Properties of Pure Substances

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Chapter 2
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Properties of Pure Substances

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Chapter Summary
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Simple Pure Substance
• Phase Change Process
• T-v, P-v, P-T Diagram and P-v-T Surfaces
• Vapour Pressure and Phase Equilibrium
• Property Tables
• Ideal Gas Equation of State
• Compressibility Factor
• Other Equation of States

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Why Properties Important
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Recall Definition of Thermodynamics Science of
  Relationship between heat, work properties of
  substance which causes changes in state
• Why Study Thermodynamics To produce work from
  heat (power plant) Move heat around by applying
  work (refrigerator)
• Since to produce work requires change of state
  and to change state requires change of properties
  Need to know how properties vary

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Simple Pure Substance
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• A Homogeneous Substance is a substance which has
  uniform thermodynamics property throughout.
• A substance that has a homogeneous and invariable
  chemical composition is called a pure substance.
• Pure Substance doesnt have to be of single
  chemical composition or compound.
• Pure Substance doesnt have to be of single phase
• State Postulate The equilibrium state of simple
  pure substance can be determined by specifying
  any two independent intensive properties

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Intensive Properties
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Pressure (Pa)
• Temperature (K)
• Specific Volume, v V/m 1/? (m3/kg)
• Specific Enthalpy, h (kJ/kg)
• Specific Internal Energy, u (kJ/kg)
• Specific Entropy, s (kJ/kgK)
• For simple compressible substance the state is
  fully determined by specifying 2 of the
  properties

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Phases of A Pure Substance
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• A Phase is identified as having a distinct
  molecular arrangement that is homogeneous
  throughout and separated from the others by
  easily identifiable boundary surfaces.
• Solid Phase Molecules arranged in 3D lattice,
  Molecules closely packed together, Strong
  molecular bonds, Molecules oscillates about
  equilibrium position, Lowest energy level
• Liquid Phase Same molecular spacing as solid,
  Molecules not fixed relative to each other.
• Gas Phase No molecular order, Molecules far
  apart, Continuously moving at random, Weakest
  bond, Highest Energy Level

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Phase Change Process
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• A pure substance exists in different phases
  depending on its energy level. In the liquid
  phase, a substance that is not about to vaporize
  is called a compressed or subcooled liquid.
• A liquid which is about to vaporize is called a
  saturated liquid
• In the gas phase, a substance that is not about
  to condense is called a superheated vapor.
• A gas which is about to condense is called a
  saturated vapour

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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Phase Change Process
T-v Diagram
v V/m
Constant Pressure Heating Process
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Phase Change Process
gt
Constant Pressure Heating Process at Different
Pressure
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Saturation Temperature and Pressure
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Saturation Temperature The temperature at which
  liquid starts boiling or change phase at a
  specific pressure gt Tsat(P)
• Saturation Pressure The pressure at which
  liquid change phase at a specific temperature
  gt Psat(T)
• During phase change process Pressure and
  Temperature are dependent properties

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Property Diagram (Tv)
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• A diagram giving relationship between 2
  independent properties e.g. Tv, Pv and PT
• Tv Diagram

Compressed Liquid T lt Tsat(P) Saturated
Region T Tsat(P) Superheated Region T gt Tsat(P)
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Property Diagram (Pv)
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Pv Diagram

Compressed Liquid P gt Psat(T) Saturated
Region P Psat(T) Superheated Region P lt Psat(T)
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Pv Diagram with Solid Phase
Substance that contract on freezing
Substance that expand on freezing
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
PvT Surface
Substance that contract on freezing
Substance that expand on freezing
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
PT Diagram (Phase Diagram)
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Vapour Pressure Phase Equilibrium
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Vapour Pressure, Pv Pressure of water vapour
  
• Patm Pair Pv
• Pv ?Psat(T)
• ? relative humidity of the air
• Condition for phase equilibrium Vapour pressure
  in the air must be equal to the saturation
  pressure of water at the water temperature
• Pv Psat(T)

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Property Tables
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Because of the complexity of the relationship
  between properties it is usually impossible to
  represent them in simple equation gt Thus usually
  properties relationship are normally tabulated
• Usually in term of 2 independent properties that
  are measurable. E.g. P and T.
• Table A4 and A5 Saturated water Temperature and
  Pressure (In saturated region P T are
  dependent)
• Table A6 Superheated Vapour
• Table A7 Compressed Liquid

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Saturated Liquid Saturated Vapour
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Table A4
vfg vg - vf
hfg hg - hf Enthalpy of Vapourization
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Saturated Liquid-Vapour Mixture

• In a saturated liquid-vapor mixture, the mass
  fraction of the vapor phase is called the quality
  and is defined as
• x 0 (saturated liquid) and x 1
  (saturated vapor)
• In the saturated mixture region, the average
  value of any intensive property y is determined
  from
• where f stands for saturated liquid and g for
  saturated vapor.

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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Saturated Liquid-Vapour Mixture
x (vav-vf)/(vg-vf)
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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Superheated Vapour

• Region above saturated vapour line
• P lt Psat (T)
• T gt Tsat (P)
• v gt vg
• u gt ug
• h gt hg

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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Compressed Liquid

• P gt Psat (T)
• T lt Tsat (P)
• v lt vf
• u lt uf
• h lt hf
• general approximation is to treat as a saturated
  liquid at the given temperature, that is,where
  y stands for v, u, or h.

• For enthalpy
• h hf_at_T vf (P-Psat(T))

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Equation of State
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• An equation giving simple relations among the
  properties
• Any equation that relates the pressure,
  temperature and specific volume of substance is
  called Equation of State
• It predicts P-v-T behaviour of the substance

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Ideal Gas Equation of State
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• The simplest and best-known equation of state is
  the ideal-gas equation of state, given
  aswhere R is the gas constant. Caution should
  be exercised in using this relation since an
  ideal gas is a fictitious substance. Real gases
  exhibit ideal-gas behaviour at relatively low
  pressures and high temperatures.

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Region Where Steam Can be Treated as Ideal Gas
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
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Compressibility Factor
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• The deviation from ideal-gas behavior can be
  properly accounted for by using the
  compressibility factor Z, defined as

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Compressibility Factor
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• The Z factor is approximately the same for all
  gases at the same reduced temperature and reduced
  pressure, which are defined aswhere Pcr and
  Tcr are the critical pressure and temperature,
  respectively. This is known as the principle of
  corresponding states.

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Compressibility Factor
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
(Continued from previous slide)

• When either P or T is unknown, Z can be
  determined from the compressibility chart with
  the help of the pseudo-reduced specific volume,
  defined as

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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Compressibility Factor For Various Gasses
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Other Equations of State
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• The P-v-T behavior of substances can be
  represented more accurately by the more complex
  equations of state. Three of the best known are
  van der Waalswhere

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Other Equations of State (cont..)
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Beattie-Bridgeman where

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Other Equations of State (cont..)
Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances

• Benedict-Webb-Rubin
• Virial Equation of State

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Department of Mechanical Engineering
Dr Zamri

Chap. 2 Properties of Pure Substances
Comparisons of Diff. Equations of State for
Nitrogen