Welcome back in today's lecture. I shall take
up the subject of air conditioning and we begin this subject with the topic called psychrometry
okay. So the specific objectives of this particular
lecture are to discuss atmospheric air and its composition, estimation of moist air properties
important psychrometric properties and their relationship psychrometric chart thermodynamic
wet bulb temperature wet bulb thermometer and its use and finally some empirical equations
for vapour pressure. So at the end of the lesson you should be
able to define atmospheric air and its composition, explain methods of estimating properties of
moist air, list important psychrometric properties and develop relationships between them be
able to find moist air properties from psychrometric equations. And psychrometric charts explain
the concept of thermodynamic wet bulb temperature and its use and explain the principle of wet
bulb thermometer. So we begin psychrometry with a small introduction
atmospheric air makes up the environment in almost every type of air conditioning system
a thorough understanding of the properties of atmospheric air and the ability to analyze
various processes involving air is fundamental to air conditioning design Psychrometry is
the study of the properties of mixtures of air and water vapour. This is very important
topic and you must understand this topic thoroughly. So first of all let us look at atmospheric
air what is atmospheric air atmospheric air as you know is a mixture of many gases plus
water vapour and a number of pollutants okay. That means you have a mixture of permanent
gases okay. Like nitrogen oxygen argon hydrogen etc, there are almost about fifteen gases,
it is said there are about fifteen gases okay. And you also have water vapour and you also
have dust particles dirt particles fuels fumes vapors etc okay. So all these are taken together
is what we call it as atmospheric air. The amount of water vapour and pollutants vary
from place to place. However concentration of water vapour and pollutants decrease with
altitude. And above ten kilometer atmospheric air consist of only dry air the pollutants
have to be filtered out before processing the air hence what we process is essentially
a mixture of various gases that constitute dry air and water vapour this mixture. That
means the mixture of various permanent gases plus water vapour is called as moist air. So as I said this entire thing is your atmospheric
air but in a typical air conditioning plant what is done is first of all we filter this
air okay. When you are filtering this air you remove the dust particles fumes etcetera
okay. So once you removed dust particles fumes etcetera you are left with a mixture of permanent
gases. And you call this portion that means the mixture of permanent gases as dry air
okay, plus water vapour okay. So this is what is actually processed or conditioned in a
air conditioning plant okay. So this mixture of dry air plus water vapour is send to an
air conditioning plant for conditioning okay. So this mixture is called as moist air. The moist air can be thought of as a mixture
of dry air and a moisture. Moisture means water vapour for all practical purposes the
composition of dry air can be considered as constant. It is observed that the composition
of dry air remains almost constant. Wherever you go, that means it does not really vary
with place to place or from altitude to altitude okay. So it remains more or less constant
okay. So in nineteen forty-nine a committee was formed to find the, or to fix the composition
of this particular dry air for calculation purposes okay.
So as I said a standard composition of dry air was fixed by the international joint committee
on Psychrometric data okay. So what is this standard composition?
This according to this committee this is the standard composition of dry air okay. So it
consists of oxygen it consist of nitrogen, it consist of argon and it consist of carbon
dioxide. Of course it also consists of many other gases. Such as hydrogen helium etc but
these gases the concentration of these gases are very small okay. So as a result it was
decided by the committee that dry air means essentially these four components okay. And
the properties of these components are as you know oxygen molecular weight is thirty-two
and it is mole fraction in dry air is found to be point two zero nine five.
And nitrogen molecular weight is twenty-eight point zero one six. And it is mole fraction
is point seven eight zero nine okay. And argon the molecular weight is thirty-nine point
nine four four. It is mole fraction in dry air is point zero zero nine three and finally
carbon dioxide molecular weight is forty-four point zero one. And it is concentration or
mole fraction is point zero zero zero three in dry air okay. So this is the mole fraction
of various gases in dry air okay. So based on this composition the molecular
weight of dry air is found to be twenty-eight point nine six six and the gas constant R
is two eighty-seven point zero three five Joule per kg Kelvin. It is important to remember
these values because we, I will be using these values in calculations okay. So molecular
weight of dry air is twenty-eight point nine six six gas constant of dry air is two eighty-seven
point zero three five Joule per kg Kelvin. While the, as I said while the composition
of dry air is constant the amount of water vapour present in the air may vary from zero
to a maximum value. That means you can have a perfectly dry air okay. That means there
is no moisture at all or you can also have a saturated air. That means air having a maximum
amount of moisture. That means it can hold at a given pressure and temperature a certain
maximum amount of moisture or water vapour okay. So this is the maximum that the air
can contain okay. So the in a general the amount of water vapour in air can vary between
zero to this maximum amount okay. When the moisture content is maximum then the air is
known as saturated air. The amount of saturated air is established by neutral equilibrium
between the moist air and the liquid or solid phases of water okay.
So when you say that air is saturated. That mean, the essentially, there is an neutral
equilibrium between the moist air containing water vapour and water liquid or solids okay.
That means equilibrium between liquid water and moist air or between ice and moist air.
For calculatin purposes we can use take the molecular weight of water as eighteen point
zero one five and the gas constant of water vapour as four sixty-one point five two Joule
per kg Kelvin. Now let us look at the estimation of properties
of moist air. As I said in most of the time in air conditioning you will be dealing with
air okay. So in most of the calculations for example if you want calculate what is the
energy required for cooling air what is the energy required for heating the air. You,
I will have to know the properties of air okay.
What is the density of air what is the specific volume? What is its specific heat? What is
its enthalpy? Right, so you we have to find out various properties of air right. Air is
not a pure fluid just, now we have seen that it is a mixture of several gases plus water
vapour okay. So by some means we must be able to find the,
or estimate the properties of moist air for further calculation and design of air conditioning
systems okay. It is difficult to estimate the exact property values of moist air. As
it is a mixture of several permanent gases and water vapour if you want a hundred percent
accurate or exact value. It is very difficult because it is a mixture of several gases and
water vapour okay. However moist air it is found that moist air up to three atmosphere
pressure obeys perfect gas laws with accuracy sufficient for engineering calculation. That
means we assume that moist air behaves like an ideal gas or a perfect gas. So that you
can apply the perfect gas laws and it is observed that this does not really give arise to a
huge error. For very high accuracy of course one has to
consider the real gas behavior of moist air by considering interaction between molecules
of various gases and water vapour this requires application of a principles of statistical
mechanics. So for most of the time we need not really bother about the real gas behavior
of various gases and water vapour okay for our engineering purposes. If you treat it
as a mixture of ideal gases that means you treat dry air as an ideal gas. And also take
up treat moist air that is water vapour also as an ideal gas and take moist air as a mixture
of ideal gases okay. This will give you reasonably good accurate values but in some cases you
may require much higher accuracy okay. In such cases you have to consider the actual
real gas behavior of various gases okay. So when you consider the real gas behavior
of various gases and all you must consider the interaction. This way between the molecules
of various gases and between the molecules of the same gas okay. Because in a real gas
the molecular interaction is very much present okay. So one must consider the interactions
and one must evaluate the properties by taking all these interactions by taking the volume
of the volume occupied by the molecules etcetera into account okay.
So this requires the application of the fundamental principles of statistical mechanics okay.
So using this method and gaf and grace have formulated tables for psychrometric properties
okay. So these tables are based on the real gas behavior of moist air okay. So that will
give you very good very accurate properties. However unfortunately the gaf and grace charts
or tables are valid for one atmosphere barometric pressure okay. So if you want the psychrometric
values at different barometric pressures then again you have to do the calculations okay.
So generally the calculations are found to be very complex okay. Because of the number
of gases involved okay. So what we I will do is and what is generally done is assumed
that it is a mixture of ideal gases and apply the ideal gas laws and evaluate the properties
that is what is done in this lecture okay. So as I said moist air is treated as a perfect
gas mixture of dry air and water vapour. What is the justification, how do you justify this
assumption that dry air behaves as an ideal gas and water vapour behaves as an ideal gas
this is justified. Because dry air may be assumed to be a perfect gas as it is temperature
is high relative to it is saturation temperature okay. The saturation temperature of dry air
is very low. So the actual temperature at which the air conditioning systems operate
are much higher compared to the saturation temperature okay. So under these circumstances
dry air behaves more or less like a an ideal gas okay, so the assumption is justified.
When it comes to water vapour water vapour may be assumed to be a perfect gas. Because
its pressure is low relative to it's saturation pressure okay. So normally in air the amount
of water vapour that that is there in air is very low. So it exits very low small partial
pressure okay. So this pressure is much lower than the saturation pressure. So we can treat
this as an ideal gas. And these assumptions result in accuracies that are sufficient for
engineering calculations. And it is shown that the errors because of these assumptions
is less than point seven percent for total pressure below three atmosphere and this is
shown by Threlkeld . Okay, so since we are treating moisture as
a mixture of perfect gases. That means moisture itself behaves as an ideal gas or a perfect
gas. So we can apply the Gibb's-Dalton law and you know that Gibbs-Dalton law for a mixture
of perfect gases is given like this. According to Gibbs Dalton law each perfect gas behaves
as though it is occupying the whole volume right. And there will not be any interaction
between the molecules of different gases right. So these are the assumptions. So since each
gas is behaving as though it is occupying the whole volume when you apply the ideal
gas equation the volume occupied by each gas is the total volume okay. And since you are
talking about the equilibrium the temperature of the all the gases have will be same okay.
Since then we get this equation. For example, let us say the gap for gas. One
ideal gas equation is this P one V is n one Ru T where Ru is universal gas constant and
one is the number of moles of P one. I mean number of moles of one and T is the absolute
temperature. Similarly for gas two P two V is n two Ru T similarly for gas three P three
V is n three R u T like that okay. And when you apply this one and the conservation of
number of molecules. That means n is n one plus n two plus n three etcetera. You finally
find that the total pressure okay Pt is nothing but the summation of the individual pressure.
That means Pt is equal to P one plus P two plus P three etcetera okay where P one P two
P three etcetera are the partial pressures exhibited by the individual gases.
So when you apply this Gibbs Dalto law to moist air in our case we have only two gases
that is dry air and water vapour okay. Both as I said are assumed to behave as perfect
gases okay. So if you apply this to moist air you find that total pressure or the barometric
pressure Pt is equal to Pa plus Pv where Pa is the partial pressure of dry air and Pv
is the partial pressure of water vapour. Now let us look at important psychrometric
properties these psychrometric properties what I will do is define the psychrometric
properties and give equations for the psychrometric properties. And these equations are derived
based on the assumptions made earlier that means the based on the perfect gas model okay.
The first and the most important property of course is the dry bulb temperature in short
form DBT and it is denoted by small t and it is as you know this is DFT is the temperature
of the moist air as measured by a standard thermometer or other temperature measuring
instruments. So I actually dry bulb temperature is nothing but the temperature okay. So we
call it as we add the term dry bulb. Because we also have another temperature called as
wet bulb temperature okay. So to distinguish between these two we call
this temperature as dry bulb temperature okay. So dry bulb temperature is nothing but the
normal temperature measured by a standard or normal temperature measuring instruments
such as the thermometer okay. Next important property is the saturated vapour pressure
P sat this is the saturated partial pressure of water vapour at the dry bulb temperature.
The saturated vapour pressures can be obtained from thermodynamic tables and charts. We have
seen the thermodynamic tables and charts. And we have used these saturated vapour pressures
of refrigerants while doing calculations. So for water also you can use similar tables
and charts and you can get the saturated vapour pressure value if you know the temperature.
So ASHRAE suggested a regression equation for saturated vapour pressure of water which
is valid for zero to hundred degree centigrade. That means I, if you have the thermodynamic
tables or charts. Then straight away you can get the values of saturated vapour pressure
of water if you know the temperature okay. If you want to computerize this and if you
want to do the calculation from the computer. Then you need these kinds of form of an equation
okay. So ASHRAE suggested very accurate regression equation for the saturated vapour pressure
of water okay this equation is like this lnPsat okay, is equal to, you can see that C one
by T plus C two plus C three T plus C four T square plus C five T cube plus C six natural
log of T. Where Psat is saturated vapour pressure in Pascals it's very important to note the
units okay. Because you must use the same units to get thesame values okay. Otherwise
it, I will give wrong results and T is the temperature and it is in degrees Kelvin okay.
So these correlation is the valid for these units.
That means pressure in Pascals temperature in Kelvin okay. Of course because you have
to use these constant values okay. So these constants values are valid for these units
okay. And the values of constants C one to C six are given here C one C two C three C
four C five and C six. So you substitute these values then P sat is a function of temperature
only. Of course you know the temperature you can calculate the saturation pressure of water
vapour. And as I said this is valid for zero degrees to hundred degrees centigrade. Next important property's relative humidity,
it is, symbol is phi. But sometimes RH is also used it is defined as the ratio of the
mole fraction of water vapour in moist air to mole fraction of water vapour in saturated
air at the same temperature and pressure okay. So it is a ratio of, first of all it is a
ratio of mole fractions of, what mole fractions of water vapour. That means actual mole fraction
of water vapour to mole fraction of water vapour in saturated air okay, at the same
temperature and pressure. Here, pressure means barometric pressure and temperature means
dry bulb temperature. Now using perfect gas equation the mole fraction ratio can be replaced
with partial pressure ratio okay. So the, you can replace mole fraction by partial pressures.
So you can write finally relative humidity as partial pressure of water vapour divided
by saturation pressure of pure water vapour at same temperature. That means Pv divided
by P sat P sat can be obtained from the equation given just now or from the thermodynamic tables
and charts. Normally the relative humidity is expressed as the percentage and if it,
if you say that phi is hundred percent. That means relative humidity is hundred percent.
That means the air is saturated because Pv is equal to P sat so the air is saturated. Next important property is called as humidity
ratio and the symbol is capital W and it is defined as the mass of water vapour associated
with each kilogram of dry air okay. So it is important to note that this is the mass
of water vapour associated with each kilogram of dry air. And we can get an expression for
this assuming both water vapour and dry air to be perfect gases the humidity ratio is
given by this expression humidity ratio W is kg of water vapour divided by kg of dry
air k. That means mass of water vapour okay, ma I mean mv divided by ma and mv and ma are
written in terms of pressures volumes and temperature using the perfect gas equation.
Because we know that pv is MRT as the as well as the perfect gas equation is concerned.
So we replace the mass is by these quantities okay. So ma mv by ma that means mass of water
vapour by mass of dry air is written as pv into V by Rv T divided by pa into V by Ra
T okay. Where pv and pa are the partial pressures of water vapour and dry air Rv and Ra are
the gas constants not universal gas constants. These are the actual gas constants and V for
the volumes and T's are the temperatures. Since temperatures are same volumes are same.
These things gets cancelled then we write pa in terms of total pressure pt and vapour
pressure of water Pv using the Dalton's law of partial pressures okay. So pa is replaced
by pt minus pv. So finally you find that W is equal to pv
by Rv divided by pt minus pv by Ra where Rv and Ra are the gas constants. And if you substitute
the values of Rv and Ra i have given the values of gas constants you finally find that humidity
ratio W is given by point six two two pv by pt minus pv. Let me repeat ones again pv is
the vapour pressure of water vapour and pt is the total pressure or the barometric pressure.
So you can see that the humidity ratio depends on the vapour pressure of water as well as
the barometric pressure okay. Next property is called as the degree of saturation
the symbol is mew this is defined as the ratio of humidity ratio W to the humidity ratio
of a saturated mixture Ws at the same temperature and pressure okay. So mew is given by W by
Ws where Ws is the saturated humidity ratio at the same derival temperature and the total
pressure and of course value of Ws can be obtained easily from barometric pressure and
saturation pressure. Next comes the property called Dew-point temperature
or DPT if let me explain this. If unsaturated moist air is cooled at constant pressure.
Then the temperature at which the moisture in the air begins to condense is known as
dew point temperature of air okay. I am sure that you know what is dew point temperature.
But let me explain this with the help of a TS diagram. This is the TS diagram of water
vapour okay. Let us say that this is your pressure okay total pressure this is the saturate
pressure at the dry bulb temperature T okay so P is P sat.
Now let us say that the water vapour exists at this point okay. That means it is in a
super heated condition right. So at this point the temperature of the water vapour is same
as the dry bulb temperature t. But it is, partial pressure is lower than the saturated
hm pressure of water vapour okay. You can see that this is the saturated pressure and
this is the actual partial pressure that means Psat is greater than Pv. Now if you cool this
water vapour isobarically so that means along the constant pressure line. So this is an
isobar okay. So if you cool the water vapour along the constant pressure line. It is pressure
reduces, I mean it is, pressure remains constant sorry, its temperature reduces. And you find
that at a particular point the water vapour begins to condense okay. So this is the point
where beginning of condensation occurs okay. And you call this temperature at which the
first drop of water forms is called as the Dew-point temperature okay. And actually if
you look at the TS diagram what is Dew-point temperature Dew-point temperature is nothing
but the saturated temperature corresponding to the partial pressure of water vapour okay.
So if you have the equation for partial pressure of water vapour. Then you can easily solve
that equation and find the dew point temperature okay. Of course when the air is saturated
then Dew-point temperature is same as diry bulb temperature. In that case your condition
is somewhere here okay. It s an approximate but very useful equation
for Dew-point temperature is given by this. DPT is Dew-point temperature that is equal
to four zero three zero into DBT plus two thirty-five divided by four zero three zero
minus DBT plus two thirty-five into natural log of phi where this phi is the relative
humidity expressed as a fraction okay. Not as a percentage and here DBT and DPT are in
degree centigrade. So using this equation you can find out the dew point temperature
if you know the dry bulb temperature and relative humidity. Next is the specific volume small v this as
you know is defined as the number of cubic meters of moist air per kilogram of dry air.
All these properties are moist air properties okay. Please keep that in mind. So when I
say specific volume that is the, that means specific volume of moist air right. So from
perfect gas equation since the volumes occupied by the individual substances are the same
the specific volume is also equal to the number of cubic meters of dry air per kilogram of
dry air okay. Since each gas behaves as though it is occupying the whole volume you can write
the specific volumes of moist air in terms of the volume and in terms of the mass of
the dry air using this equation okay. This is the specific volume using the perfect
gas equation for dry air pa into v is equal to Ra into T where pa is the partial pressure
of dry air v is the specific volume. And Ra is the gas constant and T is the derival temperature
and pa from Gibb's-Dalton law is nothing but pt minus pv okay. So v is equal to Ra T by
pt minus pv and the units are meter cube per kg dry air okay. Before we go to next properties
I just want to bring if your notice that, so far humidity ratio and specific volumes
etcetera. These are all intensive properties. They are defined on basis of one kg of dry
air okay. That means in denominator you have kg of dry air okay. So this may look a little
surprising because we are talking about the properties of moist air. So if it is a specific
or intensive property then it should have been the mass of dry air. That means kg of
moist air sorry it should have been the kg of moist air but we are writing this in terms
of kg of dry air. What is the reason behind this?
The reason is like this okay. So okay, so there is a small problem anyway. Let me explain
why we take the mass or the denominator as kg of dry air. That means why all the intensive
properties are based on the mass of dry air. This is a because of the fact that the amount
of dry air in any air-conditioning process always remains constant. Whereas the amount
of water vapour may get reduced or may increase okay. For example if you are demodifying the
moist air. Then the amount of water vapour reduces. On the other hand if you are demodifying
the air then the amount of water vapour increases. That means the mass of that moist, total mass
of the moist air may change okay. During a given process. But the mass of the dry air
always remains constant okay. For if you write all the intensive properties in terms of the
mass of dry air then the calculations become very easy okay. This is the reason why all
the intensive properties of moist air are based on the mass of dry air okay. Next important property for the calculations
is the enthalpy the enthalpy of moist air is the sum of the enthalpy of the dry air
and the enthalpy of the water vapour okay. Because moist air consist of dry air as well
as water vapour. So the total enthalpy of the moist air is because of the contributions
of the dry air part plus contribution of the moist air okay. And for enthalpies we know
that we have to define you cannot have an absolute value of enthalpy. So you have to
have a difference values so here the differences are like this for dry air. The enthalpy of
dry air is taken as zero kilo Joule per kg at zero degree centigrade. This is the difference
value for dry air whereas for water the enthalpy of saturated liquid water is taken as zero
kilo Joule per kg at zero degree centigrade. So these are the difference enthalpy values
based on which we define the enthalpy of moist air.
So the enthalpy of moist air is given by ha plus W into hg okay. So where ha this is an
intensive property. So the unit is kilo Joule per kg of dry air right so everything is in
terms of kg of dry air. So ha is nothing but the contribution of the dry air part and it
is nothing but the enthalpy of the dry air okay. And W into hg is the contribution of
the water vapour in this hg is the enthalpy of the water vapour and W is the humidity
ratio okay. So the first term takes care of the contribution of the dry air and the second
term takes care of the contribution of water vapour okay.
And if you assume or if you use an average value of specific heat cp and if you take
these reference values and then you can write ha plus W hg in terms of specific heats and
temperatures like this. That means finally enthalpy of moist air is written as Cp into
t where Cp is the specific heat of the dry air specific heat at constant pressure of
the dry air t is the dry bulb temperature. W is the humidity ratio h fg is the latent
heat of vaporization of water Cpw is the specific heat of water vapour at constant pressure.
And t is the dry bulb temperature okay. And h fg is actually the latent heat of vaporization
at zero degree centigrade. Because the difference is the zero degree centigrade. So you can
take an approximate value of two thousand five hundred and one kilo Joule per kg okay.
So remember that when you are writing this enthalpy in terms of in terms of specific
heat that when you are writing the delta h as Cp into delta t. That means we are using
a average value of specific heat okay. So substituting approximate values of Cp Cpw
and h fg we obtain this expression h is one point zero zero five t plus W into two thousand
five hundred and one plus one point eight eight t okay. This is obtained by taking specific
heat value of one point zero zero five kilo Joule per kg Kelvin for dry air okay. So this
is the Cp of dry air and this is the latent heat of vaporization at zero degree centigrade
and this is the Cp of water vapour okay. So if you remember these things or these simple
equation. Then it is very easy to calculate the various properties okay.
For example enthalpy it is all if you know other properties right. Next property is the
humid specific heat that is nothing but the specific heat of the moist air the symbol
is C subscript pm from the equation of for enthalpy of moist air the humid specific heat
of moist air can be written as Cpm is Cp plus W into C pw. Where Cp is the specific heat
of the dry air W is the humidity ratio and Cpw is the specific heat of the water vapour
at constant pressure. And of course the units of Cpm are in kilo Joule per kg dry air per
Kelvin okay. And for all practical purposes you can take you can use the mean value of
humidity ratio and you can take the value of Cpm as one point zero two one six kilo
Joule per kg dry air Kelvin okay. Next let us look at psychrometric chart what
is a psychrometric chart. So far we have seen the psychrometric equation then let us look
at the psychrometric chart. A psychrometric chart graphically represents the thermodynamic
properties of moist air it is nothing but a graphical representation of moist air. Standard
psychrometric charts are bounded by the dry bulb temperature line and the abscissa. And
the vapour pressure or humidity ratio as an ordinate and the left hand side of the psychrometric
chart is bounded by the saturation line okay. Let me show the psychrometric chart now. Okay,
so this is the skeleton of a psychrometric chart.
As I said you have the dry bulb temperature DBT on the X-axis and here you have the humidity
ratio W on the Y axis. Of course you can also have in place of W you can also have vapour
pressure of water okay. Because these are related okay. And very important thing is
that the in order to find the way we will come to that in order to fix the status moisture.
We need to know three independent properties okay. So that means the degree of freedom
are three. Because we are talking about a binary mixture okay. But the psychrometric
chart is a two dimensional representation of the properties. So how is it possible this
is made possible by giving the psychrometric charts for standard barometric pressures okay.
That is how a three dimensional figure has been reduced to a two dimensional chart okay.
That means any psychrometric chart is valid for that particular barometric pressure. And
if you look at any psychrometric chart they always mentioned the barometric pressure at
which the chart has been obtained okay. So we always say the P values for example
if it is standard atmosphere they said P is zero hundred one point three two five kilo
Pascal okay. That means it is one atmospheric pressure like that psychrometric charts are
of course available for different barometric pressures okay. So you must whenever you are
using psychrometric chart you have to be careful and first of all you have to see for what
barometric pressure that particular chart is valid okay. So you cannot use the same
chart at all altitudes okay. Now coming back to psychrometric chart the psychrometric chart
as I said is a graphical representation of psychrometric properties. And using the psychrometric
chart you can find the properties of all psychrometric properties okay. And this as I said is a saturation
curve in the left hand side . Saturation curve means relative humidity is
hundred percent and on the same chart you find constant relative humidity lines. These
are the constant relative humidity lines okay. For example this could be the seventy-five
percent relative humidity line this could be for the fifty percent relative humidity
line this could be twenty five percent relative humidity line like that okay. So that is those
are the constant relative humidity lines. Of course since the dry bulb temperature is
the X axis and humidity ratio is the Y axis obviously these lines are the constant dry
bulb temperature lines okay. There not exactly vertical but for all practical purposes. They
are almost vertical okay. So the vertical lines are dry bulb temperature all the horizontal
lines these lines are the constant humidity ratio lines okay. And as I said these curve
lines are here the relative humidity lines and these dash lines okay.
These are the specific volume lines okay. All these dash lines are specific volume lines
and finally you have these thick inclined lines okay. All these thick inclined lines
are constant enthalpy lines okay. So you can see that all the required properties are specified
on the psychrometric chart okay. So if you know any two properties any two psychrometric
properties you can find the rest of the properties. For example if you know the dry bulb temperature
and relative humidity. Let us say this is your dry bulb temperature. This is your dry
bulb temperature. Let us say and this is your relative humidity okay. That means this is
the straight of the air this point then you can find out their humidity ratio like this
you can find out the specific volume like this you can find out the enthalpy value by
reading this line like that okay. So remember again that this is for a given
pressure okay. So you if you need to know the properties you need to know the barometric
pressure plus any other two properties okay. So once you have these three properties you
can find the rest of the properties using the psychrometric chart okay. This actually
shows this picture is not very clear but this is the psychrometric chart given by ASHRAE
and ASHRAE's provided psychrometric chart which can be used for different elevations
and this particular chart is valid for one atmospheric pressure okay, barometric pressure.
They have also given similar charts for different elevations. For example for fifteen hundred
meter elevation for thousand meter elevation like that. That means for different charts
for different elevations and different conditions and again. As I said you have the dry bulb
temperature here and you have the saturation humidity ratio as the ordinate and all these
curved lines okay, are your relative humidity lines and these slant lines are specific volume
lines and enthalpy lines okay. So using the psychrometric relations one can construct
a psychrometric charts this is the usefulness of having a psychometrical relations. You
can construct your own psychrometric chart using the simple relations okay.
This is very easy all that you have to do is, you have to take the dry bulb temperature
in the x axis and take the humidity ratio on the y axis and you have to have the steam
table or the steam charts or the regression equation for the saturation pressure of water
vapour. So if you have these three then using the psychrometric relation you can construct
the psychrometric chart. The advantage of constructing your own psychrometric chart
is you can construct the psychrometric chart for any barometric pressure okay. There is
no limitation but of course remember that all these relations are based on the assumptions
of ideal gas okay. Psychrometric charts are extremely useful in the analysis of air conditioning
systems we will be using these charts again and again for showing the psychrometric processer
for estimating psychrometric properties etcetera. Now measurement of psychrometric properties
based on Gibb's phase rule thermodynamic state for moist air is uniquely fixed if the barometric
pressure and two other independent properties are known as I have already mentioned. If
you apply the Gibb's phase rule that is number of p plus V C plus two where p is the number
of phases present and V is the degree of freedom and C is the number of components. You find
that the degrees of freedom or number of independent components to be specified are three for moist
air okay, when you treat it as a mixture of two components right. So minimum number of
three parameters have to be three independent parameters have to be specified to fix the
state of the moist air okay. So what are those three parameters unless you fix these three
unless you specify these three you cannot find the properties of moist air okay.
Normally barometric pressure is specified because we know the barometric pressure. So
at a given barometric pressure the state of moist air can be determined by measuring any
two independent properties okay. So given the barometric pressure we need still two
more properties. One of them could be the dry bulb temperature as the measurement of
temperature is fairly simple and accurate okay. So if the, if you need three independent
properties one of them is barometric pressure because it is known to us okay. So if we need
to fix it other one could be dry bulb temperature right what is the third property okay. What
is the third property which can be specified and which can be measured easily so that you
can fix the state of air okay. Third property could be theoretically third
property could be anything for example the third property could be relative humidity
third property could be humidity ratio. It could be for example enthalpy of course enthalpy
cannot be measured. So there is no point in taking that as an independent variable but
theorotically speaking it can be any intensive property right. But there are some problems
it solve the independent in the intensive properties. For example if you want to specify
humidity ratio as an independent propertyit's not very convenient. Because accurate measurement
of humidity ratio is very difficult in practice. Since measurement of temperature is easier
it would be convenient if the other independent parameter is also a temperature. So one of
the independent parameter is this dry bulb temperature if the other independent parameter
is also a temperature then it will be very convenient to us. Because it can be measured
very easily right. So temperature measurement are easier right but could it be the dew point
temperature. Accurate measurements of dew point temperature is difficult. So even though
dew point temperature is also a temperature spaces taking that as an independent parameter
is difficult in practice because measurement of dew point temperature is very difficult
okay, just like humidity ratio okay. Hence a new independent temperature parameter
the wet bulb temperature is conceptualized okay.Because of this difficulty that means
because of the difficulty of measuring other properties such as the humidity ratio or relative
humidity or dew point temperature people have come out with a new concept of wet bulb temperature
okay. So this concept is very useful because we shall see that measurement of wet bulb
temperature is relatively easy compared to dew point temperature okay. So compared to
as I said compared to dew point temperature it is easier to measure the wet bulb temperature
of moist air. To understand the concept of wet bulb temperature
it is essential to understand the process of combined heat and mass transfer. So we
have to have combined heat and mass transfer when we discuss combined heat and mass transfer
with reference to a mixture of air and water vapour. Then we have to talk about a law called
as straight line law what is a straight line law. Straight line law states that when air
is transferring heat and mass. Here mass means water vapour to or from a wetted surface the
condition of air shown on a psychrometric chart drives towards the saturation line at
the temperature of the wetted surface okay. So this is the straight line law let me explain
this. Let us say that we have moist air okay. For the time being let us assume that this
is unsaturated okay. That means its relative humidity is less than hundred percent and
let us say that we have a moist surface okay. So this is the wet surface that means on this
surface we have a layer of water let us say okay. And for argument saying let us assume
that this water is at different temperature compared to this air or for the time being
let us say that this water temperature is tw. tw is less than the air temperature t
one okay. And on the psychrometric chart let us say this is the condition of the air at
this point at point one. It is at some tribal temperature t one okay. And at some humidity
ratio W one so air at this condition is coming in contact with a wet surface at which is
at temperature tw. When you have a wet surface at a temperature
tw a concentration boundary layer develops near the wet surface. And air in the mediate
vicinity of the wet surface will be saturated. That means in the immediate vicinity of this
wet layer you have a saturated water vapour layer and since this temperature is also same
as tw the condition of that layer will be represented by this point okay. So this is
the condition of the saturated water vapour next to the wet layer okay.
So air is coming in contact with this. Now you can see that there is a temperature difference
between this saturated air and this air okay. That at this temperature difference is there
similarly there is a vapour pressure difference or humidity ratio difference okay. Humidity
ratio difference means vapour pressure difference is also there okay. Since the vapour pressure
and temperature of this air are greater than the water vapour. Saturated water vapour heat
transfer will take place sensible heat transfer will take place from air to the water. And
latent heat transfer will also take place from air to the water. That means this warm
air when it comes in contact to the cold wetted surface it gets cool and dehumidifies okay.
So what you are getting outside that means what you get at point two is a cold and dehumidified
air. Now the question is what will be the condition of this air okay. How do you determine
this condition of this air or where does this point lie okay. This is where the straight
line law is useful okay. The straight line law says that the condition of this point
okay, lies on a straight line joining these two points okay. That means joining the points
of the saturated water vapour condition and the inlet air condition okay. The straight
line joins these two points is this and that means this exit condition must lie on this
straight line okay. For example on this point so this is what is known as straight line
law. So straight line law is applicable to air water mixture as for these mixtures the
lewis number is close to one. Now let us look at another concept that is
thermodynamic wet bulb temperature and the process of adiabatic saturation. Adiabatic
saturation temperature is defined as that temperature at which water by evaporating
into air can bring the air to saturation at the same temperature adiabatically okay. An
adiabatic saturator is a device using which one can measure theoretically the adiabatic
saturation temperature of air okay, let may describe this okay. So this is an adiabatic
schematic of a adiabatic saturator. So what we have is an infinitely long infinitely long
duct let us say okay. And this duct is perfectly insulated right and it consist of water okay.
Now moist air at this condition dry bulb temperature t one humidity ratio W one and total pressure
p flows through this insulated infinitely long duct okay. And as it flows through this
it comes in contact with this water okay. So as a result you have sensible as well as
latent heat transfers takes place, sensible heat transfer plus latent heat transfer takes
place okay. And if the, if you are measuring let us say using this thermometer. We are
measuring the temperature of this water and if this duct is infinitely long and if the
system reaches the steady state you find that at steady state for an infinitely long duct
the exit temperature of the moist air will be same as the temperature indicated by this
thermometer. That means the exit temperature of water moist
air will be same as the steady state temperature of the water okay. Both will indicate the
same temperature of course during this process water vapour evaporates to take care of that
we have to continuously supply some make up water okay. So this kind of a device is called
as an adiabatic saturator at steady-state condition the temperature indicated by the
thermometer immersed in this sump is the thermodynamic wet bulb temperature okay. That means thermodynamic
wet bulb temperature is nothing but the temperature indicated by thermometer which measures the
water kept in the sump of this infinitely long duct okay. Now certain combinations of air conditions
will result in a given sump temperature okay. From energy balance for adiabatic saturator
based on one kg per second of dry air flow rate we can derive this energy balance equation
okay. So if you take this as a control volume take this as a control volume and apply energy
balance equation you find that energy coming in is energy going out and energy coming in
everything is on based of one kg of dry air. So energy coming in is nothing but h one plus
this energy this is nothing but W two minus W one into h f where W two minus W one is
nothing but the amount of water evaporated in the adiabatic saturator. And h f is the
saturated liquid water enthalpy at this temperature t two okay.
So this is the energy entering and what is the energy leaving energy leaving is nothing
but h two okay. So assuming the moist air specific heat Cpm to be constant energy balance
equation can be written in this form okay. So we can write the energy balance equation
like this where t two is the exit or thermodynamic wet bulb temperature t one is the inlet dry
bulb temperature h fg two is the latent heat of vaporization at temperature t two Cpm is
the moist specific heat W two and W one are the exit and inlet humidity ratios. Since the outlet condition is saturated thus
the exit properties W two h fg two are functions of temperature t two only okay. Because the
outlet condition is saturated of course this is at a given barometric pressure. Hence from
the energy balance t two is equal to t one minus h fg two by Cpm into W two minus W one
okay. So what I am saying here is W two this is the function of temperature only. And this
is also a function of temperature t two only okay. So from this implies that t two, that
means the exit temperature is the function of t one and W one only right. Because you
have temperature t two on this side apart from t two you have only t one and W one.
That means t two is a function of t one and W one t one and W one are the properties of
the inlet state. So finally what we are saying is the temperature measured by the thermometer
is nothing but the function of inlet state okay.
In other words the thermodynamic wet bulb temperature t two is the property of moist
air thus measuring dry bulb temperature wet bulb temperature and barometric pressure one
can fix the state of air and find all the required properties of moist air okay. So
what we are saying finally is that if you can have an adiabatic saturator and if you
can measure the temperature of the water in the adiabatic saturator at steady state then
you have another property of moist air okay. So one property is dry bulb temperature and
the other property is thermodynamic wet bulb temperature okay. So from these two temperature
values and the barometric pressure you can find out the rest of the psychrometric properties
okay. Now t two is a function of t one and W one
this is not a unique function. Because in the sense that there can be several combinations
of t one and W one which can result in the same sump temperature in the adiabatic saturator
okay. That means several inlet conditions can result in this same sump temperature.
That means they can they all have same thermodynamic wet bulb temperature. Thus all inlet conditions
that result in the same sump temperature have the same wet bulb temperature. A line passing
through all these points is a constant wet bulb temperature line because all these points
have a same wet bulb temperature line. Obviously line passing through all these points
is a constant wet bulb temperature line the line one-two is a straight line as per the
straight line law and represents the path of the air as it passes through the adiabatic
saturator okay. That means let us say that this is our inlet condition to the adiabatic
saturator and the outlet condition is the saturated air. So it is lies on the saturated
line okay. And the process follows the straight line joining one to two according to the straight
line law. That means the line joining one to two is
a constant wet bulb temperature line okay, where as this line what is shown here is a
constant enthalpy line. So that there is a difference between constant enthalpy line
and constant wet bulb line and what is the difference from energy balance you can show
that the difference is nothing but W two minus W one into h f. The thermodynamic wet bulb temperature will
be less than the entering air dry bulb temperature. But greater than the dew point temperature
obviously dry bulb temperature wet bulb temperature and dew point temperature will be same when
the air is saturated. Normally lines of constant wet bulb temperature are shown on the psychrometric
chart. So psychrometric chart also has lines of constant wet bulb temperature the difference
between actual enthalpy. And the enthalpy obtained by following constant wet bulb temperature
is equal to W two minus W one into hf this is from the energy balance for the adiabatic
saturator okay. Now let us quickly look at what is known as
the wet bulb thermometer in practice. It is not convenient to measure the wet bulb temperature
using an adiabatic saturator instead a thermometer with a wetted wick is used to measure the
wet bulb temperature okay. We cannot find the in practice you cannot have a infinitely
long and perfectly insulated duct and wait for its steady state and measure its temperature
okay. It s not convenient it is not practically feasible okay. So in practice what we use
is what is known as the wet bulb thermometer okay what is a wet bulb thermometer? A wet
bulb thermometer is nothing but an ordinary thermometer. But it is bulb sensing bulb is
covered with a wet wick okay. So this is covered with wet wick that means you have a moist
wick okay. And air flows over this one right and the temperature measured by this is your,
we call it as wet bulb temperature or WBT okay.
And if you are applying the straight line law you find that if this is the inlet condition
to the wet bulb wet bulb thermometer and if this is the of the moist air on the bulb okay.
Then you find that outlet the condition lies on this here okay. And it is called the Lewis
number. So when lewi number becomes one then the temperature measured by the wet bulb thermometer
is same as the thermodynamic wet bulb temperature okay. So this is the principle. Of course it should be noted that unlike thermodynamic
wet bulb temperature the wet bulb temperature of wet bulb thermometer is not a thermodynamic
property. As it depends upon the rate of heat and mass transfer between the wick and air.
So precautions have to be taken while measuring WBT using wet bulb thermometer. For example
when you are using the wet bulb thermometer you should make sure that the wick is always
clean and wet air around the bulb should not be stagnant water used should have a temperature
closer to wet bulb temperature or sufficient time must be allowed for steady state. And
radiation shields must be required to reduce errors due to radiation etcetera. Okay, so for air water mixtures we assume
that the temperature measured by wet bulb thermometer is equal to the thermodynamic
wet bulb temperature. But this may not be valid for other gas vapour mixtures okay.
There can be appreciable differences when you are talking about other gas vapour mixture
and an instrument used for measuring the psychrometric state of air is called as a psychrometer okay.
There are different types of psychrometer. So at this point I stop this lecture okay.
Thank you.
