Lecture 8
Saturated Adiabatic Processes
Phase Changes
condensation
Liquid
evaporation
Gas
(Vapor)
melting
deposition
sublimation
freezing
Solid
(Ice)
Energy absorbed
Energy released
Latent Heat
Heat released or absorbed during a phase
change of water
AMS Glossary
Latent Heats at 0C
Latent heats of vaporization (evaporation)
and condensation (Lv): ~ 600 calg-1
Latent heats of fusion (freezing) and
melting (Lf): ~ 80 calg-1
Latent heats of sublimation and deposition
(Ls): ~ 680 calg-1
Conversion: 1 calg-1 = 4.1855 x 103 Jkg-1
Exercise
Convert Lv to Jkg-1
Lv = (600 calg-1) x 4.1855x 103Jkg-1
= 2.5 x 106 Jkg-1
Exercise
Suppose that the mixing ratio (w) of a
parcel is 2.0 x 10-2

(20g water vapor per kg of dry air)
Suppose that 10% of the vapor condenses
How much does the parcel warm?

(Assume constant pressure.)
Solution, Part 1
Q = -Lvmv, where mv is the mass of
water vapor

(Why the negative sign?)
q  -Lv w
= - (2.5 x 106 Jkg-1)(-2.0 x 10-3)
= 5.0 x 103 Jkg-1
Solution, Part 2
Temperature change at constant pressure:
q
T 
cp
But, cp  1000 Jkg-1 kg-1

5.0 x103 J  kg1
T 
1.00x103 J  kg1  K 1
 5.0 K
A Saturated Adiabatic System
Consider a parcel consisting of dry air,
water vapor, and liquid water

Closed system, saturated
Consider adiabatic transitions

i.e., no heat enters or leaves system
Saturated Adiabatic Transitions
Expansion  cooling  condensation



i.e., water vapor decreases, liquid water increases
Condensational heating partially offsets cooling due
to expansion
Result: Cooling rate less than dry adiabatic rate
Compression  warming  evaporation



i.e., water vapor increases, liquid water decreases
Evaporative cooling partially offsets heating due to
compression
Result: Heating rate less than dry adiabatic rate
Comparison
Unsaturated parcel
z
Saturated parcel
Temperature
Dry and Saturated Adiabats
Dry
Pressure
Saturated
Temperature
Temperature of Lifted Parcel
Consider a parcel that is initially
unsaturated
Parcel is lifted to LCL and beyond
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
z
LCL
Temperature
Wet-Bulb Temperature, Tw
The wet-bulb temperature is the temperature
associated with a wick-covered
thermometer on a psychrometer.
Measuring Humidity: Sling psychrometer
A psychrometer consists of two glass thermometers with one
covered with a wick (cloth) that is wet. This measures the
‘wet-bulb’ temperature.
Physical Basis of Tw
Evaporation will occur on a wick at a steady
rate (as sling is slung).
Heat must be continually supplied in an
amount = the latent heat of vaporization of
the water.
Heat is taken from the air passing over the
wick of the thermometer – resulting in a
drop in temperature!
Physical Basis of Tw
If air is saturated, no evaporation takes
place.
Temperature of the wet bulb is same as dry
bulb.
If air is very dry, the wet-bulb depression
may be substantial. Wet-bulb depressionis
the T-Tw
Dew Point vs. Wet Bulb Temperature
Dew point is when we cool a volume of air until
saturation is reached while keeping moisture
content constant.
Wet-bulb temperature we obtain if we cool air to
saturation by evaporating water into it.
Therefore, saturation is reached at a higher
temperature than dew point.
Td ≤ Tw ≤ T
Normand’s Rule
States that the wet-bulb temperature may be
determined by lifting a parcel of air
adiabatically to its LCL and then following
a moist adiabat from that temperature
back down to the parcel’s actual
temperature.
Relationship between dew point, wetbulb and dry bulb temperatures