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**Non equilibrium Thermodynamics**

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 Heat conducting bar define properties Specific property Extensive property

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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 affinities fluxes

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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 T1 T2 x dx A

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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 : I dx 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. Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above

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End of Lecture

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**Thermoelectric phenomena**

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. Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above

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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. Je=0. 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 a b JQ, ab Je 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 JQ, surr Je**

dx 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.**

above eq. becomes (for homogeneous material, 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. Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above

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Lecture slides by Mehmet Kanoglu

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