Gas-Vapor and Air Conditionning

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Chapter 13 Lyes KADEM [Thermodynamics II] 2007

as!"apor Mi#t$res

Air is a mixture of nitrogen and oxygen and argon plus traces of some other gases. When water-vapor is not included, we refer to it as dry air. If water-vapor is included, we must properly accountfor it.Usually, we will consider air and water-vapor (even if water-vapor is at the saturation state) as ideal

gases. he error using this assumption will !e around ".#$.

herefore, from %alton&s law'he total pressure is the sum of the partial pressure aof the dry air and the partial pressure vofwater-vapor (called vapor pressure)'

vaP P P= +

ince we assume the water-vapor as an ideal gas, its enthalpy is only dependent on thetemperature. herefore, we will consider the enthalpy of water-vapor as the enthalpy of saturatedwater-vapor at the same temperature.

v

( ) ( )g

h T h T =

his approach is accepta!le for situations in which the pressure is relatively low (near atmospheric

pressure) and the temperature is !elow a!out *"+.

13%1% &ome de'initions(

13%1%1% )e*ati+e h$midity

It is the ratio of the mass of water-vapor m vto the maximum amount of water-vapor mg the air canhold at the same temperature.

v

g

m

m=

as!"apor Mi#t$res and Air Conditionin, 59


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using ideal gas law'

v v v

v

/

/g g

P V R T P

P V R T P= = with !etween " and .

13%1%2% The h$midity ratio -speci'ic h$midity.(

It is the ratio of the mass of water-vapor to the mass of dry air'

v

a

m

m=

using ideal gas law'

v v v v/ /

/ /a a a a

P V R T P R

P V R T P R= =

!ut' v"./*0 1231mol 4a".#56 1231mol 4

herefore'v v

v

0.622 0.622a

P P

P P P= =

And using the relative humidity'

g0.622

a

P

P

=

13%1%3% Dry /$*/ temperat$re(

It is the temperature of the air as measured !y a conventional thermometer.

13%1%% De!point temperat$re -Tdp.(

It is the temperature at which condensation !egins if air is cooled at constant pressure.

i,$re%13%1%%ew-point temperature.


E#amp*eAI

#0+, atm

ma 1gmv"." 1g

mv, max"."# 1g

pecific humidity' "." 1g 7#831g dry airelative humidity' 0"$.


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13%1%% Adia/atic sat$ration and et!/$*/ temperat$re

It is 9uit difficult to accurately determine directly the relative humidity and the humidity ratio.7owever, two indirect methods exists'

- Adia!atic saturation process.- Wet !ul! temperature.

13%1%%a% Adia/atic sat$ration process

his method uses a relatively long insulated channel. Air with un1nown relative humidity () enters,moisture is added to the air !y the pool of water, and saturated air exits. his process involves noheat transfer !ecause the channel is insulated.

i,$re%13%2%Adia!atic saturator.

An energy !alance on this control volume, neglecting 1inetic and potential energy changes, with:W", gives'

v1 v1 1 1 2 2 2 v2 v2a a f f a am h m h m h m h m h

+ + = +& & & & &

!ut

1 2

v1 v2

a a a

f

m m m

m m m

= =

+ =

& & &

& &

using '


E#amp*e

he air at #0+ and "" 1a in a ;;; m


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1 a 2a fm m m + =& & &

su!stituting with, hvhg

1 1 1 2 1 2 2 2 2( )

a g a a a f a a a g m h m h m h m h m h + + = +& & & & &

!ut at state #, #""$.

o'2

2

2

0.622 g

g

P

P P =

And,( )2 2 2 1

1

1 2

fg p

g f

h C T T

h h

+ =

o 1now #, we have to measure and #and the total pressure .

he pro!lem with adia!atic saturation process is that it re9uires a long channel to achieve

saturation conditions at the exit.

4ote(usually the amount of dry air in the air-water-vapor mixture remains constant, !ut the amountof water-vapor changes. herefore, the enthalpy of atmospheric air is expressed per unit mass ofdry air instead of per unit of air-water-air mixture.

13%1%%/% 5et /$*/ temperat$re

A much simpler approach is to wrap the !ul! of a thermometer with a cotton wic1 saturated withwater. hen, we can !low air over the wic1 or swing the thermometer through the air until thetemperature reaches a steady state' this is the wet-!ul! temperature.he adia!atic saturation temperature is essentially the same as the wet-!ul! temperature if thepressure is approximately atmospheric.

i,$re%13%3%dry-!ul! and wet !ul! temperatures.


E#amp*e

he dry and the wet-!ul! temperatures of atmospheric air at atm (".


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13%2% Aditiona* in'ormation(

6 Act$a* method to dermine the re*ati+e h$midity and the h$midity ratio(

Actually new devices !ased on the capacitance change of a thin polymer film are used to detemine

and .

6 Did yo$ no that hair *en,th increases ith h$midity8 he range !etween dry and saturated air can account for a difference in hair length of a!out threeper cent.In moist air, people with naturally curly hair experience the fri==ies as their hair increases in length.Under the same conditions, people with long, straight hair find it going limp.7air is such a relia!le indicator of good or !ad weather, in fact, that it is the primaryelement of the hair hygrometer, an instrument that was used for years to measure humidity.Invented in 65*"s. ?orits time, it was a very accurate humidity-measuring device, although not in widespread

meteorologicaluse today.

6 9$mide# 'actor(

@he humidex is a +anadian innovation, first used in >*0. It was devised !y +anadianmeteorologists to descri!e how hot, humid weather feels to the average person.@he humidex is !ased on the o!servation that intense heat accompanied !y a high vapour content,!ring a!out a physical malaise. In extreme cases, when the com!ined effects of the temperatureand moisture approach the normal temperature of the !ody (+! 10.



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7 is humidex index, is temperature in +, vis the water vapor pressure in milli!ar (m!ar)B

)an,e o' h$mide# De,ree o' com'ortCess than #> Do discomfort !y Antarcticexplorers, aul iple and +harles assel. hese hardy scientists measured how long it too1 forwater to free=e in a small plastic cylinder when it was placed outside in the wind. 8ver the years, theformula was modified somewhat, !ut remained !ased on the Antarctic experiments.@his formula was o!solete and in certain circumstances created confusion. ather than !e !asedon a water cylinder, @the new index is !ased on a model of how fast a human face loses heat. Wechose the face !ecause it is the part of the !ody most often exposed to severe winter weather,

assuming the rest of the !ody is clothed appropriately for the weather@.

he wind chill formula is'

) : 13%12 ; 0%?21 T @ 11%37 -"01?. ; 0%3=? T -"01?.where G is the wind chill indexF is the air temperature in degrees +elsius (+)F H is the windspeed at " metres (standard anemometer height), in 1ilometres per hour (1m3h) B

13%3% The psychrometric chart and air!conditionin, processes

13%3%1% The psychrometric chart

All the e9uations introduced in the upper section are very useful when wor1ing at pressures higherthan the atmospheric pressure.?or a standard atmospheric pressure, the most conveniant way to determine the various propertiesassociated with a water-vapor mixture is to use a psychrometric chart (?ig.


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i,$re%13%%sychrometric chart (principle).

13%3%2% Air conditionin, processes(

Eenerally, people feel most comforta!le when the air is the comfort =oneJ' the temperature is

!etween ##+ and #6+ and the relative humidity is !etween /"$ and *"$ (?ig.


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i,$re%13%%he conditioning of air.

13%3%2%1% Air!conditionin, processes ana*ysis

Most air-conditioning processes can !e modeled as steady-flow processes.

Mass !alance for dry air' = outletainleta mm

Mass !alance for water' = outletvinletv mmDeglecting L4and L, the first law can !e written as'

outoutoutletinlet

inin WQhmhmWQ ++=++

13%3%2%2% &imp*e heatin, and coo*in, -:Ct.

i,$re%13%?%imple heating.

Dote' the relative humidity of air decreases during a heating process (#O) even if the humidityratio remains constant. his is !ecause the relative humidity is the ratio of moisture content to themoisture capacity of air at the same temperature, and the moisture capacity increases withtemperature.

?irst law (neglecting L4and Land usually the wor1 of the fan is also neglected) can !e writtenunder the simple form'

( )12 hhmQ a =

13%3%2%3% 9eatin, ith h$midi'ication(

o overcome the pro!lem of decreasing with simple heating, air is passed first through a heatingsection and then through a humidifying section

i,$re%13%7%7eating and humidification.



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If steam is used


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i,$re%13%=%Lvaporative cooling.

his process is at constant enthalpy and constant wet !ul! temperature (constant enthalpy andconstant wet !ul! temperature lines on the psychrometric chart are almost the same).

13%3%2%?% Adia/atic mi#in, o' airstreams

i,$re%13%10%adia!atic mixing.

herefore, when two airstreams at two different states (state and #) are mixed adia!atically, thestate of the mixture (state


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In power plants or refrigeration plants, the wasted heat is usually reRected to the sea, la1e or river.7owever, when the water supply is limited, this heat must !e reRected to the atmosphere. his isperformed using a wet cooling tower.

Air is drawn into the tower from the !ottom and leaves through the top. Warm water from thecondenser is pumped to the top of the tower and is sprayed into the airstream. he purpose ofspraying is to expose a large surface of water to air. As the water droplets fall under the influence ofgravity, a small fraction of water (usually a few percent) evaporates and cools the remaining water.he temperature and the moisture content of the air increase during this process. he cooled wateris collected at the !ottom of the tower and is pumped !ac1 to the condenser to pic1 up additionalwaste heat (ref. +engel).

i,$re%13%10%Wet cooling towers. (left) An induced-draft couterflow cooling tower.(right) A natural-draft cooling tower.

13%3%3% Additiona* in'ormation

he human !ody operates li1e a heat engine, the energy input is food (many than1s to Mc%8 Q)and some wasted energy is eRected to the environment. he rate of heat generation for a mandepends on the level of activity'

leeping 56 Westing of doing office wor1 0 WKowling #roced$re or Ca*c$*atin, The >roperties ' Moist Air

. %etermine what properties you need to calculate. his depends on the pro!lem. %onSt forgetthat the rinciples of thermodynamics and the rocess descriptions are independent of themethod for calculating the roperties.

#. ?rom the rocess description, determine the pressure of the moist air. his is thepressure that would !e measured !y a pressure gage.


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0. If the relative humidity, phi, is 1nown from the rocess description, write it down and go onto calculating the actual partial pressure of the water vapor in the moist air, v, from thee9uation

v3 g

hen calculate the humidity ratio, omega, from the e9uation

".*##Tv3 ( - v)

*. 8nce omega is 1nown, you can calculate the moist air properties from the e9uations givena!ove.

6. If the relative humidity (phi) is not 1nown, !ut the humidity ratio (omega) is 1nown and youwant to 1now the relative humidity, you can calculate vfrom

v T 3 (N ".*##)

And then get phi from its definition,

v3 g5. If neither nor is 1nown, !ut the wet !ul! temperature w!is 1nown, then w!can !e

used, along with d!(the dry !ul! temperature, where d! ), to find omega from thee9uation given a!ove,

(cpaT(w!- d!) N gThfg) 3 (hv(d!) - hf)

Where omegagis the humidity ratio at saturation at the wet !ul! temperature, w!,

omegag ".*##Tg3 ( - g)

Dote that g, hf, and hfgare found from the aturated team emperature a!le at the et/$*/temperature (w!).

>. he relations !etween , , d!, w!, are shown graphically on the sychrometric chart. heenthalpy and volume (per unit mass of dry air) can also !e found, although not veryaccurately, from the chart, !ut the entropy is not shown at all.


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