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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 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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Postulate II Entropy gen rate affinities fluxes

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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 J k is 0 when affinities are zero,

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where kinetic Coeff Postulate III Relationship between affinity & flux from other sciences

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NON-EQLBM THERMODYNAMICS Heat Flux : Momentum : Mass : Electricity :

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Postulate IV Onsager theorem {in the absence of magnetic fields}

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Entropy production in systems involving heat Flow T1T1 T2T2 x dx A

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NON-EQLBM THERMODYNAMICS Entropy gen. per unit volume

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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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Total entropy prod / unit vol. with both electric & thermal gradients 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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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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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. J e =0. Using the above expression for J e we get Seebeck effect

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

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Further from the basic eqs for J e & J Q, for J e = 0 we get

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For coupled systems, we define thermal conductivity as This gives

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Substituting values of coeff. L ee, L Qe, L eQ calculated above, we get

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Using these expressions for various kinetic coeff in the basic eqs for fluxes we can write these as :

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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 J Q, ab JeJe 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 J Q, surr JeJe JQJQ JeJe JQJQ dx Using the basic eq. for coupled flows

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THOMSON EFFECT The heat interaction with the surroundings due to gradient in J E is

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Since J e 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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