Objectives
• Describe psychrometric quantities
• Given any two psychrometric quantities, calculate any other quantity
• Use Tables A4 or psychrometric charts to look up psychrometric quantities
• Calculate psychrometric quantities at non-standard conditions
• Evaluate psychrometric processes (8.1-8.4)
Humidity Ratio, W
• W = mw/ma
• Degree of saturation, µ = W/Ws
• Humidity ratio is hard to measure, but very useful in calculations
• What are units?
• Is W a function of temperature? What about Ws?
Ws = humidity ratio at saturationma = mass of dry airmw = mass of water vapor
Relative Humidity
• Φ = xw/xw,s = Pw/Pws
• Function of T
• Easy to measure and useful in some contexts, but often need to know temperature as well
W
Ws
622.0
622.0
x = mole fractionP = pressureμ = degree of saturationW = humidity ratio
Dew-point temperature, td
• Temperature at which condensation will form• Under appropriate surface conditions
• Vapor is saturated
• Φ = ?
• Ws(P, td) = W
Wet-bulb temperature, t*
• Temperature at which water, by evaporating into the air, will bring air to saturation adiabatically
• * superscript is designation that variable is evaluated at the wet-bulb temperature
• Note, distinct from that measured by a sling psychrometer• Section 9.5
Tables for Moist Air (P = 1 atm)
• Tables A.4 in your text
• Ability to get Ws for calculations
• Subscripts:• a = dry air, s = saturated air
v = va+µvas
h = ha+µhas
s = sa+µsas
Psychrometric Chart
• Need two quantities for a state point• Can get all other quantities from a state point
• Can do all calculations without a chart• Often require iteration• Many “digital” psychrometric charts available
• Can make your own
• Best source is ASHRAE fundamentals (Chapter 6)• Also in your text (back cover fold-out)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Examples
• What is enthalpy of air in the classroom right now?
• Condensation on windows when taking a shower
• How cold does it have to be outside for condensation to form on windows?
– Assumption is that windows are the same temperature as outside air
– 80 °F, RH = 80%
Alternate calculation for W
• PV = mRT (IGL)
• What do we know about R ratio?
• P = Pw + Pa
w
a
a
w
TRVP
TRVP
a
w
R
R
P
P
m
mW
a
a
w
w
w
w
PP
PW
622.0
R = gas constantP = pressureV = volumeT = absolute temperatureW = humidity ratio
Subscripts: w is water vapor, a is dry air
A diversion…
• For an ideal gas,• ha = ∫cpadT, hw = ∫cpwdT
• So, ha = cpat which assumes a reference state of 0 °F or 0 °C – Tables A4• Note different reference
• hw = cpwt + hg0
• h = cpat + W(cpwt + hg0)
• h = cpt + W∙hg0, cp = cpa + Wcpw
cp = specific heath = enthalpyT = absolute temperaturet = temperature W = humidity ratio
Subscripts: w is water vapor, a is dry air, g is saturated water vapor
Approximating Psychrometric Processes
• Δhs = cpΔt, ΔhL = hwΔW=(cpwt + hg0) ΔW
• Where do these come from?
• Δh = h2 – h1, Δt = t2 – t1, ΔW = W2 – W1,
• t = (t1 + t2)/2, W = (W1 + W2)/2
• Δh = Δhs + ΔhL
• Major result• Δhs = cpΔt , ΔhL = hwΔW
Summary
• Describe psychrometric quantities
• Given any two psychrometric quantities, calculate any other quantity
• Use Tables A4 or psychrometric charts to look up psychrometric quantities
• Calculate psychrometric quantities at non-standard conditions
Psychrometric Processes
• Adiabatic mixing of two streams
• Sensible heating and cooling
• Dehumidification by cooling
• Humidification
• Evaporative cooling
Adiabatic mixing
• Governing equation hmQhmoutin
Sensible heating
tcmQ p
Dehumidification by Cooling