Module 8

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Module 8

• Non equilibrium Thermodynamics

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Lecture 8.1

• Basic Postulates

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NON-EQUILIRIBIUM THERMODYNAMICS
Steady State processes. (Stationary)
Concept of Local thermodynamic eqlbm
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NON-EQLBM THERMODYNAMICS
Postulate I
Although system as a whole is not in eqlbm.,
arbitrary small elements of it are in local
thermodynamic eqlbm have state fns. which
depend on state parameters through the same
relationships as in the case of eqlbm states in
classical eqlbm thermodynamics.
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NON-EQLBM THERMODYNAMICS
Postulate II
Entropy gen rate
fluxes
affinities
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NON-EQLBM THERMODYNAMICS
Purely resistive systems
Flux is dependent only on affinity
at any instant
at that instant
System has no memory-
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NON-EQLBM THERMODYNAMICS
Coupled Phenomenon
Since Jk is 0 when affinities are zero,
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NON-EQLBM THERMODYNAMICS
where
kinetic Coeff
Relationship between affinity flux from other
sciences
Postulate III
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NON-EQLBM THERMODYNAMICS
Heat Flux
Momentum
Mass
Electricity
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NON-EQLBM THERMODYNAMICS

• Postulate IV
• Onsager theorem in the absence of magnetic
  fields

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NON-EQLBM THERMODYNAMICS

• Entropy production in systems involving heat Flow

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NON-EQLBM THERMODYNAMICS
Entropy gen. per unit volume
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NON-EQLBM THERMODYNAMICS
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NON-EQLBM THERMODYNAMICS
Entropy generation due to current flow
Heat transfer in element length
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NON-EQLBM THERMODYNAMICS
Resulting entropy production per unit volume
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NON-EQLBM THERMODYNAMICS
Total entropy prod / unit vol. with both electric
thermal gradients
affinity
affinity
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NON-EQLBM THERMODYNAMICS
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Analysis of thermo-electric circuits

• Addl. Assumption Thermo electric phenomena can
  be taken as LINEAR RESISTIVE SYSTEMS

higher order terms negligible
Here K 1,2 corresp to heat flux Q, elec flux
e
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Analysis of thermo-electric circuits

• ? Above equations can be written as

Substituting for affinities, the expressions
derived earlier, we get
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Analysis of thermo-electric circuits
We need to find values of the kinetic coeffs.
from exptly obtainable data.
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End of Lecture
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Lecture 8.2

• Thermoelectric phenomena

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Analysis of thermo-electric circuits

• The basic equations can be written as

Substituting for affinities, the expressions
derived earlier, we get
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Analysis of thermo-electric circuits
We need to find values of the kinetic coeffs.
from exptly obtainable data.
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Analysis of thermo-electric circuits

• Consider the situation, under coupled flow
  conditions, when there is no current in the
  material, i.e. Je0. Using the above expression
  for Je we get

Seebeck effect
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Analysis of thermo-electric circuits
or
Seebeck coeff.
Using Onsager theorem
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Analysis of thermo-electric circuits

• Further from the basic eqs for Je JQ, for Je
  0
• we get

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Analysis of thermo-electric circuits

• For coupled systems, we define thermal
  conductivity as

This gives
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Analysis of thermo-electric circuits

• Substituting values of coeff. Lee, LQe, LeQ
  calculated above, we get

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Analysis of thermo-electric circuits
Using these expressions for various kinetic coeff
in the basic eqs for fluxes we can write these as

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Analysis of thermo-electric circuits

• We can also rewrite these with fluxes expressed
  as fns of corresponding affinities alone

Using these eqs. we can analyze the effect of
coupling on the primary flows
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PETLIER EFFECT

• Under Isothermal Conditions

Heat flux
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PETLIER EFFECT
Heat interaction with surroundings
Peltier coeff.
Kelvin Relation
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PETLIER REFRIGERATOR
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THOMSON EFFECT
Total energy flux thro' conductor is
Using the basic eq. for coupled flows
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THOMSON EFFECT
The heat interaction with the surroundings due to
gradient in JE is
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THOMSON EFFECT
Since Je is constant thro' the conductor
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THOMSON EFFECT
Using the basic eq. for coupled flows, viz.
Thomson heat
Joulean heat
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THOMSON EFFECT
reversible heating or cooling experienced due to
current flowing thro' a temp gradient
Thomson coeff
Comparing we get
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THOMSON EFFECT
We can also get a relationship between Peltier,
Seebeck Thomson coeff. by differentiating the
exp. for ?ab derived earlier, viz.
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End of Lecture
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Analysis of thermo-electric circuits

• ? Above equations can be written as

Substituting for affinities, the expressions
derived earlier, we get
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Analysis of thermo-electric circuits
We need to find values of the kinetic coeffs.
from exptly obtainable data.