Dalton’s Law states that the total pressure exerted by a mixture of perfect gases is the same as that exerted by the constituent gases independently. The sum of the partial pressures above, therefore, is the total pressure exerted by the moist air.
Mole Fraction, x
Mole fraction is the number of moles of a component per number of moles of the sample. From the ideal gas law, the mole fraction of the constituents of moist air can be expressed in terms of the partial pressures.
Psychrometric Terms
The following terminology is used to describe the physical and thermal properties of moist air.
Figure 1. Adiabatic saturation of air in an insulated chamber. The exiting air is at a
lower temperature and higher humidity ratio. Adapted from Singh and Heldman, 1993.
These physical and thermodynamic properties can be calculated using the equations outlined in Table 1. A psychrometric chart, however, may be more useful as it is a graphical representation of these properties. The chart is also useful in analyzing typical air-conditioning and processing (heating, cooling, dehumidification, drying, etc.) problems. The figures on the following pages are graphic representations of these processes.
Table 1. Empirical equations to psychrometric properties.
Component and Property |
Value or Equation |
Units and Comments |
||
| Standard Dry Air | ||||
| Molecular weight | 28.9645 | g/mol | ||
| Gas constant, Rair | 287.055 | m3 Pa/kg K | ||
| Specific volume, u air | u air = (Rair T) ÷ Pair | m3/kg Use absolute temperature (K) |
||
| Average specific heat, cpair | 1.005 | kJ/kg K Valid for a temperature range of –40 to 60oC |
||
| Enthalpy, hair | hair = 1.005 (T – T0) | kJ/kg | ||
| Water Vapor | ||||
| Molecular weight of water | 18.01534 | g/mol | ||
| Gas constant, RH2O | 461.52 | m3 Pa/kg K | ||
| Specific volume, u H2O | u H2O = (RH2O T) ÷ PH2O | m3/kg Valid for temperatures below 66oC |
||
| Specific heat, cpH2O | 1.88 | kJ/kg K Valid for a temperature range of –71 to 124oC |
||
| Enthalpy, hH2O | hH2O = 2501.4 + 1.88 (T - T0) | kJ/kg | ||
| Air-Vapor Mixtures | ||||
| Total pressure, Ptotal | Ptotal = Pair + PH2O | kPa | ||
| Humidity ratio, W | W = mH2O ÷ mair | kg H2O/kg dry air | ||
| W = 0.622 (xH2O ÷ xair) | ||||
| W = 0.622 {PH2O ÷ (Ptotal -PH2O)} | ||||
| Relative humidity, f | f = (PH2O ÷ PH2O,sat) x 100 | % | ||
| f = (r H2O ÷ r sat) x 100 | Valid for
conditions where perfect gas laws hold |
|||
| Specific volume, u | u = (0.082 T + 22.4) (1/29 + W/18) m3/kg | |||
 |
Wet-bulb temperature, Twb |
|
||
Source: Singh and Heldman, 1993; ASHRAE Fundamentals 1997
Psychrometric Chart and Its Uses
When using a psychrometric chart to describe a moist air sample, at least two properties of the moist air must be defined to properly identify the state of the mixture. The vertical lines represent dry bulb temperature while the horizontal lines represent the humidity ratio. Specific volume is identified by diagonal lines in 0.5 increments. The enthalpy and wet bulb temperature lines are the same oblique lines with different axes shown on the upper left boundary. The enthalpy scale is the upper leftmost scale while the scale for the wet-bulb temperature is on the saturation line.
The saturation line is the 100% relative humidity curve. If the state of a moist air
sample is at 100% relative humidity, the
sample's capacity to hold water vapor has been reached and further cooling (i.e., moving
to the left of this curve) will result in the condensation of the water vapor.
Figure 3 shows that drawing a horizontal line to the saturation curve (i.e., holding a constant humidity ratio) from the state point 1 of a moist air sample gives the dew-point temperature of the sample.
Figure 3. Determining the dew-point temperature of a moist air sample
The removal or addition of heat to the moist air, while keeping a constant
humidity ratio, can also be shown by drawing a horizontal line from state point 1 to state
point 2 (Figure 4 a and b).
Figure 4. Cooling and heating processes.
In some cases, however, a nearby heat sink causes the moist air to transfer its heat and mass to the sink, thereby driving the condition of the air toward the saturation curve. Effectively, the air is cooled to a temperature below its initial dew-point and is dehumidified (Figure 4 (c)). The combustion of a fuel results in not only heating of the moist air, but also the addition of moisture (Figure 4 ( d)).
Grains are typically dried by forcing heated air through the grain bed. This is an
example of an adiabatic saturation process. Heat is not transferred through conduction or
radiation. Instead, as heated air passes through the grain bed, most its sensible heat is
converted to latent heat and the air picks up moisture from the grain. This process occurs
along a constant enthalpy and wet bulb line in the direction where the humidity ratio
increases (Figure 5 (a)). The reverse process is chemical dehumidification (Figure 5 (b))
where moisture is removed from the air by an absorbent (e.g., silica gel in desiccators).
The process occurs along a constant enthalpy line towards a lower humidity ratio.
When two air mixtures of different states are mixed, the resulting air lies in between the
straight line connecting the two initial conditions (Figure 3.6). This is a common process
in air-conditioning systems.
The governing equations for this process are
Example 1. (Adapted from Singh and Heldman 1993, page 367)
Determine the rate of thermal energy required to heat 15 m3/s of outside air at 27oC dry bulb temperature and 80% relative humidity to a dry bulb temperature of 35oC.
SOLUTION
The process occurs along a constant humidity ratio line.
State 1
State 2
Tdb1 = 27oC
Tdb2 = 35oC
f 1 = 80%
f 2 = 51%
h1 = 73 kJ/kg dry air
h2 = 82 kJ/kg dry air
W1 = 0.0191 kg H2O/kg dry air W2
= 0.0191 kg H2O/kg dry air
air
u 1 = 0.874 m3/kg dry air
u 2 = 0.896 m3/kg dry air
Example 2. (Adapted from Singh and Heldman 1993, page 370)
Heated air at 45oC and 10% relative humidity is used to dry rice in a bin dryer. The air exists the bin under saturated conditions. Determine the amount of water removed per kg of dry air.
SOLUTION
The process occurs along a constant enthalpy line.
State 1 State 2
Tdb1 = 45oC Tdb2 = 23.3oC
f 1 = 10% f 2 = 100%
h1 = 70 kJ/kg dry air h2 = 70 kJ/kg dry air
W1 = 0.0078 kg H2O/kg dry air W2 = 0.0182 kg H2O/kg dry air
Amount of moisture removed ® W1 - W2 = (0.0182-0.0078) kg H2O/kg dry air
W1 - W2 = 0.0104 kg H2O/kg dry air
Example 3
A carton of eggs was removed from the refrigerator and left on the kitchen counter. The refrigerator was set at a temperature of 5oC and the kitchen at 24oC, 30% relative humidity. Will condensation occur (i.e., "sweat" appear on eggs)?
SOLUTION
The corresponding dew-point temperature at 24oC and 30% relative humidity is 4.5oC. Since 4.5oC < 5oC, condensation will not occur.