Download Chp-1. Pure substances

Pure Substances
Engineering systems have an inherent requirement of some substance to act as working fluid i.e.
transport agent for energy and mass interactions. Number of working fluids are available and are
being used in different systems suiting to the system requirements. Steam is also one of such
working fluids used exhaustively because of its favorable properties. In thermal power plants
steam is being extensively used. Water has capacity to retain its chemical composition in all other
phases i.e. steam and ice, and also it is almost freely available as gift of nature. Pure substance
refers to the substance with chemical homogenecity and constant chemical composition. Water is
a pure substance it meets both the above requirements. Any substance, if it undergoes a chemical
reaction, cannot be pure substance.
Matter:
Anything which has mass & occupies space is called matter.
Ex: Book, pencil, water, air living beings.
Matter can exist in three physical states, viz. solid, liquid & gas.
In solids, particles are very close to each other in an orderly fashion & there is not much freedom
of movement, i.e. solids have definite volume & shape.
In liquids, particles are close to each other & they can move around, i.e. liquids have definite
volume but not the definite shape. They take the shape of the container in which they are placed.
In gases, particles are far apart as compared to those present in solid or liquid states & their
movement is easy & fast, i.e., gases have neither definite volume nor definite shape. They
completely occupy the container in which they are placed.
These three states of matter are interconvertible by changing the conditions of temperature &
pressures.
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Terminology of Thermodynamics:
System: Any specified portion of matter under study which is separated from the rest of the
universe with a bounding surface.
A system may consist of one or more subs.
Surroundings: The rest of the universe which might be in a portion to exchange energy & matter
with the system is called the surroundings.
Isolated system: A system which can exchange neither energy nor matter with its surroundings is
called as isolated system.
Closed system: A system which can exchange energy not matter with its surroundings is called as
closed system.
Open system: A system which can exchange matter as well as energy with its surroundings is
called as an open system.
State of a system: is fixed by its important state variables- pressure, temperature, volume,
composition & mass.
Extensive property: It is a property of a system which depends upon the amounts of
substance/substances present in the system.
Ex: Mass, volume, energy, enthalpy, entropy.
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Intensive property: It is the property of a system which is independent of the amount of
substance/substances present in the system.
Ex: temperature, pressure, concentration (composition), density, viscosity, refractive index,
surface tension & specific heat.
Extensive property of a pure or single substance will depend upon the number of moles (n) of the
substance present & also on any two of the three variables- P,V & T (called independent
variables). If ‘n’ is kept constant, the extensive property of a system will depend only on the two
independent variables- P & T.
Isothermal process: if the temperature of the system remains constant during each stage of the
process.
Isobaric process: if the pressure if the system remains constant during each stage of the process.
Adiabatic process: If neither heat enter nor leaves the system during any stage of the process.
Internal Energy,’U’: Every substance/system is associated with a definite amount of energy which
depends upon its chemical nature, temperature, pressure & volume; & is called as internal
energy,’U’.
Enthalpy: It represents the total energy stored in the system, & is given by;
H=U+ PV
Heat capacity, ‘C’: It is defined as the quantity of heat required to raise the temperature of the
system from the lower to the higher temperature, divided by temperature difference.
If the mass of the system is 1gm, the heat capacity is called specific heat of the system; if
however, is 1 mole, the heat capacity is termed as molar heat capacity & is denoted by ‘C’.
i.e., C= dq/dT; Cv= (ƋU/ƋT)V; CP=(ƋH/ƋT)P
Thus, molar heat capacity of a system of mass 1mole at constant volume is defined as the
increase in internal energy of the system per degree rise in temperature; & that at constant
pressure is defined as the increase in enthalpy of the system per degree rise in temperature.
CP-CV= R, viz, 1.987 cal or 8.314 J
Entropy: It is defined as the amount of heat exchanged, q, at a temperature T, from initial to final
states of the system, independent of the path followed.
i.e., dS=dq/dT
Physical significance of entropy:
As measure of the disorder of the system
As a measure of probability.
Properties of Pure substances:
Pure substances have fixed composition.
Ex: Cu, Ag,
Au, H2O, glucose; in water & glucose, the constituents have fixed composition.
Pure substances cannot be separated by simple physical methods.
An element consists of only one type of particles which may be atoms or molecules. Ex: H2, O2
etc.
When two or more elements/molecules of different elements combine, a compound is formed.
Ex: H2O, NH3, CO2 etc.
A pure substance which is homogeneous retains its chemical composition when it undergoes a
change of phase during a thermodynamic process.
Water is the classic example of the pure substance, which can exist in three different phases
viz. in the solid phase, as ice; in the liquid phase as water; & in the gaseous phase as steam- having
the same chemical composition, H2O.
When ice melts, it transforms from the solid phase to the liquid phase to form water. Similarly,
when water is heated beyond the boiling point, it starts evaporating & transforms form the liquid
phase to the gaseous phase to form steam, which may be defined as the vapor of water.
This transformation is known as vaporization, it remains as two phase mixture of water & steam.
After the vaporization is complete, it exists purely in the gaseous phase, as steam.
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Two property rule:
In the absence of effects of gravity, motion, capillarity, magnetism, the thermodynamic
state of a pure substance can be completely specified by two independent (intensive) properties
of the substance.This is called the two property rule for a pure substance & such a pure substance
is referred to as a “Simple compressible substance”.
Two property rule states that, “The state of a simple compressible system is fixed
completely by the values of any two of its intensive properties, provided these two properties are
independent of each other.”
If the values for two properties of a pure substance are fixed, then the values for all other
properties are fixed, i.e. there is a definite relation between the two independent properties &
each other properties.
Each of these relations is called equation of state for a pure substance.
The equation of state for a pure substance can be in any of the forms:
Algebraic equation (Equation for a perfect gas: PV=mRT, for an ideal gas)
Tables (Steam tables)
Charts (Mollier chart for steams, p-h diagram for refrigerants)
Different thermodynamics states of simple compressible substances can be represented by: TH diagram, P-T diagram, T-V diagram, P-V diagram, T-S diagram & H-S diagram in the
thermodynamic analysis of systems.
T-H diagram:
The formation of steam can readily be followed by T-H diagram, at a given constant pressure.
Consider, a 1kg of ice below 00C, i.e., say -70C, at constant pressure of 1 atm is represented by
point ‘A’ in the diagram.
A-B: solid state; B-C: Melting; C-D: Liquid state; D-E: Vaporization; E-F: Vapor state
When the ice at point A is heated at constant pressure, its temperature will rise till it starts
to melt, i.e., at point B.
Further addition of heat will not increase the temperature but, converts ice into water, along BC.
Along line BC, there exists a mixed phase of ice & water; the temperature of mixed phase
remains constant at 00C; & there is normal decrease in volume. The transformation of phase from
solid to liquid is called the melting or fusion of ice.
‘The quantity of heat required for complete transformation of ice into water at constant
temperature of 00C is called latent heat of fusion.’
At normal atmospheric pressure of 1.01325 bar (1 atm), it equals to 335 KJ/kg.
At point C, entire ice melts, resulting in only one phase, i.e., liquid-water at 00C. Rise in
temperature of water occurs with supply of heat & that continues till boiling point is reached at
point D. The boiling point depends upon the pressure at which heat is being supplied.
The boiling temperature is called ‘Saturation temperature’, Ts, & at normal atmospheric
pressure, its value is 1000C.
The pressure corresponding to saturation temperature is called saturation pressure.
Thus, at Psat = 1.01325 bar, Tsat = 1000C.
There is a decrease in volume when temperature rises from 0 0C to 40C & thereafter the
volume increases up to the commencement of boiling temperature at point D.
“The heat required for change from liquid state to vaporization/boiling point is called sensible
heat, hf.”
The sensible heat is also called as the heat of liquid or the enthalpy of liquid. When more
heat is added, evaporation of water starts, with change of phase, along DE.
Along line DE, there exists two phase mixture of water & its vapor; the temperature remains
constant till all the water gets converted into vapor; the process of vaporization is both isobaric &
isothermal; & there is considerable increase in volume.
At point E, all the water has vaporized & the state of steam at this point is called dry &
saturated steam.
The phase transformation from liquid to vapor is called vaporization.
“The quantity of heat required for complete transformation of water to its vapor at constant
temperature is called latent heat of evaporation or enthalpy of vaporization & is denoted by hfg.”
For water evaporating at 1000C under standard atmospheric condition of 1.01325 bar (1 atm), it
equals to 2256.9 KJ/kg.
On heating the steam further, at the same constant pressure, increases its temperature
above the saturation temperature, Ts. The temperature of the steam above the saturation
temperature at a given constant pressure is called super heated temperature.
During this process of heating, the dry steam will be heated from its dry state & this
process of heating is called super heating, which takes place along EF. The steam when
superheated is called superheated steam.
The amount of heat required to increase the temperature of dry steam from its saturation
temperature to any desired higher temperature, at a given constant pressure, is called the amount
of superheat or the enthalpy of superheat.
The difference between the superheated temperature & the saturation temperature is defined as
‘degree of super heat’.
The distance between saturated liquid line & the dry saturated vapor line goes on
decreasing with increase of pressure & saturation temperature. The point at which this distance
becomes zero is called the critical point, CP.
Critical point represents the highest temperature & pressure above which a liquid cannot
exist. At the critical point the liquid is directly & fully converted into dry vapor without going into
the phase of evaporation, & as such, latent heat is zero; the liquid & vapor are indistinguishable; &
the properties of saturated liquid & saturated vapor are identical.
The temperature & pressure at the critical point are called critical temperature (tc) critical pressure
(Pc).
For water, the critical values are;
tc= 374.140C; Pc= 220.9 bar & critical volume, Vc=0.003155 m3 kg-1.
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Superheated steam:
Once the steam attains dry & saturated state, its temperature & volume starts increasing with
further supply of heat. The steam so obtained called as super heated steam & it behaves like a
perfect gas.
Advantages of superheated steam in steam-power plants:
Increases the working capacity without increase of pressure.
Greater heat content of superheated steam leads to less steam consumption for a given output &
that results in saving in the cost of fuel.
Moisture content of steam leaving the steam turbine/engine can be kept within safe limits.
Accordingly, the heat losses due to condensation of steam are avoided to a large extent.
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Superheating is done by utilizing the heat of waste furnace gases which otherwise passes uselessly
to the atmosphere.
Steam generation process, as derived above, has been under standard atmospheric pressure. At
different pressures below critical pressure the nature of the various processes will be identical but
the saturation temperature will have different values. In actual practice, the steam is generated at
pressure varying from 10-200 bar.
Recently, methods have been developed to produce steam at pressures much above the critical
pressure of 220.9 bar. The steam so produced at p> pc is called super pressure steam, and its
formation takes place without boiling or bubbling of water.
Different states of steam:
The steam as it is being generated can exist in three different states, viz. wet steam or dry
saturated steam or super heated steam.
Wet steam: When the water is heated beyond the saturation state at constant pressure, it starts
evaporating. The steam evolving from the surface of the water entrains finely divided water
molecule in it.
This entrained water molecule suspended in the steam will be at the saturation
temperature & will not yet have been absorbed the latent heat & evaporated into steam. Both
entrained water molecules & steam coexist to form two phase mixture, called wet-steam, which
will be in thermal equations, because both of them will be at the same saturation temperature.
Thus, a wet-steam is defined as a two phase mixture of entrained water molecules & steam
in thermal equation at the saturation temperature, corresponding to a given constant pressure.
Dryness fraction of steam:
A wet steam can be of different qualities, i.e., having different proportions of water
molecules & dry steam. Therefore, it is necessary to state the quality of wet steam.
The quality of wet steam is specified by the dryness fraction, which indicates the amount
of dry steam present in the given quality of wet steam & is denoted by ‘x’.
The dryness fraction of a steam is defined as, the ratio of mass of the actual dry steam present in a
known quality of wet steam to the total mass of the wet steam.
i.e., x= mg/m = mg/ mf + mg
Where m=mass of wet steam; mg = mass of dry steam present in a known quantity of wet
steam; & mf = mass of suspended water molecules in the sample quality of wet steam. The
dryness fraction of the wet steam will always be less than 1.
Dry Saturated Steam:
Steam which is in contact with water from which it has been formed will be in thermal equation
with the water is said to be a dry saturated steam.
(Thermal equation: the heat passing from steam into the water is balanced by the equal quantity
of heat passing from the water into the steam.)
A saturated steam at the saturation temperature corresponding to a given constant pressure &
having no water molecules entrained in it is defined as dry saturated steam or simply dry steam.
Since the dry saturated steam doesn’t contain any water molecule in it, its dry fraction will be
unity.
Superheated steam: when a dry saturated steam is heated further at a given constant pressure its
temperature raises beyond its saturation temperature. The steam in this state is said to be
superheated.
A superheated steam is defined as the steam which is heated beyond its dry saturated
state to temperatures higher than its saturated temperature at a given constant pressure.
Definitions of various terms involved in the formation of steam:
Enthalpy of steam: Enthalpy is defined as the sum of the internal energy & the product of
pressure & volume & is denoted by ‘h’.
i.e.
h= u+ pv
from the first law of thermodynamics, dQ= du+P.dv
= du+ d(Pv)-vdp
(because, d(Pv)= vdP + Pdv)
= d(u+Pv)-vdP
For a process at constant pressure, dP=0
Therefore,
dQ = d(u+Pv) = dh
i.e. dQ=dh
Therefore, for a given constant pressure of steam generation process, the amount of heat
supplied to the water to convert into steam is equal to change in enthalpy.
Enthalpy of Dry saturated steam: It is defined as, “the total amount of heat supplied at a given
constant pressure to convert 1kg of water into 1kg of dry saturated steam at its saturation
temperature.
It is denoted by ‘hg’ & will be equal to sum of the sensible heat, hf & latent heat of evaporation,
hfg.
i.e. hg = hf+ hfg KJ/kg
Enthalpy of wet steam: since a wet steam contains water molecules entrained in it, it will have
absorbed only a fraction of the latent heat of evaporation proportional to the mass of the dry
steam contained in the wet steam.
Thus, it is defined as, “the total amount of heat supplied at a given constant pressure to convert
1kg of water to 1kg of wet steam at the specified dryness fraction.”
It is denoted by, ‘hwet’ & will be equal to sum of sensible heat & the product of dryness fraction
with latent heat of evaporation.
i.e. hwet = hf + x. hfg KJ/kg
Enthalpy of superheated steam: To superheat the steam, the heat is supplied at a given constant
pressure to the dry saturated steam to increase its temperature beyond its saturation
temperature.
Hence, it is defined as, “the total amount of heat supplied at a given constant pressure to convert
1kg of water at 00C into 1kg of superheated steam at the saturated superheated temperature.”
It is denoted by, ‘hsup’ & will be equal to sum of the enthalpy of dry saturated steam & the amount
of superheat.
i.e. hsup = hg + Cps (Tsup + Ts) KJ/kg
Where Cps – specific heat of superheated steam;
Tsup – superheated temperature; Ts – saturated temperature;
Cps(Tsup -Ts) gives the amount of superheat
Or hsup = (hf + hfg) + Cps(Tsup -Ts) KJ/kg
Specific volume:
It is the volume occupied by the unit mass of a substance & is expressed in m 3kg-1.
Specific volume of saturated water: It is the volume occupied by 1 kg of water at the saturation
temperature at a given constant pressure & is denoted by, vf.
Specific volume of dry saturated steam: When the steam is wet, its specific volume will be equal
to the sum of the volume occupied by the dried-up portion of the steam in 1 kg of wet-steam &
the volume occupied by the entrained water molecules in the same 1kg of wet steam.
If ‘x’ is the dryness fraction of the steam, & then, mass of the water molecules = (1-x) kg.
Let ‘v’ be the specific volume of the wet steam,
V= xvg + (1-x) vf m3kg-1
Or v= xvg m3kg-1
Since x<<1 & therefore, 1-x ≈ 1; & (1-x) vf is very low & can be neglected.
Specific volume of superheated steam:
It is the volume occupied by 1 kg of superheated steam at a given constant pressure & at
superheated temperature, & is denoted by, ‘vsup’.
The superheated steam behaves like a perfect gas, & therefore its specific volume is determined
approximately using Charl’s law.
At a given constant pressure, if vg= specific volume of dry saturated steam, Ts= saturated
temperature, Tsup= superheated temperature; & vsup= specific volume of super heated steam,
then,
vsup/ vg = Tsup/ Ts
or vsup=
Tsup. vg/ Ts m3kg-1
Internal energy of steam:
Since the latent heat of evaporation comprises of internal latent heat & external work of
evaporation, the enthalpy or the total heat energy of a dry saturated steam at a given constant
pressure will be equal to the sum of sensible heat, internal latent heat & external work of
evaporation.
But, the heat energy of external work of evaporation is not present in steam & comprises of only
the sensible heat & internal latent heat. This actual energy stored in the system is called internal
energy of the steam,
It is defined as, ‘the difference between the enthalpy of the steam & the external work of
evaporation, & is denoted by ‘u’.
It is obtained by substracting the external work of evaporation from the enthalpy.
(CRW)
Steam table:
The properties of steam which are likely to be used are: pressure saturation temperature, specific
volume, enthalpy etc.
These properties have been determined experimentally at various pressures & are tabulated in a
table known as steam table.
The tabulations in the steam tables may be on pressure basis as shown in Table 1 or on saturation
temperature basis as shown in Table 2.
P-T Diagram:
Consider P-T diagram for pure substances which expand on freezing & contract on heating as
illustrated in the following figure.
[Graph (CRW)]
This diagram is often called the phase diagram, since all the three phases are separated from each
other by three lines.
The sublimation line separates the solid & vaporization; the vaporization line separates the liquid
& vapor region; & the melting (or fusion) line separates the solid & liquid region.
These three lines meet at the triple point, TP, where all the three phases coexist in equilibrium.
The vaporization line ends at the critical point, CP, because no distinction can be made between
liquid & vapor phases above the critical point.
Substances that expand or contract on freezing differ only in the melting line- which slants
towards pressure axis for the substances that expand on freezing; slants away from pressure axis
for substances that contract on freezing.
Water is the classic example of the pure substances which expand on freezing & as such has vital
consequences in nature.
If water contracted on freezing as most other substances do, the ice formed would be heavier
than the liquid water & it would settle to the bottom of lakes, rivers & oceans instead of floating
at the top.
The sun rays would never reach these ice layers & the bottom of many lakes, rivers & oceans
would be covered with ice year round, seriously disrupting marine life.
During skating on ice there is an increase is pressure on ice at constant temperature. This makes
the top layer of the ice to melt & this act as a lubricant to slide smoothly on the surface of the ice.
Thus, the properties of ice that it expands on freezing makes- (i) the existence of marine life
possible & (ii) the skating on ice is possible.
T-V Diagram:
T-V diagram for heating at constant pressure for a pure substance is illustrated in the following
diagram.
[(CRW)]
Consider a unit mass of a simple compressible substance initially in a solid phase at state point 1.
As indicated in figure.
Let the solid be heated at constant pressure. Both the temperature & volume of the substance
increase till the melting temperature of the solid is reached at state point 2.
Any further heating of the substance will result in a change of phase from S to L along the line 2-3
when the volume of the substance increases at constant temperature.
Further heating will result in an increase in temperature & volume of the liquid till the boiling
point temperature of the substance is reached at state point 4, i.e., along line 3-4. The boiling
point temperature depends on the pressure at which the substance exists. Higher the pressure,
higher will be the boiling point temperature.
Further addition of heat will result in a change of phase from L to V along the line 4-5, when the
volume of the substance increases at constant temperature.
Further heating will result in an increase in temperature & volume of the vapor. The vapor is
reaches at state point 6. i.e., along line 5-6.
State-2: is referred to as saturated solid state;
State-3: as liquid state with respect to solidification;
State-4: as saturated liquid with respect to vaporization; &
State-5: as saturated or dry vapor state.
Definition of States of a pure substance with respect to water as an example
If the T-V diagram process for a pure substance, like water, is repeated at different pressure & if all
the corresponding saturated state points are joined, a complete P-V diagram for a simple
compressible substance is obtained.
Graph (CRW)
1. Sub-cooled liquid state or compressed liquid state: If the temperature of a pure substance is less
than the boiling point temperature (or saturation temperature) of the substance. Corresponding
to the pressure at which it is existing, then the substance is said to be in sub-cooled liquid state or
compressed liquid state i.e. point ‘a’.
2. Saturated liquid state: If the temperature of a pure substance is equal to the boiling point
temperature (or saturation temperature) of the substance corresponding to the pressure at which
it is existing & if the entire pure substance is in liquid phase then the substance is said to be in
saturated liquid state i.e. point ‘b’.
3. Mixture of saturated liquid & vapor state or wet vapor state: If the temperature of the substance
is equal to the boiling point temperature (or saturation temperature) corresponding to the
pressure at which it is existing & if the substance is partly in liquid phase & partly in vapor phase,
then the substance is said to be in mixture of saturated liquid & vapor state or wet vapor state, i.e.
point ‘c’.
4. Saturated vapor state or Dry vapor state: If the temperature of pure substance is equal to the
boiling point temperature (or saturation temperature) corresponding to the pressure at which it is
existing & if the entire substance is in vapor phase then the substance is said to be in saturated
vapor state or dry vapor state. i.e. point ‘d’.
5. Super heated vapor state: If the temperature of the pure substance is more than the boiling point
temperature (or saturation temperature) corresponding to the pressure at which it is existing,
then the substance is said to be in super heated vapor state. i.e. point ‘e’.
Dryness fraction or Quality of wet vapor
During a change of phase from liquid phase to vapor phase or vice versa, temperature & pressure
cannot be considered as two independent properties to fix a thermodynamic state of the
substance; since for a given pressure then is a definite temperature at which the change of phase
can take place.
(for example, in P-V diagram of water, the states represented by point ‘b’, point ‘c’ & point ‘d’ are
having the same temperature & pressure, but they are of different thermodynamic states)
Thus, in order to fix the thermodynamic state during a change of phase, P or T can be used as one
of the independent properties volumes can be used as the other independent properties.
Since it is difficult to measure volume in a laboratory dryness fraction, which can be measured
easily in a lab, is used as the other independent properties to fix the state of a wet vapor.
Dryness fraction or quality of wet vapor is defined as: the ratio of the mass of the dry vapor
present in the wet mixture to the total mass of the wet mixture & is represented by ‘x’
Equation(CRW)
Properties of a wet vapor
Properties of a wet vapor can be expressed in terms of the corresponding properties of a
saturated vapor & dryness fraction of the vapor.
[Equation(CRW)]
Determination of dryness fraction in a lab:
Dryness fraction of wet steam can be determined by;
1. Separating colorimeter method,
2. Throttling colorimeter method; &
3. Combined separating throttling calorimeter method.
The disadvantage of Method 1 is that there is no guarantee that all liquid present in the wet vapor
will collect at the bottom of the separator & also the steam at the top portion of the separator
may still contain same transition of liquid-water.
The disadvantage of Method 2 is, even after the throttling process the steam is not dry saturated.
The steam has to be ensued superheated to overcome the disadvantages of 1 & 2 methods, &
therefore, method 3 is in common practice.
Combined separating throttling calorimeter method
A steam sample of mass, ‘m’ & enthalpy, ‘h’, at pressure P1, (consisting of saturated liquid water of
mass, mf, whose enthalpy, hf; & dry steam of mass, mg, whose enthalpy of vaporization, hfg).
Is made to enter the separator where most of the liquid water of mass, mf, will collect at the
bottom of the separator in a measuring jar.
Almost dry steam, of enthalpy, h2, which is at the top of the separator, will undergo throttling
process.
The throttled steam of mass, mg, & enthalpy, h3, at pressure, P3 & temperature T3 is condensed &
collected in a measuring jar.
[Diagram (CRW)]
Applying steady flow, steady state energy equation, the dryness fraction is calculated as:
[Equation (CRW)]
is the expression for the calculation of dryness fraction of sample steam. The above equation can
also be written as:
x=x1=x2
When x1= mg/( mf + mg)= dryness fraction,
When only separating calorimeter is used; &
x2= (h3 –hf1)/ hfg1 = dryness fraction,
when only throttling calorimeter is used.
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