Lecture 8Lecture 8

Saturated Adiabatic ProcessesSaturated Adiabatic Processes

Phase ChangesPhase Changes

Liquid

Gas(Vapor)

Energy absorbed

Energy released

Solid (Ice)

melting

evaporation

deposition

freezing

sublimation

condensation

Latent Heat Latent Heat

Heat released or absorbed during a phase Heat released or absorbed during a phase change of waterchange of water

AMS GlossaryAMS Glossary

Latent Heats at 0Latent Heats at 0CC

Latent heats of vaporization (evaporation) Latent heats of vaporization (evaporation) and condensation (Land condensation (Lvv): ~ 600 cal): ~ 600 calgg-1-1

Latent heats of fusion (freezing) and Latent heats of fusion (freezing) and melting (Lmelting (Lff): ~ 80 cal): ~ 80 calgg-1-1

Latent heats of sublimation and deposition Latent heats of sublimation and deposition (L(Lss): ~ 680 cal): ~ 680 calgg-1-1

Conversion: 1 calConversion: 1 calgg-1-1 = 4.1855 x 10 = 4.1855 x 1033 J Jkgkg-1-1

ExerciseExercise

Convert LConvert Lvv to J to Jkgkg-1-1

LLvv = (600 cal = (600 calgg-1-1) x 4.1855x 10) x 4.1855x 1033JJkgkg-1-1

= 2.5 x 10= 2.5 x 106 6 JJkgkg-1-1

ExerciseExercise

Suppose that the mixing ratio (w) of a Suppose that the mixing ratio (w) of a parcel is 2.0 x 10parcel is 2.0 x 10-2-2

(20g water vapor per kg of dry air)(20g water vapor per kg of dry air)

Suppose that 10% of the vapor condenses Suppose that 10% of the vapor condenses

How much does the parcel warm?How much does the parcel warm? (Assume constant pressure.)(Assume constant pressure.)

Solution, Part 1Solution, Part 1

Q = -LQ = -Lvvmmvv, where m, where mvv is the mass of is the mass of

water vaporwater vapor (Why the negative sign?)(Why the negative sign?)

q q -L -Lv v ww

= - (2.5 x 10= - (2.5 x 1066 J Jkgkg-1-1))(-2.0 x 10(-2.0 x 10-3-3))

= 5.0 x 10= 5.0 x 1033 J Jkgkg-1-1

Solution, Part 2Solution, Part 2

Temperature change at constant pressure:Temperature change at constant pressure:

pc

qT

But, cp 1000 Jkg-1 kg-1

K 5.0

1000.1

100.5113

13

KkgJx

kgJxT

A Saturated Adiabatic SystemA Saturated Adiabatic System

Consider a parcel consisting of dry air, Consider a parcel consisting of dry air, water vapor, and liquid waterwater vapor, and liquid water Closed system, saturatedClosed system, saturated

Consider adiabatic transitionsConsider adiabatic transitions i.e., no heat enters or leaves systemi.e., no heat enters or leaves system

Saturated Adiabatic TransitionsSaturated Adiabatic Transitions

Expansion Expansion cooling cooling condensation condensation i.e., water vapor decreases, liquid water increasesi.e., water vapor decreases, liquid water increases Condensational heating partially offsets cooling due to Condensational heating partially offsets cooling due to

expansionexpansion Result: Cooling rate less than dry adiabatic rateResult: Cooling rate less than dry adiabatic rate

Compression Compression warming warming evaporation evaporation i.e., water vapor increases, liquid water decreasesi.e., water vapor increases, liquid water decreases Evaporative cooling partially offsets heating due to Evaporative cooling partially offsets heating due to

compressioncompression Result: Heating rate less than dry adiabatic rateResult: Heating rate less than dry adiabatic rate

ComparisonComparison

z

Temperature

Unsaturated parcel

Saturated parcel

Dry and Saturated AdiabatsDry and Saturated Adiabats

Temperature

Pre

ssu

re

Dry

Saturated

Temperature of Lifted ParcelTemperature of Lifted Parcel

Consider a parcel that is initially Consider a parcel that is initially unsaturatedunsaturated

Parcel is lifted to LCL and beyondParcel is lifted to LCL and beyond

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

z

LCL

Wet-Bulb Temperature, TWet-Bulb Temperature, Tww

The wet-bulb temperature is the temperature The wet-bulb temperature is the temperature associated with a wick-covered associated with a wick-covered thermometer on a psychrometer.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 TPhysical Basis of Tww

Evaporation will occur on a wick at a steady Evaporation will occur on a wick at a steady rate (as sling is slung).rate (as sling is slung).

Heat must be continually supplied in an Heat must be continually supplied in an amount = the latent heat of vaporization of amount = the latent heat of vaporization of the water.the water.

Heat is taken from the air passing over the Heat is taken from the air passing over the wick of the thermometer – resulting in a wick of the thermometer – resulting in a drop in temperature!drop in temperature!

Physical Basis of TPhysical Basis of Tww

If air is saturated, no evaporation takes If air is saturated, no evaporation takes place. place.

Temperature of the wet bulb is same as dry Temperature of the wet bulb is same as dry bulb. bulb.

If air is very dry, the If air is very dry, the wet-bulb depressionwet-bulb depression may be substantial. Wet-bulb depressionis may be substantial. Wet-bulb depressionis the T-Tthe T-Tww

Dew Point vs. Wet Bulb TemperatureDew Point vs. Wet Bulb TemperatureDew point is when we cool a volume of air until Dew point is when we cool a volume of air until

saturation is reached while keeping moisture saturation is reached while keeping moisture content constant.content constant.

Wet-bulb temperature we obtain if we cool air to Wet-bulb temperature we obtain if we cool air to saturation by evaporating water into it. saturation by evaporating water into it.

Therefore, saturation is reached at a higher Therefore, saturation is reached at a higher temperature than dew point. temperature than dew point.

TTdd ≤ T≤ Tww ≤ T ≤ T

Normand’s RuleNormand’s Rule

States that the wet-bulb temperature may be States that the wet-bulb temperature may be determined by lifting a parcel of air determined by lifting a parcel of air adiabatically to its LCL and then following adiabatically to its LCL and then following a moist adiabat from that temperature a moist adiabat from that temperature back down to the parcel’s actual back down to the parcel’s actual temperature.temperature.

Relationship between dew point, wet-bulb and dry bulb temperatures