Prof. Fred RemerUniversity of North Dakota
Phase ChangesPhase Changesand Latent Heatand Latent Heat
Where’s the heat?Where’s the heat?
SolidSolidLiquidLiquid
GasGas
Prof. Fred RemerUniversity of North Dakota
ReadingReading Hess
– Phase Diagram pp 49 – 51
– Dew Point, Wet Bulb Temperature and Wet Bulb Potential Temperature
pp 60 – 63
Bohren & Albrecht– pp 218-223
Wallace & Hobbs– p. 84
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able to describe the changes in temperature, equilibrium pressure, volume and heat during various phase changes
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able to recall from memory the definition of critical point
Be able to recall from memory the definition of triple point
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able recall from memory the values of temperature and pressure for the triple point of water
Be able to recall from memory the values of temperature and pressure at the critical point of water
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able to show isobaric, isochoric and isothermal changes on phase diagrams
Be able to determine changes of boiling and melting temperatures with changes in atmospheric pressure
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able to recall from memory the definition of latent heat
Be able to determine whether latent heat is released or absorbed during a phase change
Be able to provide the name given to each type of phase change
Prof. Fred RemerUniversity of North Dakota
ObjectivesObjectives
Be able to describe how enthalpy and latent heat are related
Be able to perform calculations to determine the amount of latent heat released during a phase change
Be able to perform calculations to determine the change in latent heat with temperature
Prof. Fred RemerUniversity of North Dakota
ObjectiveObjective
Be able to recall from memory the definition of wet bulb temperature
Be able to compare the differences between wet bulb temperature and dew point temperature
Prof. Fred RemerUniversity of North Dakota
SolidSolidLiquidLiquidGasGas
Phase ChangesPhase Changes
Phase change results in a transformation of the molecular structure
Prof. Fred RemerUniversity of North Dakota
TT
Phase ChangePhase Change
Temperature of substance does not change during transformation
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Equilibrium (or saturation) pressure does not change during phase change
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Can Occur at Various Temperatures and Equilibrium Pressures
VaporVapor
WaterWater
Water &Water &VaporVapor
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
Ice & VaporIce & Vapor TT11
IceIce
TT22
TT33
TT44
TT55
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Volume changes significantly during phase change
CondensationCondensation
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Entropy also changes
SolidSolid LiquidLiquid GasGas
Increasing EntropyIncreasing Entropy
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
– Vapor to Ice– Water to Ice– Triple Line
The thermodynamic state at which three phases of a substance exist in equilibrium.
VaporVapor
WaterWater
Water Water &&
VaporVapor
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
Ice & VaporIce & Vapor00ooCC
TT
IceIce
Ice & WaterIce & Water
Phase Change (P-V Diagram)
Triple LineTriple Line
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
– Triple Line T = 273.16K es = 6.107 mb
VaporVapor
WaterWater
Water Water &&
VaporVapor
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
Ice & VaporIce & Vapor00ooCC
TT
IceIce
Ice & WaterIce & Water
Phase Change (P-V Diagram)
Triple LineTriple Line
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
– Vapor to Water Critical Point (Pc)
– The thermodynamic state in which liquid and gas phases of a substance coexist in equilibrium at the highest possible temperature.
Phase Change (P-V Diagram)
VaporVapor
WaterWater
Water Water &&
VaporVapor
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
Ice & VaporIce & Vapor00ooCC
TT
IceIce
Ice & WaterIce & WaterCritical Critical PointPoint
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
– Vapor to Water Critical Point (Pc)
– No liquid phase can exist at temperatures higher than the critical temperature
– Tc = 647 K
– Pc = 222,000 mb
Phase Change (P-V Diagram)
VaporVapor
WaterWater
Water Water &&
VaporVapor
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
Ice & VaporIce & Vapor00ooCC
TT
IceIce
Ice & WaterIce & WaterCritical Critical PointPoint
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Phase Change (P-T Diagram)
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
eessww
GasGaseessii
SolidSolid
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Isothermal Compression
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
eessww
GasGaseessii
SolidSolid
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Isobaric Cooling
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
eessww
GasGas
eessii
SolidSolid
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Changes in Atmospheric Pressure
TemperatureTemperature
Pre
ssu
reP
ress
ure LiquidLiquid
GasGas
SolidSolid
-.-.007007ooC C atmatm-1-1
– Change in Freezing Point
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Changes in Atmospheric Pressure
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
GasGas
SolidSolid
– Change in Boiling Point
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Critical Point
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
Critical Critical PointPoint
GasGaseessii
SolidSolid
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Triple Point
TemperatureTemperature
Pre
ssu
reP
ress
ure
LiquidLiquid
Critical Critical PointPoint
GasGas
0.010.01ooCC
eessii
6.11 mb6.11 mb Triple Triple PointPoint
SolidSolid
Prof. Fred RemerUniversity of North Dakota
Three Dimensional Phase Three Dimensional Phase DiagramDiagram
Ice & waterIce & water
WaterWater&&
VaporVapor
Vapor
Vapor
WaterWater
Ice & WaterIce & Water
(hidden)(hidden)
Triple StateTriple StateIc
e
Temperature
TemperatureSpecific VolumeSpecific Volume
Vap
or P
ress
ure
Vap
or P
ress
ure
Critical PointCritical Point
Prof. Fred RemerUniversity of North Dakota
Three Dimensional Phase Three Dimensional Phase DiagramDiagram
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Liquid Water Molecule– Hydrogen Bonds– Shearing Energy too great
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Ice– Volume Increases
Prof. Fred RemerUniversity of North Dakota
SolidSolidLiquidLiquid
GasGas
Phase ChangePhase Change
Heat is absorbed or released during the phase changes
Prof. Fred RemerUniversity of North Dakota
SolidSolidLiquidLiquid
GasGas
MeltingMelting
SublimationSublimationEvaporationEvaporation
Phase ChangePhase Change
Heat Absorbed
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Heat Released
SolidSolidLiquidLiquid
GasGas
FreezingFreezing
DepositionDepositionCondensationCondensation
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Latent Heat– The heat required to change the
molecular configuration of a substance
SolidSolidLiquidLiquidGasGas
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Latent Heat
SolidSolidLiquidLiquid
GasGas
FusionFusion(l(lff))
SublimationSublimation(l(lss))
Vaporization Vaporization (l(lvv))
Prof. Fred RemerUniversity of North Dakota
Phase ChangePhase Change
Latent Heat– Increase in internal energy results from
the change in molecular configuration
SolidSolidLiquidLiquidGasGas
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
First Law of Thermodynamics– Internal Energy changes– Temperature is constant!– Pressure is constant– Volume changes
Work is done
pddudq
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Rearrange
pddudq
pddqdu
vv = specific volume of vapor = specific volume of vapor
ww = specific volume of liquid = specific volume of liquid
)(ppd wv
For a phase change from liquid to vapor
Prof. Fred RemerUniversity of North Dakota
pddqdu
uuvv = internal energy of vapor = internal energy of vapor
uuww = internal energy of liquid = internal energy of liquid
)(ppd wv
Define the change in Internal Energy
Latent HeatLatent Heat
Substitute
Into )(pdqdu wv
)(pdquu wvwv
Prof. Fred RemerUniversity of North Dakota
)(pdquu wvwv
Latent HeatLatent Heat
Latent Heat (lv) = Change in Heat (dq)
)(pluu wvvwv
Rearrange
)pu()pu(l wwvvv
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Enthalpy is defined as
Substitute
)pu()pu(l wwvvv
puh
wvv hhl dhlv oror
Latent Heat is a change in Enthalpy!
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Latent Heat of Transformation (l)– ratio of the heat absorbed (Q) to the
mass undergoing a phase change
m
dQdhl
dqdhl
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
The amount of heat absorbed (or released) during a phase change is
lmdQ
m
dQl
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Representative Values at 0oC
– Latent Heat of Fusion (lf) 3.34x105 J kg-1
– Latent Heat of Vaporization (lv)
2.500x106 J kg-1
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Latent Heat of Sublimation (ls) at 0oC
ls = lf + lv
ls = 2.834x106 J kg-1
TemperatureTemperature
Pre
ssu
reP
ress
ure LiquidLiquid eessww
GasGas
0.010.01ooCC
eessii
SolidSolid
6.11 mb6.11 mb Triple Triple PointPoint
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Varies with temperature
VaporVapor
WaterWater
Volume (V)Volume (V)
Pre
ssu
re (
e)P
ress
ure
(e)
00ooCCTT
IceIce
dQdQ
dQdQ
dQdQ
dQdQ
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Let’s examine the latent heat of vaporization
dqm
dQlv
It’s easier to show the variation using entropy, but we’ll follow Hess
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
First Law of Thermodynamics
pddudq
dqm
dQlv
Substitute
pddulv
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Expand
And since w << v
pddulv
)(e)uu(l wvswvv
vswvv e)uu(l
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
The Ideal Gas Law (or Equation of State)
Substitute
vswvv e)uu(l
vvs TRe
vwvv TR)uu(l
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Differentiate with respect to temperature
vwvv TR)uu(l
vwvv R
dT
du
dT
du
dT
dl
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Remember from your early childhood
vwvv R
dT
du
dT
du
dT
dl
v
vv dT
duc
v
ccvvvv = specific heat of vapor at a constant volume = specific heat of vapor at a constant volume
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
The internal energy of water is a little more tricky!
vw
vvv R
dT
duc
dT
dl
?dT
duW
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Back to the First Law
pddudq
Differentiate with respect to temperature for water (remembering es is constant)
dT
de
dT
du
dT
dq ws
w
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
But the change in specific volume of water with temperature is very small
dT
de
dT
du
dT
dq ws
w
dT
du
dT
dqc ww
dT
de
dT
du
dT
dq ws
w
ccww = specific heat of liquid water = specific heat of liquid water
Prof. Fred RemerUniversity of North Dakota
vw
vv R
dT
duc
dT
dlv
dT
duc ww
Variation of Latent HeatVariation of Latent Heat
Substitute into
vwvv Rcc
dT
dlv
Prof. Fred RemerUniversity of North Dakota
Variation of Latent HeatVariation of Latent Heat
Another repressed memory ...
vwvv Rcc
dT
dlv
vvp Rccvv
wpv cc
dT
dlv
Prof. Fred RemerUniversity of North Dakota
wpv cc
dT
dlv
Variation of Latent HeatVariation of Latent Heat
Change in the Latent Heat of Vaporization with Temperature – Difference between
Specific Heat of Vapor (at constant pressure) Specific Heat of Liquid Water
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Evaluate wpv cc
dT
dlv
ccpvpv = specific heat of vapor = 1952 J K = specific heat of vapor = 1952 J K-1-1 kg kg-1-1
ccww = specific heat of liquid water = 4218 J K = specific heat of liquid water = 4218 J K-1-1 kg kg-1-1
1111v kgJK4218kgJK1870dT
dl
11v kgJK2348dT
dl
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
Is this a factor to be considered?
llvv = latent heat of vaporization @ 273.16K = 2.5 x 10 = latent heat of vaporization @ 273.16K = 2.5 x 1066 J kg J kg-1-1
11v kgJK2348dT
dl
116
11
v
v
K%09.Jkg1050.2
kgJK2348
ldTdl
Prof. Fred RemerUniversity of North Dakota
Latent HeatLatent Heat
A small factor
1v K%09.dT
dl
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Specific Heat – The amount of heat required to raise the
temperature of a unit mass of a substance by one degree
dT
dqc
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Specific Heat– Dry Air
Constant Volumecv = 717 J K-1 kg-1
Constant Pressurecp = 1004 J K-1 kg-1
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Specific Heat– Water Vapor
Constant Volume– cvv
= 1463 J K-1 kg-1
Constant Pressure– cpv
= 1870 J K-1 kg-1
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Specific Heat– Liquid Water (0oC)
cw = 4218 J K-1 kg-1
cw = 1 cal g-1 K-1
– Ice (0oC) ci = 2106 J K-1 kg-1
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Latent Heat– The heat required to change the
molecular configuration of a substance
SolidSolidLiquidLiquidGasGas
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Latent Heat– The change in enthalpy between states
dhl
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Latent Heat– The amount of heat absorbed (or
released) during a phase change
SolidSolidLiquidLiquid
GasGas
FusionFusion(l(lff))
SublimationSublimation(l(lss))
Vaporization Vaporization (l(lvv))
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Latent Heat– The ratio of the heat absorbed (Q) to the
mass undergoing a phase change
dqm
dQl
dqm
dQl
Prof. Fred RemerUniversity of North Dakota
SummarySummary
Latent Heat– Vaporization
lv = 2.50 x 106 J kg-1
– Fusion lf = 3.34 x 105 J kg-1
– Sublimation ls = 2.834 x 106 J kg-1
Prof. Fred RemerUniversity of North Dakota
Moisture VariablesMoisture Variables
Wet-Bulb Temperature (Tw)
– The temperature to which air is cooled by evaporating water into it at constant pressure until the air is saturated
TTww
Prof. Fred RemerUniversity of North Dakota
Moisture VariablesMoisture Variables
Wet Bulb Temperature (Tw)
– Two methods to compute Thermodynamic (or Isobaric) Method Adiabatic Method
vp mldTc
Prof. Fred RemerUniversity of North Dakota
Themodynamic Wet Bulb Themodynamic Wet Bulb TemperatureTemperature
Different than Dew Point Temperature
TTww
TTdd
Prof. Fred RemerUniversity of North Dakota
Moisture VariablesMoisture Variables
Dew Point (Td)
– Temperature to which air must be cooled at constant pressure in order for it to become saturated with respect to liquid water
TTdd
Prof. Fred RemerUniversity of North Dakota
Dew Point TemperatureDew Point Temperature
TemperatureTemperature
Pre
ssu
reP
ress
ure
eess
TTatmosphereatmosphere
eesaturationsaturation
RH = 100%RH = 100%
TTdd
IsobaricIsobaricCoolingCooling
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
TemperatureTemperature
Pre
ssu
reP
ress
ure
eess
TTatmosphereatmosphere
ee
RH = 100%RH = 100%
TTdd
EvaporationEvaporation
TTww
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Moisture is added to the atmosphere by evaporation
Heat for evaporation comes from air and water
TTww
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Heat Balance
VaporizeWaterAir dQdQ
Heat lost by Heat lost by airair
Heat required to Heat required to vaporize watervaporize water==
TTww
dQdQ
dQdQccp p = specific heat of air = specific heat of air
ccw w = specific heat of water = specific heat of water
mmvv = mass of water that evaporates = mass of water that evaporates
llv v = latent heat of vaporization = latent heat of vaporization
vvwp dmldT)cc(
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
TTww
ccppdd = specific heat of dry air= specific heat of dry air
ccppvv = specific heat of water vapor= specific heat of water vapor
ccw w = specific heat of liquid water = specific heat of liquid water
mmdd = mass of dry air = mass of dry air
mmv v = mass of water vapor = mass of water vapor
vvwwvpvdpd dmldT)cmcmcm(
vvwp dmldT)cc(
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
TTww
TT
TTww
wwTTw w = wet bulb temperature= wet bulb temperature
TTaa = temperature of the air = temperature of the air
)TT)(cmcmcm( wairwwvpvdpd
)mm(l unsatvsatvv
vvwwvpvdpd dmldT)cmcmcm(
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
TTww
TT
TTww
wwmmvvsatsat
= mass of water vapor of saturated air = mass of water vapor of saturated air
mmvunvunsatsat = mass of water vapor of unsaturated air = mass of water vapor of unsaturated air
mmvunvunsatsat-- mmvunvunsat sat
= amount of water vapor = amount of water vapor
evaporated into airevaporated into air
)TT)(cmcmcm( wairwwvpvdpd
)mm(l unsatvsatvv
vvwwvpvdpd dmldT)cmcmcm(
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Divide both sides by md
TTww
TT
TTww
ww
wwsatsat
= mixing ratio of saturated air = mixing ratio of saturated air
wwunsatunsat
= mixing ratio of unsaturated air = mixing ratio of unsaturated air
)TT)(cmmwcc( wairwdwvpdp
)ww(l unsatsatv
)TT)(cmcmcm( wairwwvpvdpd
)mm(l unsatvsatvv
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
As md increases, wcpv
and mw/md decreases
– Can be neglected
TTww
TT
TTww
ww
)ww(l)TT(c unsatsatvwairdp
)TT)(cmmwcc( wairwdwvpdp
)ww(l unsatsatv
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Substitute for mixing ratioTTww
TT
TTww
ww
)ww(l)TT(c unsatsatvwairdp
p
e
ep
ew
)ee(p
l)TT(c sat
vwairdp
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Solve for e
TTww
TT
TTww
ww
)ee(p
l)TT(c sat
vwairdp
)TT(l
pcee wair
v
dpsat
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Psychrometric Equation
TTww
TT
TTww
ww
)TT(l
pcee wair
v
dpsat
vdp
l
pc Psychrometric Constant
Prof. Fred RemerUniversity of North Dakota
TTww
TT
TTww
ww
w’w’
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Other Factors– Ventilation– Radiation– Instrumentation
Prof. Fred RemerUniversity of North Dakota
TTww
T,wT,wss
TTww
ww
w’w’
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Measure T & Tw
esat is a Function of Tw via Claussius-Clapeyron
e is a Function of T via Claussius-Clapeyron
)TT(l
pcee wair
v
dpsat
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Must Be Solved Iteratively or…..
)TT(l
pcee wair
v
dpsat
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Psychrometric Charts– Equation Solved for Various Temperatures
Relative Humidity %
Dry Bulb oF
Prof. Fred RemerUniversity of North Dakota
Thermodynamic Wet Bulb Thermodynamic Wet Bulb TemperatureTemperature
Psychrometric Tables
Prof. Fred RemerUniversity of North Dakota
Adiabatic Wet Bulb Adiabatic Wet Bulb TemperatureTemperature
The temperature an air parcel would have if cooled to saturation and then compressed adiabatically to the original pressure in a moist adiabatic process
Prof. Fred RemerUniversity of North Dakota
Adiabatic Wet Bulb Adiabatic Wet Bulb TemperatureTemperature
TTTTdd TTww
Prof. Fred RemerUniversity of North Dakota
Wet Bulb Potential Wet Bulb Potential Temperature (Temperature (w w ))
The wet bulb temperature the air would have if it were expanded or compressed adiabatically from its existing pressure and wet bulb temperature to a standard pressure of 1000 mb.
286.
ww P
1000T
Prof. Fred RemerUniversity of North Dakota