The document discusses thermodynamic concepts including: 1) Phases and pure substances, intensive properties that define state, processes like isothermal and adiabatic, and ideal gas behavior. 2) Temperature-volume, pressure-volume phase diagrams showing single-phase, two-phase, and critical point regions. 3) Properties of saturated liquids and vapors including quality, saturated vapor pressure, and appropriate reference states. 4) Approximations for properties of liquids and ideal gases.

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Evaluating Properties
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Not a Pure Substance..?
Phase: a quantity of matter that is homogeneous throughout in both
chemical composition and physical structure.
!
Pure substance: one that is uniform and invariable in chemical
composition.
Gas Gas(1) (2)
(3) (4)

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The State Principle
Two independent, intensive, thermodynamic properties are
required to fix the state of a simple compressible system.
For example:
P and v
T and u
x and h
Intensive thermodynamic properties:
h – specific
enthalpy
u – specific internal
energy
x – quality
(steam only)
s –specific entropy
P –absolute
pressure
T – absolute
temperature
v – specific
volume
Less used:
g - Gibbs free energy
a - Helmholz free energy
Coordinate
• Time: t
• Space: x, y, z
• Thermodynamics: P, T (or two independent properties)
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P-v-T Relations
- Single phase regions
- Two phase regions
- Saturation states
- Triple line
- Critical Point

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P-T (phase diagram)
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http://en.wikipedia.org/wiki/
Image:Thermally_Agitated_Molecule
.gif#file
http://socs.berkeley.edu/
~murphy/Movies/movie.html
Solid Liquid Gas
http://en.wikipedia.org/wiki/
Image:Thermally_Agitated_Mole
cule.gif#
Solid - Liquid - Gas

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Expands or Contracts on Freezing
Expands on freezing (water) Contracts on freezing
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P-T (phase diagram)
Triple point: solid/liquid/gas
coexists
Critical point: no distinction
between gas and liquid
• Vaporization line
• Melting line
• Sublimation line
Psat, Tsat
Psat=f(Tsat)
Ideal gas

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Saturated Vapor Pressure
Saturated vapor pressure
Therefore, usually Psat increases as Tsat increases.
# of molecules leaving liquid =
# of molecules returning to
liquid
Courtesy of V. Carey Psat = f Tsat( )
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P-v Diagram
Isotherm
Pv = RT

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Expands or Contracts on Freezing
Expands on freezing (water) Contracts on freezing
L+S
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T-v Diagram
Subcooled
Liquid
Pv = RT

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Quality, x
• For Saturated Mixture
(Liquid-Vapor) Region
– Quality; x; an intensive
property
– x gives fraction that is vapor
(gas)
– (1-x) gives Moisture Content
0 ≤ x ≤ 1;
x = 0 → Saturated Liquid (subscript‘f’)
x = 1 → Saturated Vapor (subscript‘g’)
‘fg’→‘g’-’f’ x ≡
mg
mf + mg
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Quality Relations
LET b = ANY INTENSIVE PROPERTY
– (b = v, u, h, s, etc.)
x =
b − bf
bg − bf
=
b − bf
bfg
b = bf + x ⋅bfg
bfg = bg − bf
b = x ⋅bg + 1− x( )⋅bf

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Processes
• Adiabatic process: No thermal interaction with its surroundings
!
• Isothermal process: A process that occurs at constant temperature
!
• Isobaric process: A process that occurs at constant pressure
!
• Isometric (isochoric) process: A process that occurs at constant volume
!
• Isenthalpic process: A process that occurs at constant enthalpy
!
• Isentropic process: A process that occurs at constant entropy
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Find out whether you are interested in
• Compressed liquid
• Wet vapor
• Superheated vapor
• Ideal gas

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Reference States
At triple point (water, 0.6113 kPa, 0.01°C),
thermodynamic properties of saturated
liquid are zero (as a standard)
• Compressed liquid
• Wet vapor
• Superheated vapor
• Ideal gas
Use saturated liquid data
or incompressible
approximation
Ideal gas law & table
Look up the table
Look up the table
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Enthalpy
Enthalpy is a property constructed due to the frequent
occurrence of the above combination of properties.
Enthalpy of wet vapor
Class note
[J]
[J/kg]
H =U + PV
h = u + Pv

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Specific Heat (heat capacity)
Specific heat at constant volume
Specific heat at constant pressure
Specific heat ratio
cv
=
∂u
∂T
"
#
$
%
&
'
v
cP
=
∂h
∂T
"
#
$
%
&
'
P
k =
cP
cv
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Approximation for Liquids
• Using Saturated Liquid Data
(‘Compressed Liquid Rule’)
v T,P( )≈ vf
T( )
u T,P( )≈ uf
T( )
h T,P( )≈ hf
T( )
s T,P( )≈ sf
T( )
at fixed temperature
(not pressure)Class note

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Approximation for Liquids
• Using‘Incompressible Substance Model’
Class note
cP
= cv
= c
u2
− u1
= c T2
− T1( )
h2
− h1
= u2
− u1
+ v P2
− P1( )
h2
− h1
≈ c T2
− T1( )
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Ideal Gas
Class note
The Ideal Gas Model:
When specific heats
are assumed
constant
Requirement:PV = Nk B
T
= nRu
T
= mRT
R =
Ru
MW
P ≪ Pc or T ≫ Tc
u = u T( )
h = u T( )+ Pv
= u T( )+ RT
= h T( )
cv
(T) =
du
dT
=
R
k −1
cp
(T) =
dh
dT
=
kR
k −1
cp
(T) = cv
(T) + R
u2
− u1
= cv
T2
− T1( )
h2
− h1
≈ cp
T2
− T1( )
Pv= RT

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Linear Interpolation
y − y1 =
y2 − y1
x2 − x1
x − x1( )
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A vertical piston-cylinder assembly containing 0.05 kg of ammonia,
initially a saturated vapor, is placed on a hot plate. Due to the
weight of the piston and the surrounding atmospheric pressure,
the pressure of the ammonia is 1.5 bars. Heating occurs slowly,
and the ammonia expands at constant pressure until the final
temperature is 25 ºC. Show the initial and final states on T-v and
P-v diagrams, and determine
!
(a)The volume occupied by the ammonia at each state, in m3.
(b)The work for the process, in kJ.

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A closed, rigid container of volume 0.5 m3 is placed on a
hot plate. Initially, the container holds a two-phase
mixture of saturated liquid water and saturated vapor
at P1 = 1 bar with a quality of 0.5. After heating, the
pressure in the container is P2 = 1.5 bar. Indicate the
initial and final states on a T-v diagram, and determine
!
(a)The temperature, in ºC, at each state
(b)The mass of vapor present at each state, in kg
(c)If heating continues, determine the pressure, in bar,
when the container holds only saturated vapor.
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A well-insulated rigid tank having a volume of 0.25 m3
contains saturated water vapor at 100 ºC. The water is
rapidly stirred until the pressure is 1.5 bars. Determine
the temperature at the final state, in ºC, and the work
during the process, in kJ.

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Water contained in a piston-cylinder assembly undergoes two
processes in series from an initial state where the pressure is 10
bar and the temperature is 400 ºC.
!
Process 1-2: The water is cooled as it is compressed at a constant pressure of
10 bar to the saturated vapor state.
Process 2-3: The water is cooled at constant volume to 150 ºC.
!
(a)Sketch both processes on T-v and P-v diagrams.
(b)For the overall process determine the work, in kJ/kg
(c) For the overall process determine the heat transfer, in kJ/kg.
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One pound of air undergoes a thermodynamic cycle consisting of three
processes.
!
Process 1-2: constant specific volume
Process 2-3: constant-temperature expansion
Process 3-1: constant-pressure compression
!
At state 1, the temperature is 300 K, and the pressure is 1 bar. At state
2, the pressure is 2 bars. Employing the ideal gas equation of state,
(a)Sketch the cycle on P-v coordinates.
(b)Determine the temperature at state 2, in K
(c) Determine the specific volume at state 3, in m3/kg