chapter 2 pure substance behavior...pure substance: a pure substance is one that has a homogeneous...
TRANSCRIPT
Pure substance: A pure substance is one that has a homogeneous andinvariable chemical composition.
Air is a mixture of several gases, but it is considered to be a pure substance.
Nitrogen and gaseous air are pure
substances.
A mixture of liquid and gaseous
water is a pure substance, but a
mixture of liquid and gaseous air
is not.
Chapter 2 Pure Substance Behavior
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M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Phase Change Process of Pure Substances
Compressed liquid (subcooled liquid): A substance that it is notabout to vaporize (not ready yet).
Saturated liquid: A liquid that is about to vaporize.
At 1 atm and 20°C,
water exists in the liquid
phase (compressed
liquid).
At 1 atm pressure and 100°C,
water exists as a liquid that is
ready to vaporize (saturated
liquid).
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M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Saturated vapor: A vapor that is about to condense.
Saturated liquid–vapor mixture: The state at which the liquid and vapor phases coexist in equilibrium.
Superheated vapor: A vapor that is not about to condense.
As more heat is transferred,
part of the saturated liquid
vaporizes (saturated liquid–
vapor mixture).
At 1 atm pressure, the
temperature remains
constant at 100°C until the
last drop of liquid is vaporized
(saturated vapor).
As more heat is
transferred, the
temperature of the
vapor starts to rise
(superheated vapor).
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Saturation Temperature and Saturation Pressure
The temperature at which water starts boiling depends on the pressure; therefore, if the
pressure is fixed, so is the boiling temperature.
Saturation temperature Tsat: The temperature at which a pure substance changes
phase at a given pressure.
Saturation pressure Psat: The pressure at which a pure substance changes phase at a
given temperature.
The liquid–
vapor
saturation
curve of a
pure
substance
(numerical
values are for
water).
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
T-v diagram for the heating process of water at constant pressure.
saturated vapor
saturated liquid the latent heat
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
The critical-point data for
more substances are given
in Aksel’s Table 2.1.
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
The P–v–T Surface
P-v-T surface of a substance
that contracts on freezing.
P-v-T surface of a substance that
expands on freezing (like water).
The P-v-T surfaces present a great deal of information at once, but in a thermodynamic
analysis it is more convenient to work with two-dimensional diagrams, such as the P-v
and T-v diagrams.
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The P–v–T Surface
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Sublimation: Passing from
the solid phase directly into
the vapor phase.
At low pressures (below the triple-
point value), solids evaporate
without melting first (sublimation). P-T diagram of pure substances.
Phase Diagram
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
In a saturation state, pressure and
temperature are not independent
properties. Therefore, knowing P & T
is not going to be enough to fix the
state !
Independent Properties of a Pure Substance
The state of a pure substance is fixed by any two independent, intensive
properties
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Tables of Thermodynamic Properties
superheated vapor
compressed-solid region
the saturated-solid and saturated-liquid region
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
The Two–Phase States
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By definition Vfg = Vg - Vf
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
You can calculate any specific property ‘y’ in two phase region by
knowing the quality
, , ,
f g
f fg
y v u h or s
y y y
y y x y
f
g f
v vx
v v
Saturated Liquid and Saturated Vapor States
Table 2.5.1 Properties of Saturated Water (Liquid-Vapor): Temperature Table
Table 2.5.2 Properties of Saturated Water (Liquid-Vapor): Pressure Table
Partial displays of Tables 2.5.1 & 2.5.2
Tem
pera
ture
Sa
tura
tio
n p
ressu
re a
t
giv
en tem
pera
ture
Specific
Volu
me o
f
Satu
rate
d V
apor
Specific
Volu
me o
f
Satu
rate
d L
iquid
*10
00
Pre
ssure
Specific
Volu
me o
f
Satu
rate
d V
apor
Specific
Volu
me o
f
Satu
rate
d L
iquid
*10
00
Satu
ration t
em
pera
ture
at
giv
en p
ressure in saturated liquid–
vapor mixture region
or two phase region
or wet region
0: satureted liquid, yf,
1: satureted vapor, yg.
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0 1Quality
Pressures are in convenient incrementsTemperatures are in convenient increments
What are the saturated
pressure, specific volume of
liquid and vapor at 90°C
temperature?
Specific Volume of
Sat. Liquid, Vf =
1.0361*10-3 (m3/kg)
Specific Volume of Sat.
Vapor, Vg=2.361 (m3/kg)Specific Volume of
Sat. Liquid, Vf =
1.0434*10-3 (m3/kg)
Specific Volume of Sat.
Vapor, Vg=1.694 (m3/kg)
What are the saturated
temperature, specific volume
of liquid and vapor at 100 kPa
pressure?
Using Table 2.5.1 Using Table 2.5.2
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Vf = Vs & Vg = Vb
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M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
As an example, let us calculate the specific volume of saturated steam at 200°C
having a quality of 70 %.
specific volume of liquid, Vs=Vf=1.1565*10-3 (m3/s)
specific volume of vapor, Vb=Vg=0.1272 (m3/s)
Vfg=0.126044 (m3/s)
V=0.089387 (m3/s)
3 3 31.1565 10 0.7 * (0.1272 1.1565 10 ) 0.0894 /v x x m kg
( )f fg f g fv v xv v x v v
or
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M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
The Liquid and Solid States
The compressed liquid specific properties depend on
temperature much strongly than they do on pressure.
Therefore, a compressed liquid specific property may
be approximated as a saturated liquid specific
property at the given temperature, i.e.,
Suppose that we want to know v at 10 MPa & 100°C.
From tables its exact value is 0.001 0386 m3/kg & vf =
0.001 0437 m3/kg at 100°C.
Therefore, if we take 𝑣 ≅ 𝑣𝑓@100°𝐶 less than 1 % error
would be introduced !
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Compressed liquid (or
subcooled) is characterized by
@
@
sat T
sat P
f
at a givenT if P P
at a given P if T T
at a given PorT if y y
@T@ & fa given T P y y
The properties of a solid are mainly a function of
temperature, as the solid is nearly incompressible,
meaning that the pressure cannot change the
inermolecular distances and the volume is unaffected
by pressure. Thus,
@T@ & ia given T P y y
Saturated Solid and Saturated Vapor
Table 2.5.4 of the steam tables gives the
properties of saturated solid and
saturated vapor that are in equilibrium.
The first column gives the temperature,
and the second column gives the
corresponding saturation pressure.
As would be expected, all these
pressures are less than the triple-point
pressure.
saturated solid and
saturated vapor
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Compared to saturated vapor, superheated
vapor is characterized byThe region to the right of the saturated
vapor line and the temperatures above
the critical point temperature is called as
the superheated vapor region.
Table 2.5.3 also includes
compressed liquid properties.
Above the line, the
properties are given for
the compressed liquid or
subcooled region
Below the line, the
properties are given for
the superheated regionA partial display of Table 2.5.3.
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The Superheated Vapor States
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
@
@
sat T
sat P
g
at a givenT if P P
at a given P if T T
at a given PorT if y y
Other Property Tables
Property tables also includes thermodynamic tables for several
other substances; refrigerants such as ammonia, R-12, and R-
134a and the cryogenic fluids such as nitrogen and methane.
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Linear InterpolationExample 2.5Determine the pressure for water at 200°C with v = 0.4 m3/kg.
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
SolutionStarting with Table B.1.1 with 200°C and note that v > vg = 0.127 36 m3/kg, so we have
superheated vapor. Proceed to Table B.1.3 at any subsection with 200°C; suppose we
start at 200 kPa. There v = 1.08034 m3/kg, which is too large, so the pressure must be
higher. For 500 kPa, v = 0.42492 m3/kg, and for 600 kPa v = 0.35202 m3/kg, so it is
bracketed. This is shown in the figures given below.
A linear interpolation, between the two
pressures is done to get P at the desired v.
0.4 0.42492500 (600 500) 534.2
0.35202 0.42492P kPa
Equation of state: Any equation that relates the pressure, temperature, and specific
volume of a substance.
The simplest and best-known equation of state for substances in the gas phase is the
ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite
accurately within some properly selected region.
R: gas constant (kJ/kg.K)
M: molar mass (kg/kmol)
𝑅: universal gas constant (kJ/kmol.K)
Different substances have different gas constants.
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The Ideal Gas States
& /Pv RT R R M
𝑅: 8.31447 (kJ/kmol.K)
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M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Various Forms of Ideal Gas Equation
22
𝑃 = 𝜌𝑅𝑇
𝑉 = 𝑚𝑣 → 𝑃𝑉 = 𝑚𝑅𝑇
𝑚𝑅 = 𝑀𝑁 𝑅 = 𝑁 𝑅 → 𝑃𝑉 = 𝑁 𝑅𝑇
𝑉 = 𝑁 𝑣 → 𝑃 𝑣 = 𝑅𝑇
P = absolute pressure (kPa)
𝑣 = molar specific volume (m3/kmol)
T = absolute temperature (K)
𝑅 = universal gas constant 8.31447 (kJ/lmol.K)
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
The Compressibility Factor
The compressibility factor is unity for an ideal gas.
Compressibility factor Z A factor that accounts for the deviation of real gases from
ideal-gas behavior at a given temperature and pressure.
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
03-21
24
T–v Diagram for Water
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Comparison of Z factors for various gases.
Reduced
temperature
Reduced
pressure
Pseudo-reduced
specific volume
25
The General Compressibility Chart for Gasses
U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
A) If the pressure is very low (that is, P « Pc), the ideal-gas model can be assumed with
good accuracy, regardless of the temperature
A
B) at high temperatures (that is, greater than about ) pressures as high as four
or five times2 cT T
B
4 5 cP P
Ideal G
as A
ssu
mp
tio
n
Reg
ion
of
Z~
1
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Other Equations of State
Many such equations have been proposed and
used to correlate the observed behavior of
gases. As an example, the class of relatively
simple equation known as cubic equations of
state
Equation of state accurately represents the P-v-T behavior for a particular gas over the
entire superheated vapor region
As an example, the class of relatively simple equation known as cubic equations of state
2 2
RT aP
v b v cbv db
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ
Computerized Tables
Most of the tables in the booklet are supplied in a computer program which operates
with a visual interface in the Windows environment on a PC–type computer.
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U N I V E R S I T Y O F G A Z I A N T E P M E 2 0 4 : T H E R M O D Y N A M I C S I
M E C H A N I C A L E N G I N E E R I N G D E P A R T M E N T A S S O C . P R O F . D R . E M R A H Ö Z A H İ