chapter2 pure substances 2.pdf

Chapter-2
Properties of Pure Substances
MECH-189.2
BY
Er. VIJAY PAUDEL
8/3/2021 Prepared by Er. Vijay Paudel, OCEM 1

Pure Substances
• A homogeneous material which contains particles (atoms or molecules ) of only one kind
and has a definite set of properties( melting point , boiling point) and which cannot be
separated into other kinds of matter by any physical process.
• eg:-Elements : Metals and Non-metals , Compounds : Salts. .
• A substance that has a fixed chemical composition throughout is called a pure substance.
Examples
• Water, mixtures of liquid water and water vapor.
• nitrogen,
• helium, and
• carbon dioxide, etc.
• A pure substance does not have to be of a single chemical element or compound.
• A mixture of various chemical elements or compounds also qualifies as a pure substance as
long as the mixture is homogeneous.
• However, a mixture of oil and water is not a pure substance.
• Since oil is not soluble in water, it will collect on top of the water, forming two chemically
dissimilar regions.

A pure substance is a system which is
(i) homogeneous in composition,
(ii) homogeneous in chemical aggregation, and
(iii) invariable in chemical aggregation
Homogeneous in composition:
• “Homogeneous in composition” means that the composition of each part of the
system is the same as the composition of every other part.
• “Composition means the relative proportions of the chemical elements into which
the sample can be analyzed.

Homogeneous in chemical aggregation:
• “Homogeneous in chemical aggregation” means that the chemical elements must
be combined chemically in the same way in all parts of the system.
• Consideration of Fig. 3.1 again shows that the system (a) satisfies this condition
also ; for steam and water consist of identical molecules. System (b) on the other
hand is not homogeneous in chemical aggregation since in the upper part of the
system the hydrogen and oxygen are not combined chemically (individual atoms
of H and O are not uniquely associated), whereas in the lower part of the system
the hydrogen and oxygen are combined to form water.

Invariable in chemical aggregation:
• Invariable in chemical aggregation” means that the state of chemical combination
of the system does not change with time.
• Thus a mixture of hydrogen and oxygen, which changed into steam during the
time that the system was under consideration, would not be a pure substance.
• A mixture of liquid air and gaseous air, however, is not a pure substance since the
composition of liquid air is different from the composition of gaseous air, and thus
the mixture is no longer chemically homogeneous.

Phase change in pure substance
Phase:
• A phase is identified as having a distinct molecular arrangement that is
homogeneous throughout and separated from the others by easily identifiable
boundary surfaces.
• The two phases of H2O in iced water represent a good example of this.
• Even though there are three principal phases
• solid,
• liquid, and
• gas
• a substance may have several phases within a principal phase, each with a different
molecular structure.
• Carbon, for example, may exist as graphite or diamond in the solid phase

PROPERTIES AND IMPORTANT
DEFINITIONS
• Sensible heating: It refers to the heating of substance in single phase. It causes
rise in temperature of substance. In case of cooling in above conditions it shall be
called sensible cooling.
• Latent heating: It is the heating of substance for causing its phase change without
any change in it’s temperature. If heat is extracted for causing phase change
without any change in its temperature it will be called latent cooling.
• Normal boiling point: It is the temperature at which vapour pressure equals to
atmospheric pressure and at this temperature phase change from liquid to gas
begins.
• Melting point: It is the temperature at which phase change from solid to liquid
takes place upon supplying latent heat.

• Saturation states: Saturation state of a substance refers to the state at which its phase
transformation takes place without any change in pressure and temperature. These can be
saturated solid state, saturated liquid state and saturated vapour state. For example
saturated vapour state refers to the state of water at which its phase changes to steam
without varying pressure and temperature
• Saturation pressure: It is the pressure at which substance changes its phase for any given
temperature. Such as at any given temperature water shall get converted into steam at a
definite pressure only, this pressure is called saturation pressure corresponding to given
temperature. For water at 100°C the saturation pressure is 1 atm pressure.
• Saturation temperature: It refers to the temperature at which substance changes its
phase for any given pressure. For water at 1 atm pressure the saturation temperature is
100°C.
• Triple point: Triple point of a substance refers to the state at which substance can coexist
in solid, liquid and gaseous phase in equilibrium. For water it is 0.01°C i.e. at this
temperature ice, water and steam can coexist in equilibrium.

• Critical states: “Critical state refers to that state of substance at which liquid
and vapour coexist in equilibrium.” In case of water at 22.12 MPa, and
374.15°C the water and vapour coexist in equilibrium, thus it is the highest
pressure and temperature at which distinguishable water and vapour exist
together. Data for critical state of many substances is given in the table 6.1.
Specific volume at critical point for water is 0.00317 m3/kg.
• Dryness fraction: It is the mass fraction of vapour in a mixture of liquid and
vapour at any point n liquid-vapour mixture region. It is generally denoted by
‘x’. It is also called quality of steam.

• Compressed liquid or subcooled liquid: Liquid at temperature less than saturation
temperature corresponding to a given pressure is called compressed liquid or subcooled
liquid. Degree of subcooling is given by the temperature difference between liquid
temperature and saturation temperature of liquid at given pressure.
• Degree of subcooling = Saturation temperature at given pressure – Temperature of
liquid.
• Superheated steam: Steam having temperature more than the saturation temperature
corresponding to given pressure is called superheated steam. Amount of superheating is
quantified by degree of superheating. Degree of superheating is given by difference
between temperature of steam and saturation temperature at given pressure.
• Degree of superheating = Temperature of steam – Saturation temperature at given
pressure

Steam generation from Ice

Temperature vs supply heat

Temperature vs specific volume Diagram of Water

• a – b: Temperature rises from –20°C to 0°C with volume increase, (ice)
• b – c: Temperature remains constant at 0°C due to phase change and volume
decreases, (ice to water)
• c – d: Temperature increases from 0°C to 100°C and volume increases, (water).
• d – e: Temperature remains constant at 100°C, phase changes from liquid to
vapour and volume increases, (water to steam).
• e – f: Temperature increases from 100°C to 200°C and volume increases, (steam).

Pressure vs specific volume diagram
8/3/2021
Prepared by Er. Vijay Paudel, OCEM 16

PHASE TRANSFORMATION PROCESS
• Upon heating the ice its temperature increases from –10°C to 0°C while being in solid
phase. Temperature increase is accompanied by increase in volume and new state ‘b’ is
attained. This heating is sensible heating as heating causes increase in temperature in
same phase.
• After ice reaches to 0°C, the melting point, it is ready for phase transformation into water.
Further heat addition to it causes melting and now water at 0°C is available. This heating
is called latent heating and heat added is called latent heat. New state attained is ‘c’ and
volume gets reduced due to typical characteristic of water. As defined earlier state ‘b’ is
called saturation solid state as phase can change here without any change in pressure
and temperature. State ‘c’ is called saturated liquid state with respect to solidification.

• Further heating of water at 0°C shall cause increase in its temperature up to 100°C. This
heat addition is accompanied by increase in volume and state changes from ‘c’ to ‘d’ as
shown on T-V diagram. Here typical behavior of water from 0 to 4°C is neglected. This
heating is sensible heating in liquid phase. State ‘d’ is called saturated liquid state with
respect to vaporization. Thus, there are two saturated liquid states ‘c’ and ‘d’ depending
upon direction of transformation.
• Water at 100°C and 1 atmosphere is ready for getting vaporized with supply of latent heat
of vaporization. Upon adding heat to it the phase transformation begins and complete
liquid gradually gets transformed into steam at state ‘e’. This phase change is accompanied
by large increase in volume. Heating in this zone is called latent heating. State ‘e’ is called
saturated vapor state or saturated steam state.
• Steam at 100°C upon heating becomes hotter and its temperature rises. Say, the heating
causes temperature rise up to 200°C. This increase in temperature is also accompanied by
increase in volume up to state ‘f’ as shown on t-V diagram. This heating is sensible heating
in gaseous phase.

Pressure vs Temperature diagram of water

Pressure vs Temperature diagram of water
8/3/2021
Prepared by Er. Vijay Paudel, OCEM
20

P-T diagram for pure substance

Triple-point Data
S.N Substance Temp, K Pressure, mm of Hg
1 Hydrogen 13.96 54.1
2 Oxygen 54.36 1.14
3 Neon 24.57 324
4 Nitrogen 63.18 94
5 Ammonia 195.05 45.57
6 Carbon-dioxide 216.55 3.88
7 Water 273.16 4.58

Pressure vs Temperature Diagram
It is the property diagram having pressure on Y-axis and temperature on X-axis. This
can also be obtained by identifying and marking salient states during phase
transformation and subsequently generating locii of identical states at different
pressures.
• a – b: Temperature rises from –20°C to 0°C, phase is solid.
• b – c: Temperature does not rise, phase changes from ice to water (solid to liquid)
• c – d: Temperature rises from 0°C to 100°C, phase is liquid
• d – e: Temperature does not rise, phase changes from liquid to gas (water to
steam)
• e – f: Temperature rises from 100°C to 200°C, phase is gas (steam).

Equations of state for a simple compressible
substance
• Equation of state for a simple compressible substance is a function of pressure,
temperature and volume.
PV= nRT
Where, P = pressure
V = volume
n = number of moles
R = Universal gas constant
T = temperature
PV= mR’T
R’ = characteristics gas constant

Steam Tables
• Steam table is a tabular presentation of properties such as specific enthalpy, entropy,
internal energy and specific volume at different saturation pressures and
temperatures.
• Steam table may be on pressure basis or on temperature basis.
• The table on pressure basis has continuous variation of pressure and corresponding
to it:
• saturation temperature (Tsat),
• enthalpy of saturated liquid (hf),
• enthalpy of saturated vapour (hg),
• entropy of saturated liquid (sf),
• entropy of saturated vapour (sg),
• specific volume of saturated liquid (vf),
• specific volume of saturated vapour (vg),
• internal energy of saturated liquid (uf),
• internal energy of saturated vapour (ug)
8/3/2021 Prepared by Er. Vijay Paudel, OCEM
25

• Similar to above the temperature based table which gives continuous variation of
temperature and corresponding to it saturation pressure and other properties as hf , hg,
hfg, sf , sg, sfg, vf , vg, uf , ug and ufg are given.
• Similarly, steam properties for superheated steam are also estimated and tabulated at
some discrete pressures for varying degree of superheat. Super heated steam table are
available for getting enthalpy, entropy, specific volume and internal energy separately.

Temperature vs entropy diagram for water

T-s Diagram of water

• Thermodynamic properties and nomenclature used is indicated inside bracket
along with property.
• Discussion is based on unit mass of steam/mixture. T–S diagram for 2-phases i.e.
liquid and vapour has saturated liquid line and saturated vapour line meeting at
critical point.
• Three constant pressure lines corresponding to pressure P1, P2 and P3 are shown.
• Let us take a constant pressure line for pressure p1 which has states a1, b1, k1, j1, e1,
c1, d1 shown upon it. Region on the left of saturated liquid line is liquid region.
• Region enclosed between saturated liquid line and saturated vapour line is liquid-
vapour mixture region or also called wet region.

• Region on the right of saturated vapour line is vapour region. All the states lying
on saturated liquid line are liquid (water) states shown as b1, b2, b3 at different
pressures.
• States a1,a2 and a3 are the states lying in subcooled region. Compressed liquid or
subcooled liquid exists at a1,a2 and a3 at pressures, p1,p2 and p3
• Degree of sub cooling at a1 = Saturation temperature for pressure p1 – Temperature at
a1
= (T1 – T a1)

• At constant pressure p1 when we move towards
right of state b1 then the phase transformation of
water into steam (vapour) just begins.
• This conversion from liquid to vapour takes place
gradually till whole liquid gets converted to
vapour.
• Phase transformation into vapour gets completed
at c1, c2, c3 at pressures p1, p2 and p3 respectively.
• States c1, c2, c3 are called saturated vapour states
and substance is completely in vapour phase at
these points. Beyond state c1, at pressure p1 it is
vapour phase and sensible heating shall cause
increase in temperature.
• State d1 is the state of steam called superheated
steam.
• Superheated steam exists at d1, d2, and d3 at
pressures p1, p2 and p3 .

• Degree of superheat at d1 = Td1 – T1
• Similarly, degree of superheat at d2 = Td2 – T2,
degree of superheat at d3 = Td3 – T3.
• As pressure is increased up to critical pressure then constant pressure line is seen to
become tangential to critical point (CP) at which water instantaneously flashes into
vapour.
• In the wet region states k1, j1 and e1 are shown at pressure p1.
• At state b1 mixture is 100% liquid
• At state k1 mixture has larger liquid fraction, say 90% liquid fraction and 10% vapour
fraction.
• At state j1 mixture has say 20% liquid fraction and 80% vapour fraction.
• At state e1 mixture has say 10% liquid fraction and 90% vapour fraction.
• At state c1 mixture is 100% vapour.
• Similarly, from explanation given above the states b2, k2, j2, e2, c2 and b3, k3, j3, e3, c3 can
be understood at pressures p2 and p3 respectively.

• At any pressure for identifying the state in wet region, fraction of liquid and vapour must be
known, for identifying state in subcooled region, degree of subcooling is desired and for
identifying state in superheated region, degree of superheating is to be known.
• For wet region a parameter called dryness fraction is used. Dryness fraction as defined
earlier can be given as, x:
• Dryness fraction; x =
Mass of vapour
Mass of liquid + Mass of vapour
• Dryness fraction values can be defined as follows;
• Dryness fraction at state b1 = 0
• Dryness fraction at state k1 = 0.10
• Dryness fraction at state j1 = 0.80
• Dryness fraction at state e1 = 0.90
• Dryness fraction at state c1 = 1.00
• Thus, saturated liquid line and saturated vapour line are locii of all states having 0 and 1
dryness fraction values.

• For different pressures the locii of constant dryness
fraction points may be obtained and it yields constant
dryness fraction lines corresponding to xk(0.10),
xj(0.80), xe(0.90), as shown by dotted lines.
• Let us use subscript ‘f ’ for liquid states and ‘g’ for
vapour states.
• Therefore, enthalpy corresponding to saturated liquid
state = hf,
• Enthalpy corresponding to saturated vapour state = hg.
• Similarly, entropy may be given as sf and sg.
• Specific volume may be given as vf and vf.
• At any pressure for some dryness fraction x, the total
volume of mixture shall comprise of volume occupied
by liquid and vapour both.
Total volume, V = Vf + Vg.

• Similarly, Total mass, m = mf + mg, i.e. mass of liquid and mass of vapour put together
substituting for volume,
m·v = mf· vf+ mg. vg.
where m is total mass and v is specific volume of mixture
V =(1-
mg
m
). vf + (
mg
m
) .vg
• From definition, x =
mg
mf + mg
=
mg
m
v = (1 – x) · vf + x · vg
or, v = vf + x · (vg – vf )
or, v = vf + x · vf g
here vf g indicates change in specific volume from liquid to vapour
• Hence, specific volume of wet steam is given by
v = vf + x · vf g
8/3/2021 Prepared by Er. Vijay Paudel, OCEM
36

Specific volume of superheated steam:
• As superheated steam behaves like a perfect gas its volume can be found out in the
same way as the gases.
• If, vg = Specific volume of dry steam at pressure p,
• Ts = Saturation temperature in K,
• Tsup = Temperature of superheated steam in K, and
• vsup = Volume of 1 kg of superheated steam at pressure p,
Then,
𝑝.vg
Ts
=
𝑝.vsup
Tsup
vsup =
Tsup.vg
Ts

Entropy of wet steam
The total entropy of wet steam is the sum of entropy of water (sf) and entropy of evaporation
(sfg).
In other words, swet = sf + sfg
swet = sf +
x.hfg
Ts
Where, swet = Total entropy of wet steam,
sf = Entropy of water, also sf = cpwloge
T2
T1
sfg =
x hfg
Ts
= Entropy of evaporation.
If steam is dry and saturated, i.e., x = 1, then
• sg = sf +
hfg
Ts
8/3/2021
Prepared by Er. Vijay Paudel, OCEM
38

Entropy of superheated steam
• Let 1 kg of dry saturated steam at Ts (saturation temperature of steam) be heated to
Tsup. If specific heat at constant pressure is cps, then change of entropy during
superheating at constant pressure p
ssup = cpsloge
Tsup
Ts
Total entropy of superheated steam above the freezing point of water
ssup = Entropy of dry saturated steam + change of entropy
during superheating
ssup = sf +
x · hfg
Ts
+ cpsloge
Tsup
Ts
= sg + cpsloge
Tsup
Ts

Enthalpy of wet steam
• It is defined as the quantity of heat required to convert 1 kg of water at 0°C into wet
steam at constant pressure. It is the sum of total heat of water and the latent heat and this
sum is also called enthalpy.
In other words, h = hf + x (hg – hf)
Or, h = hf + x · hfg
• If steam is dry and saturated, then x = 1 and hg = hf + hfg
• here hfg is difference in enthalpy between saturated liquid and vapour states. Actually hfg
is energy or heat required for vaporization or heat to be extracted for condensation i.e.
latent heat.
• The total heat of superheated steam is given by
hsup = hf + hfg + cps (Tsup – Ts)
• Superheated steam behaves like a gas and therefore it follows the gas laws.

Sample numerical problems
• A rigid tank contains 50 kg of saturated liquid water at an absolute pressure of 50
bar. Determine the temperature in the tank and the volume of the tank.
• A rigid tank contains saturated liquid water. The pressure and volume of the tank
are to be determined
Tsat = Tsat @ 50 bar pressure = 263.9 °C
The specific volume of the saturated liquid at 50 bar pressure is, v = vf @ 50 bar
0.001286 m3/kg.
Then the total volume of the tank becomes,
V = mv = 50 kg * 0.001286 m3>kg2 = 0.0643 m3

THANK YOU

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