Chapter 3 from Moran and Shapiro

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Properties ofPure Substances
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Pure Substance

• A substance that has a fixed (homogeneous and
  invariable) chemical composition throughout is
  called a pure substance.
• It may exist in more than one phase, but the
  chemical composition is the same in all phases.

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Pure Substance

• Pure means of uniform and invariable chemical
  composition (but more than one molecular type is
  allowed). This allows air to be a pure
  substance.
• All our substances will be pure. We will drop
  the use of the word. When we refer to a simple
  system we mean one filled with a pure
  substance--a simple, pure system.

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Examples of Pure Substance

• Water (solid, liquid, and vapor phases)
• Mixture of liquid water and water vapor
• Carbon Dioxide
• Nitrogen
• Homogeneous mixture of gases, such as air, as
  long as there is no change of phases.

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Multiple phases mixture of a Pure Substance
Water
Air
vapor
vapor
liquid
liquid
Not pure, different condensation temperatures for
different components
Pure
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Thermodynamic Properties

• We have discussed extensive properties such as m,
  U, and V (for volume) which depend on the size or
  extent of a system, and
• Intensive properties such as u, v, T, and P
  (sometimes we write a p for pressure, using P
  and p interchangeably) which are independent of
  system extent.

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Important Questions ..

• How many properties are needed to define the
  state of a system?
• How do we obtain those properties?

Equation of State Property Tables
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Review - State Postulate

• The number of independent intensive properties
  needed to characterize the state of a system is
  n1 where n is the number of relevant
  quasiequilibrium work modes.
• This is empirical, and is based on the
  experimental observation that there is one
  independent property for each way a systems
  energy can be independently varied.

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Simple system

• A simple system is defined as one for which only
  one quasiequilibrium work mode applies.
• Simple compressible systems
• Simple elastic systems
• Simple magnetic systems
• Simple electrostatic systems, etc.

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Compressible

• If we restrict our system to being compressible,
  we define what that quasiequilibrium work mode is

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For a simple system,

• We may write P P(v,T)
• or v v(P,T)
• or perhaps T T(P,v)

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For a simple, pure substance

• y0 y(y1,y2), or
• P P(v,T), v v(P,T), and T T(P,v)
• What do these equations define, in space?
• Equations used to relate properties are called
  Equations of State

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Equation of State

• Any two independent, intrinsic properties are
  sufficient to fix the intensive state of a simple
  substance.
• One of the major task of Thermodynamics is to
  develop the equations of state which relate
  properties at a give state of a substance.

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Ideal gas law is a simple equation of state
Ru universal gas constant 8.3144
(kPa-m3)/(kgmol-K) 1.545 (ft-lbf)/(lbmol-R)
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Phases of a Pure Substance

• Solid phase -- molecules are arranged in a 3D
  pattern (lattice).
• Liquid phase -- chunks of molecules float about
  each other, but maintain an orderly structure and
  relative positions within each chunk.
• Gas phase -- random motion, high energy level.

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Phase Equilibrium
p
p
p
p
p
vapor
liquid
liquid
vapor
liquid
ice
ice
heat
P 1 atm T 300 oC
P 1 atm T 0 oC
P 1 atm T 20 oC
P 1 atm T 100 oC
P 1 atm T -10 oC
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Phase-change Process

• Compressed liquid -- not about to evaporate
• Saturated liquid -- about to evaporate
• Saturated liquid-vapor mixture --two phase
• Saturated Vapor -- about to condense
• Superheated Vapor -- not about to condense

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T-v Diagram
o
T, C
Isobaric process P 1 atm
300
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Superheated vapor
2
3
Saturated mixture
100
4
Compressed liquid
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1
v
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P-T Diagram (Phase Diagram) of Pure Substances
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Isothermal Process
Compressed Liquid
Superheated Vapor
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Isobaric Process
Subcooled Liquid
a
Superheated Vapor
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Water Expands on Freezing!

• Ice floats on top of the water body (lakes,
  rivers, oceans, soft drinks, etc.).
• If ice sinks to the bottom (contracts on
  freezing), the suns ray may never reach the
  bottom ice layers.
• This will seriously disrupt marine life.

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Saturation Temperature and Pressure

• Tsat -- Temperature at which a phase change takes
  place at a given pressure.
• Psat -- Pressure at which a phase change takes
  place at a given temperature.

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Saturation Temperature
Tsat f (Psat) p 1atm 101.3
kPa, T 100 C p 500 kPa,
T 151.9 C
o
o
T and P are dependent during phase change Allow
us to control boiling temperature by
controlling the pressure (i.e., pressure cooker).
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Latent Heat

• Latent heat is the amount of energy absorbed or
  released during phase change
• Latent heat of fusion -- melting/freezing
  333.7 kJ/kg for 1 atm H2O
• Latent heat of vaporization --boiling/condensation
  2257.1 kJ/kg for 1
  atm H2O

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P-v Diagram
P
Subcooled or compressed liquid region
Critical point
Superheated region --substance is 100 vapor
Two-phase or saturation region -- gas and liquid
coexist
Saturated liquid line
Saturated vapor line
v
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P-v Diagram of a Pure Substance

SUPERHEATED
Isothermal process
v
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T-v Diagram of a Pure Substance
v
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Critical Supercritical

• The state beyond which there is no distinct
  vaporization process is called the critical
  point.
• At supercritical pressures, a substance gradually
  and uniformly expands from the liquid to vapor
  phase.
• Above the critical point, the phase transition
  from liquid to vapor is no longer discrete.

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Critical Point

• Point at which the saturated vapor and saturated
  liquid lines coincide.
• If T ? Tc or P ? Pc there is no clear
  distinction between the superheated vapor region
  and the compressed liquid region.

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Critical Point

• A point beyond which T ? Tc and a liquid-vapor
  transition is no longer possible at constant
  pressure. If T ? Tc , the substance cannot be
  liquefied, no matter how great the pressure.
• Substances in this region are sometimes known as
  fluids rather than as vapors or liquids.

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Vapor (Steam) Dome

• The dome-shaped region encompassing the
  two-phase, vapor-liquid equilibrium region.
• It is bordered by the saturated liquid line and
  the saturated vapor line, both of which end at
  the triple line and end at the critical point.
• The region below the vapor dome is also called
  saturated liquid-vapor region, wet region,
  two-phase region, or saturation region.

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THERMODYNAMIC TABLES
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STEAM IS NOT AN IDEAL GAS!
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Steam Tables

• Table A-1.1
• Saturation water -- temperature table
• Table A-1.2
• Saturation water -- pressure table
• Table A-1.3
• Superheated vapor

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For Water
P
Subcooled or compressed liquid region If
TTsat, p?psat If ppsat,T?Tsat
superheated region If TTsat , p?psat If ppsat
, TgtTsat
saturation region ppsat and TTsat
v
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Two properties are not independent in the vapor
dome (the two-phase region)

• The temperature and pressure are uniquely
  related. Knowing a T defines the P and vice
  versa.
• Use quality to determine the state in two-phase
  region.

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Quality is related to the horizontal differences
of P-v and T-v Diagrams

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Quality

• In a saturated liquid-vapor mixture, the mass
  fraction (not volume fraction) of the vapor phase
  is called the quality and is defined as
• The quality may have values between 0 (saturated
  liquid) and 1 (saturated vapor). It has no
  meaning in the compressed liquid or superheated
  vapor regions.

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What is v for something in the two-phase region?

v (1-x)vf xvg vf x(vg - vf)
vf xvfg
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Enthalpy in Two-Phase Region

• H U pV
• h u pv

h (1-x)hf xhg hf x(hg - hf) hf
xhfg
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Saturated Mixture

• In the saturated mixture region, the average
  value of any intensive property y is determined
  fromwhere f stands for saturated liquid and
  g for saturated vapor.

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Saturated Mixture

v vf x(vg - vf) vf xvfg u uf x(ug -
uf) uf xufg h hf x(hg - hf) hf
xhfg s sf x(sg - sf) sf xsfg
f saturated liquid g saturated vapor
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Saturated Water (temperature)
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Superheated Vapor
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Examples 3-2 thru 3-7 Steam Tables A-1.1 and
A-1.3
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TEAMPLAY
Complete the table below as a team. The
substance is water. Make sure everybody
understands how to do it!
P (MPa) T(?C) v(m3/kg) x (if appl.)
300 1.0
0.15 0.65
0.50 300
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TEAMPLAY
Complete the table below as a team. The
substance is water. Use linear interpolation if
needed.
P(MPa) T(?C) u (kJ/kg) x (if appl.)
7.0 0.0
7.0 1.0
7.0 0.05
7.0 600
7.0 100
7.0 460
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