1. Science of Thermodynamics

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1. Science of Thermodynamics

• Concerned with knowing the physical state of a
  system at equilibrium. A concise (mathematical)
  description of the systems state at different
  conditions allows us to calculate
• heat and work effects associated with a process
• the maximum work obtained or minimum work
  required for such a transformation
• whether a process can occur spontaneously
• In CHEM 244, thermodynamics was used to derive
  relationships amongst variables (P,T)that define
  a system at equilibrium.
• Heat engines, refrigeration cycles, steam power
  plants
• Dealt only with closed systems of constant
  composition (usually 1-component systems such as
  H2O)

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CHEE 311 - Thermodynamics of Mixtures

• Thermodynamics II is concerned with the
  properties of mixtures
• 1. Quantifying phase equilibrium behaviour
• At a given pressure and temperature, how many
  phases exist in a system?
• What is the composition of each phase?
• What are the thermodynamic properties
  (U,S,Cp,Vm,) of each phase and the system as a
  whole?
• 2. Describing systems that undergo chemical
  reactions
• Under specified conditions, to what extent does a
  reaction take place?
• What is the equilibrium composition of the
  system?
• How much heat is evolved/absorbed by the reaction
  and the mixing of reactants?

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Thermodynamic Systems

• 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

• 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 Diagram for CO2
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Ideal Mixture Behaviour

• Intermediate-boiling Systems, including Raoults
  Law Behaviour

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Non-Ideal Vapour-Liquid Equilibria (VLE)

• Systems having a minimum boiling azeotrope
• We also observe systems with a maximum boiling
  azeotrope.

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Non-Ideal VLE, LLE and VLLE

• Systems having partially miscible liquid phases

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Phase Behaviour of Diethylether
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1. Phase Rule for Intensive Variables SVNA-12.2

• 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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VLE in 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 Antoines Equation
• 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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VLE in Binary Systems

• 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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VLE in Binary Systems

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

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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

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1. Why all the theory?

• Parts of CHEE 311 are quite abstract (and,
  admittedly, a little dry). It is therefore
  important that the applications of thermodynamic
  theory be stressed. At the end of the course,
  you will understand the fundamental underpinning
  of thermodynamics and you will have used this
  knowledge to solve engineering problems.
• In this lecture, three areas that draw on an
  advanced knowledge of thermodynamics are
  described and demonstrated
• A. Describing and Predicting Phase Stability
• B. Coping with Non-Ideal Behaviour
• C. Extending Experimental Data to Describe
  Complex Systems

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Phase Stability

• Thermodynamics is concerned with the state and
  properties of a system under specific conditions.
• The stability of a given phase is of practical
  concern as conditions are sought to affect a
  change in
• the system.
• Under what conditions does a phase become
  unstable, resulting in a change of state?
• What property of the system determines phase
  stability?

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Phase Stability

• As an example of phase stability, consider the
  solid-vapour equilibrium of a system in contact
  with a heat bath.
• Increased volatilization raises U and S of the
  system.
• Increased crystallization decreases U and S.
• We will see that the equilibrium state is
  determined by a balance of order and disorder
  (U and S), such that free energy (F or G) is
  minimized.
• The state of a system for which the free energy
  is minimized is that for which the total entropy
  (heat bath and system of interest) is maximized.

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Stability of Polymer Solutions

• An issue of practical importance in polymer
  production is the recovery of material from
  solution.
• Consider a solution of 5 wt of an
  acrylonitrile-butadiene copolymer (34 AN, Mw
  250,000) in acetone.
• We want to separate the polymer from the solvent
  using a clean process that yields a manageable
  material.
• What means do we have for doing so?
• How are we generating instability in the original
  solution?
• Acetone NBR Acetone NBR

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Vapour Pressure of Pure Acetone and Water

• If presented with the problem of separating water
  and acetone in the mixture by distillation, what
  would you do?
• From the vapour pressure
• curves (vap-liq line for a
• pure component), it is clear
• that acetone and water
• have different volatility.
• Does this guarantee that
  distillation is possible?
• What tools do you have/need for
  design purposes?

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Pxy diagram for Acetone-Water Mixtures 25C

• Obviously, for distillation to be effective there
  must exist conditions where a liquid and a vapour
  exist at equilibrium, and the compositions of
  these phases must differ.
• According to the phase
• rule, for two phases to
• exist in the acetone-
• water system, we have
• __ degrees of freedom.

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Txy diagram for Acetone-Water Mixtures 1 bar

• If our system were fixed at atmospheric pressure,
  we would need to vary temperature - Txy diagram
  is more appropriate.

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Coping with Non-Ideal Behaviour

• The phase equilibrium tool you are most familiar
  with, Raoults Law, adequately describes systems
  that behave ideally. This refers to the strength
  and nature of interactions between components in
  a mixture.
• Few systems of practical importance are
  sufficiently ideal to warrant the use of Raoults
  Law.
• Suppose we wanted to separate by room temperature
  distillation the acetone-water mixture that we
  created in the isolation of our polymer.
• At 25C, between what two pressures will two
  phases exist in the acetone-water system
  containing equimolar quantities of the two
  components?
• Raoults Law Phase Diagram
• Pmax
• Pmin

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Txy diagram for Acetone-Water Mixtures 3.4 bar

• At higher pressure, the acetone-water system
  becomes increasingly non-ideal, as illustrated by
  the Txy diagram below.
• How do we describe these systems?
• Can we predict complications such as azeotropes?

Note the lack of experimental data above 123C -
How can we extrapolate to higher temperatures in
an accurate manner?
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Extending Experimental Data

• Design exercises become increasingly
• complex as additional components are added.
• Suppose our polymer solution was not
• NBRacetone, but
• NBRacetone2-butanone.
• How does the acetone-MEK-water
• system behave?
• There is limited data on ternary
  systems over a wide range of
  conditions
• A principle objective of
• CHEE 311 is to give
• you the tools to handle
• non-ideal mixtures of any
• composition through the use of models that
  generalize phase behaviour and programs that
  carry out tedious calculations.