Chapter 13A: PSYCHROMETRIC PROPERTIES Agami Reddy (rev- May 2017) Definition and importance of psychrometrics Gibbs-Dalton’s law of mixtures of perfect gases Moist air properties of primary interest Determining moist air properties from tables and equations Correlations between properties Psychrometric chart - usefulness - construction - determining moist air properties HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Psychrometrics Definition: Study of the properties of mixtures of dry air and water vapor Fundamental to most HVAC processes Importance: Its proper understanding is critical for anyone involved in conditioning air supply to indoor spaces which need to be maintained at pre-specified temperature and humidity conditions Ideal gas laws are adequate for determining properties since the partial pressure of water vapor is very small Recall: Ideal gases are those that follow the law pV=mRT HCB 3-Chap 13A: Psych Properties

Change of Atmospheric Pressure with Altitude Several different empirical equations exist. One can also use the ideal gas law. Eq. 13.1 is one such correlation Constant H 1220 m (4000 ft) H > 1220 m (4000 ft) SI Units IP Units a 101.325 29.92 99.436 29.42 b -0.01153 -0.001025 -0.010 -0.0009 At Phoenix, elevation H=1120 ft, p=29.92-0.001025 x 1120=28.57 “Hg=14.0 psi HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Gibbs-Dalton’s Law of Mixtures HCB 3-Chap 13A: Psych Properties

Important Moist Air Properties (a) Dry bulb temperature: Tdb or DBT °C or °F air temperature measured by a thermometer (b) Partial pressure of water vapor (Pv or Pvap ) Do not confuse with saturated partial pressure Psat which can be found from the steam tables HCB 3-Chap 13A: Psych Properties

HCB 3- Chap 12B: Property Tables, Carnot Cycles and HX Recall HCB 3- Chap 12B: Property Tables, Carnot Cycles and HX

An expression for saturation pressure of water vapor 13.19 where temperature T is in absolute units The critical pressure of water pc is 22.1 MPa (3226 psia), and the critical temperature Tc is 647.30 K (1165.67°R) And the parameter K is: SI units: IP units: HCB 3-Chap 13A: Psych Properties

HCB 3- Chap 12B: Property Tables, Carnot Cycles and HX Recall Property Diagram- note the critical point Fig. 12.5 Pressure-volume diagram for water. HCB 3- Chap 12B: Property Tables, Carnot Cycles and HX

HCB 3-Chap 13A: Psych Properties Example psia Compare this value from that from the steam table: 0.122 psia HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties (c) Relative humidity RH or (13.8) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties (d) Humidity Ratio or W is the ratio of mass of water vapor by mass of dry air (kgw/kga , lbw/lba or grains/lba) pounds/grains of water vapor per pound dry air (7000 grains = 1 lbm) (analogy to a sponge containing water) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties (e) Wet Bulb Temperature (Twb, or WBT ) °C or °F The humidity of the passing air affects how much water will evaporate, which affects temperature reading Approximates adiabatic saturation process Easy to measure Water on sock evaporates, pushing the temperature of the sock towards the adiabatic saturation temperature Fig. 13.14 Apparatus for measuring wet and dry bulb temperatures HCB 3-Chap 13A: Psych Properties

Moist Air Properties contd… (f) Dew Point Temperature (Tdp, or TDP - °C or °F) the temperature at which the water vapor in the moist air would begin to condense if the moist air were cooled at constant pressure– the temperature T when pvap = psat - When a surface reaches the dew point temperature of air, condensation begins Condensation of water from air on the outside of a cold glass of water during summer HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties (g) Specific volume (v - m3/kg or ft3/lbm dry-air) - the volume of moist air per unit mass of dry air (h) Specific enthalpy (h or i - J/kg or Btu/lbm dry-air) - the enthalpy of moist air per unit mass of dry air Specific enthalpy of moist air h= hdry-air + hwater-vapor or h= ha + W. hvap (13.22) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Determining enthalpy: h Perfect gas assumption: Cp = cte, Cv = cte and h = f(T) (13.22) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties For greater accuracy use table for Moist Air Properties (note: this applies only to saturated conditions). Table 13.3 HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Table of moist air properties used for more accurate calculation Example: Find enthalpy at 60o F and 100% RH From Table 13.3, h=26.47 Btu/lb Compare this with that using equations first determine W=0.011 from Table 13.3 From Eq. (13.23), enthalpy h =0.24 x 60 +0.011 (1061.2+0.444 x 60) = 14.4 +11.97 =26.36 Btu/lb HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Definitions of Important Terms Dew Point Temperature: The temperature of moist air saturated at the same pressure and humidity ratio. Or more simply the temperature at which water vapor will begin to condense from a sample of air. Dry-Bulb Temperature: The temperature of air read on a standard thermometer indicating it's thermal state. Enthalpy: The thermodynamic property defined as energy per unit mass of dry air commonly used to define the internal energy of moist air. Humidity Ratio: The ratio of the mass of water vapor to the mass of dry air of a sample. Relative Humidity: The ratio of mole fraction of water vapor in a given moist air sample to the mole fraction in a saturated air sample at the same temperature and pressure. Specific Volume: The ratio of the total volume of air to the mass of dry air in a sample. Wet-Bulb Temperature :The equilibrium temperature reached as water evaporates from a thoroughly wetted psychrometer wick into an airstream. HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Correlations are used to determine certain properties knowing others: Determining humidity ratio W when DBT and RH are known (along with total pressure) Determining RH when DBT and WBT are known (along with total pressure) Determining DPT knowing DBT (along with total pressure) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties (a) Relationship between Humidity Ratio and DBT and RH (13.15) HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Psychrometric Chart Extensively used by engineers Chart displays DBT, WBT, W, RH, DPT, specific volume and enthalpy Each point on the chart represents one moist air condition Locating the point from known conditions will allow determining the other unknown conditions One chart for a specified atmospheric pressure Two additional independent states needed to fix state on chart X-axis is dry-bulb temperature and Y-axis is humidity ratio HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Fig. 13.6 HCB 3-Chap 13A: Psych Properties

Example: Use of Psych Chart Locating other properties (IP units): Fill the table cells DBT WBT RH Hum. Ratio Enthalpy Sp. Vol. DPT 90 F 40% 60 F 55 F 70 F 0.01 75 F 0.011 HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Example Locating other properties (IP units) DBT WBT RH Hum. Ratio Enthalpy Specific volume DPT 90 F 71 F 40% 0.0122 35 14.1 63 F 60 F 55 F 72 0.0081 23.8 13.3 51 70 F 62 65 0.01 28 13.5 57 75 F 60 0.011 30 13.7 Undetermined HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties

HCB 3-Chap 13A: Psych Properties Outcomes Knowledge of the definition and scope of psychrometrics Understanding of the Gibbs-Dalton’s law of partial pressures Understanding of the important moist air properties Knowledge of how to use tables and equations to determine moist air properties under different conditions Understanding of the relationships and correlations between certain properties Understanding the importance of using psychrometric charts Knowledge of how psychrometric Charts are generated Be able to use the psychrometric chart to determine individual moist air properties HCB 3-Chap 13A: Psych Properties