Psychrometrics

Psychrometrics or psychrometry are terms used to describe the field of engineering concerned with the determination of physical and thermodynamic properties of gas-vapor mixtures. The term derives from the Greek psuchron (ψυχρόν) meaning "cold"^[1] and metron (μέτρον) meaning "means of measurement".^[2]

Common applications

Although the principles of psychrometry apply to any physical system consisting of gas-vapor mixtures, the most common system of interest is the mixture of water vapor and air, because of its application in heating, ventilating, and air-conditioning and meteorology. In human terms, our comfort is in large part a consequence of, not just the temperature of the surrounding air, but (because we cool ourselves via perspiration) the extent to which that air is saturated with water vapor.

Psychrometric ratio

The psychrometric ratio is the ratio of the heat transfer coefficient to the product of mass transfer coefficient and humid heat at a wetted surface. It may be evaluated with the following equation:^[3][4]

where:

• r = Psychrometric ratio, dimensionless
• h_c = convective heat transfer coefficient, W m^-2 K^-1
• k_y = convective mass transfer coefficient, kg m^-2 s^-1
• c_s = humid heat, J kg^-1 K^-1

Humid heat is the constant-pressure specific heat of moist air, per unit mass of dry air.^[5]

The psychrometric ratio is an important property in the area of psychrometrics, as it relates the absolute humidity and saturation humidity to the difference between the dry bulb temperature and the adiabatic saturation temperature.

Mixtures of air and water vapor are the most common systems encountered in psychrometry. The psychrometric ratio of air-water vapor mixtures is approximately unity, which implies that the difference between the adiabatic saturation temperature and wet bulb temperature of air-water vapor mixtures is small. This property of air-water vapor systems simplifies drying and cooling calculations often performed using psychrometic relationships.

Psychrometric chart

A psychrometric chart for sea-level elevation.

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A psychrometric chart is a graph of the thermodynamic properties of moist air at a constant pressure (often equated to an elevation relative to sea level). The ASHRAE-style psychrometric chart, shown here, was pioneered by Willis Carrier in 1904.^[6] It depicts these properties and is thus a graphical equation of state. The properties are:

• Dry-bulb temperature (DBT) is that of an air sample, as determined by an ordinary thermometer, the thermometer's bulb being dry. It is typically the abscissa (horizontal axis) of the graph. The SI units for temperature are Kelvin; other units are Fahrenheit.
• Wet-bulb temperature (WBT) is that of an air sample after it has passed through a constant-pressure, ideal, adiabatic saturation process, that is, after the air has passed over a large surface of liquid water in an insulated channel. In practice, this is the reading of a thermometer whose sensing bulb is covered with a wet sock evaporating into a rapid stream of the sample air (see Hygrometer). When the air sample is saturated with water, the WBT will read the same as the DBT. The slope of the line of constant WBT reflects the heat of vaporization of the water required to saturate the air of a given relative humidity.
• Dew point temperature (DPT) is that temperature at which a moist air sample at the same pressure would reach water vapor “saturation.” At this point further removal of heat would result in water vapor condensing into liquid water fog or (if below freezing) solid hoarfrost. The dew point temperature is measured easily and provides useful information, but is normally not considered an independent property of the air sample. It duplicates information available via other humidity properties and the saturation curve.
• Relative humidity (RH) is the ratio of the mole fraction of water vapor to the mole fraction of saturated moist air at the same temperature and pressure. RH is dimensionless, and is usually expressed as a percentage. Lines of constant RH reflect the physics of air and water: they are determined via experimental measurement. Note: the notion that air "holds" moisture, or that moisture “dissolves” in dry air and saturates the solution at some proportion, is an erroneous (albeit widespread) concept (see relative humidity for further details).
• Humidity ratio (also known as moisture content or mixing ratio) is the proportion of mass of water vapor per unit mass of dry air at the given conditions (DBT, WBT, DPT, RH, etc.). It is typically the ordinate (vertical axis) of the graph. For a given DBT there will be a particular humidity ratio for which the air sample is at 100% relative humidity: the relationship reflects the physics of water and air and must be measured. Humidity ratio is dimensionless, but is sometimes expressed as grams of water per kilogram of dry air or grains of water per pound of air (7000 grains equal 1 pound). Specific humidity is closely related to humidity ratio but always lower in value as it expresses the proportion of the mass of water vapor per unit mass of the air sample (dry air plus the water vapor).
• Specific enthalpy symbolized by h, also called heat content per unit mass, is the sum of the internal (heat) energy of the moist air in question, including the heat of the air and water vapor within. In the approximation of ideal gases, lines of constant enthalpy are parallel to lines of constant WBT. Enthalpy is given in (SI) joules per kilogram of air or BTU per pound of dry air.
• Specific volume, also called inverse density, is the volume per unit mass of the air sample. The SI units are cubic meters per kilogram of dry air; other units are cubic feet per pound of dry air.

The versatility of the psychrometric chart lies in the fact that by knowing three independent properties of some moist air (one of which is the pressure), the other properties can be determined. Changes in state, such as when two air streams mix, can be modeled easily and somewhat graphically using the correct psychrometric chart for the location's air pressure or elevation relative to sea level. For locations at or below 2000 ft (600 m), a common practice is to use the sea-level psychrometric chart.

How to read the chart

In the ω-t chart, the dry bulb temperature (DBT) t appears as the abscissa (horizontal axis) and the humidity ratio (ω) appear as the ordinate (vertical axis). A chart is valid for a given air pressure (or elevation above sea level). From any two of the six independent properties (DBT, WBT, RH, humidity ratio, specific enthalpy, and specific volume), the balance of the six can be reckoned. This gives rise to possible combinations.

DBT: Can be determined from the abscissa [[x-axis][t–axis]], the horizontal axis

DPT: Follow the horizontal line from the point where the line from the horizontal axis arrives at 100% RH, also known as the saturation curve.

WBT: Line inclined to the horizontal and intersects saturation curve at DBT point.

RH: Hyperbolic lines drawn asymptotically with respect to the saturation curve which corresponds to 100% RH.

Humidity ratio: Marked on the y-axis.

Specific enthalpy: lines of equal values, or hash marks for, slope from the upper left to the lower right.

Specific volume: Equally spaced parallel family of lines.

Dry-bulb temperature

Common thermometers measure what is known as the dry-bulb temperature. Electronic temperature measurement, via thermocouples, thermistors, and resistance temperature devices (RTDs), for example, have been widely used too since they became available.

Wet-bulb temperature

The thermodynamic wet-bulb temperature is a thermodynamic property of a mixture of air and water vapor. The value indicated by a simple wet-bulb thermometer often provides an adequate approximation of the thermodynamic wet-bulb temperature.

A wet-bulb thermometer is an instrument which may be used to infer the amount of moisture in the air. If a moist cloth wick is placed over a thermometer bulb the evaporation of moisture from the wick will lower the thermometer reading (temperature). If the air surrounding a wet-bulb thermometer is dry, evaporation from the moist wick will be more rapid than if the air is moist. When the air is saturated no water will evaporate from the wick and the temperature of the wet-bulb thermometer will be the same as the reading on the dry-bulb thermometer. However, if the air is not saturated water will evaporate from the wick causing the temperature reading to be lower.

The accuracy of a simple wet-bulb thermometer depends on how fast air passes over the bulb and how well the thermometer is shielded from the radiant temperature of its surroundings. Speeds up to 5,000 ft/min (60 mph) are best but dangerous to move a thermometer at that speed. Errors up to 15% can occur if the air movement is too slow or if there is too much radiant heat present (sunlight, for example).

A wet bulb temperature taken with air moving at about 1-2 m/s is referred to as a screen temperature, whereas a temperature taken with air moving about 3.5 m/s or more is referred to as sling temperature.

A psychrometer is a device that includes both a dry-bulb and a wet-bulb thermometer. A sling psychrometer requires manual operation to create the airflow over the bulbs, but a powered psychrometer includes a fan for this function.

Mollier Diagram

The Mollier h-x diagram, developed by Richard Mollier in 1923,^[7] is an alternative psychrometric chart, preferred by many users in Scandinavia, Eastern Europe, and Russia.^[8]

The underlying data for the psychrometric chart and the Mollier diagram are identical; they are equivalent. At first inspection, there may appear little resemblance between the charts, but if the user rotates a chart ninety degrees and looks at it in a mirror, the resemblance is more apparent. Note that, in the Mollier diagram, the abscissa is enthalpy h (the defining feature of a Mollier diagram). In the psychrometric chart however, lines of constant enthalpy are inclined and nearly parallel.

See also

• Air
• Air conditioning
• Dalton's law of Partial Pressures
• Dew point
• Dry-bulb temperature
• Evaporative cooling
• Humidity
• Relative humidity
• Wet-bulb temperature

References

External links

• Psychrometric Chart - Detailed psychrometric chart including curves for enthalpy, air mass, and water mass.
• American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
• Universal Industrial Gases, Inc. webpage - Links to physical properties tables, to psychrometric charts that depict inter-relationships among the various physical properties of air, to online psychrometric properties calculators for easy calculation of properties, and to individual gas information pages.
• Corwin's Calculators Calculator for humidity, dew point.