Thermodynamic Systems: Definitions

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Thermodynamic Systems Definitions

• The first step in all problems in thermodynamics
  is to define a system, either a body or a defined
  region of space.
• Types of Systems
• Isolated no transfer of energy or matter across
  the system boundaries
• Closed possible energy exchange with the
  environment but no transfer of matter
• Open exchange of energy and matter with the
  environment
• Phase part of a system that is spatially
  uniform in its properties (density,
  composition,...)

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Thermodynamic Properties

• Thermodynamics is concerned with macroscopic
  properties of a body, not atomic properties
• Volume, surface tension, viscosity, etc
• Divided into two classes
• Intensive Properties (density, pressure,)
• specified at each point in the system
• spatially uniform at equilibrium
• Usually, specifying any 2 intensive variables
  defines the values of all other intensive
  variables
• Ij f(I1, I2) (j3,4,5,,n)
• This holds for mixtures as well, but composition
  must also be defined
• Ij f(I1, I2, x1,x2,,xm-1) (j3,4,5,,n)
• for an m-component mixture.

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Thermodynamic Properties

• Extensive Properties (volume, internal
  energy,...)
• Additive properties, in that the system property
  is the sum of the values of the constituent parts
• Usually, specifying any 2 intensive and one
  extensive (conveniently the system mass) defines
  the values of all other extensive variables
• Ej m f(I1, I2, x1,x2,,xm-1) (j3,4,5,,n
  )
• for an m-component mixture.
• The quotient Ei / m (molar volume, molar Gibbs
  energy) is an intensive variable, often called a
  specific property

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Phase Rule for Intensive Variables
SVNA-10.2

• For a system of ? phases and N species, the
  degree of freedom is
• F 2 - ? N
• variables that must be specified to fix the
  intensive state of the system at equilibrium
• Phase Rule Variables
• The system is characterized by T, P and (N-1)
  mole fractions for each phase
• Requires knowledge of 2 (N-1)? variables
• Phase Rule Equations
• At equilibrium ?i? ?i ? ?i ? for all
  N species
• These relations provide (?-1)N equations
• The difference is F 2 (N-1)? - (?-1)N
• 2- ? N

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The Phase Rule Applies across the Board
Example Phase diagram for CO2
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1.a Single Component VLE diagrams
Example Phase Behaviour of Diethylether
1) What is the (normal) boiling point of Et2O at
1 atm? 2) At what pressure will Et2O boil at T
0 oC?
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Phase Rule in VLE Single Component Systems

• For a two phase (p2) system of a single
  component (N1)
• F 2- ? N
• F 2- 2 1 1
• Therefore, for the single component system,
  specifying either T or P fixes all intensive
  variables.

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Correlation of Vapour Pressure Data

• Pisat, or the vapour pressure of component i, is
  commonly represented by Antoine Equation
  (Appendix B, Table B.2, SVNA 7th ed.)
• For acetonitrile (Component 1)
• For nitromethane (Component 2)
• These functions are the only component properties
  needed to characterize ideal VLE behaviour

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1b. VLE for Ideal Binary Mixtures

• (General Case)
• For a two phase (?2), binary system (N2)
• F 2- 2 2 2
• Therefore, for the binary case, two intensive
  variables must be specified to fix the state of
  the system.

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Phase Rule in VLE Binary Systems (Pxy diagrams)

• Example Acetonitrile (1) / Nitromethane (2)
  system

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Phase Rule in VLE Binary Systems (Txy diagrams)

• Alternately, we can specify a system pressure
  (often atmospheric) and examine VLE behaviour as
  a function of temperature and composition.

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VLE Calculations using Raoults Law

• Raoults Law for ideal phase behaviour relates
  the composition of liquid and vapour phases at
  equilibrium through the component vapour
  pressure, Pisat.
• Deriving this expression, relating the
  composition of each phase at a given P,T at
  equilibrium, will be the objective of the next
  two weeks of the course.
• Given the appropriate information, we can apply
  Raoults Law to the solution of 5 types of
  problems
• Dew Point Pressure and Temperature
• Bubble Point Pressure and Temperature
• P,T Flash

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Dew and Bubble Point Calculations

• Dew Point Pressure
• Given a vapour composition at a specified
  temperature, find the composition of the liquid
  in equilibrium
• Given T, y1, y2,... yn find P, x1, x2, ... xn
  
• Dew Point Temperature
• Given a vapour composition at a specified
  pressure, find the composition of the liquid in
  equilibrium
• Given P, y1, y2,... yn find T, x1, x2, ... xn
  
• Bubble Point Pressure
• Given a liquid composition at a specified
  temperature, find the composition of the vapour
  in equilibrium
• Given T, x1, x2, ... xn find P, y1, y2,... yn
  
• Bubble Point Temperature
• Given a vapour composition at a specified
  pressure, find the composition of the liquid in
  equilibrium
• Given P, x1, x2, ... xn find T, y1, y2,... yn