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Module 8. Non equilibrium Thermodynamics. Lecture 8.1. Basic Postulates. Extensive property. Heat conducting bar. define properties. Specific property. NON-EQUILIRIBIUM THERMODYNAMICS. Steady State processes. (Stationary). Concept of Local thermodynamic eqlbm. NON-EQLBM THERMODYNAMICS.
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Module 8 Non equilibrium Thermodynamics
Lecture 8.1 Basic Postulates
Extensive property Heat conducting bar define properties Specific property NON-EQUILIRIBIUM THERMODYNAMICS Steady State processes. (Stationary) Concept of Local thermodynamic eqlbm
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.
NON-EQLBM THERMODYNAMICS Postulate II Entropy gen rate fluxes affinities
NON-EQLBM THERMODYNAMICS Purely “resistive” systems Fluxis dependent only onaffinity at any instant at that instant System has no “memory”-
NON-EQLBM THERMODYNAMICS Coupled Phenomenon Since Jk is 0 when affinities are zero,
NON-EQLBM THERMODYNAMICS where kinetic Coeff Relationship between affinity & flux from ‘other’ sciences Postulate III
NON-EQLBM THERMODYNAMICS Heat Flux : Momentum : Mass : Electricity :
NON-EQLBM THERMODYNAMICS Postulate IV Onsager theorem {in the absence of magnetic fields}
dx T1 T2 A x NON-EQLBM THERMODYNAMICS Entropy production in systems involving heat Flow
NON-EQLBM THERMODYNAMICS Entropy gen. per unit volume
dx I NON-EQLBM THERMODYNAMICS Entropy generation due to current flow : Heat transfer in element length
NON-EQLBM THERMODYNAMICS Resulting entropy production per unit volume
NON-EQLBM THERMODYNAMICS Total entropy prod / unit vol. with both electric & thermal gradients affinity affinity
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”
Analysis of thermo-electric circuits Above equations can be written as Substituting for affinities, the expressions derived earlier, we get
Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above Analysis of thermo-electric circuits We need to find values of the kinetic coeffs. from exptly obtainable data.
Lecture 8.2 Thermoelectric phenomena
Analysis of thermo-electric circuits The basic equations can be written as Substituting for affinities, the expressions derived earlier, we get
Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above Analysis of thermo-electric circuits We need to find values of the kinetic coeffs. from exptly obtainable data.
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
Analysis of thermo-electric circuits or Seebeck coeff. Using Onsager theorem
Analysis of thermo-electric circuits Further from the basic eqs for Je & JQ, for Je = 0 we get
Analysis of thermo-electric circuits For coupled systems, we define thermal conductivity as This gives
Analysis of thermo-electric circuits Substituting values of coeff. Lee, LQe, LeQ calculated above, we get
Analysis of thermo-electric circuits Using these expressions for various kinetic coeff in the basic eqs for fluxes we can write these as :
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
b a Je JQ, ab PETLIER EFFECT Under Isothermal Conditions Heat flux
PETLIER EFFECT Heat interaction with surroundings Peltier coeff. Kelvin Relation
JQ, surr Je Je JQ JQ dx THOMSON EFFECT Total energy flux thro′ conductor is Using the basic eq. for coupled flows
THOMSON EFFECT The heat interaction with the surroundings due to gradient in JE is
THOMSON EFFECT Since Je is constant thro′ the conductor
(for homogeneous material, above eq. becomes THOMSON EFFECT Using the basic eq. for coupled flows, viz. Thomson heat Joulean heat
THOMSON EFFECT reversible heating or cooling experienced due to current flowing thro′ a temp gradient Thomson coeff Comparing we get
THOMSON EFFECT We can also get a relationship between Peltier, Seebeck & Thomson coeff. by differentiating the exp. for ab derived earlier, viz.
Analysis of thermo-electric circuits Above equations can be written as Substituting for affinities, the expressions derived earlier, we get
Defining electrical conductivity as the elec. flux per unit pot. gradient under isothermal conditions we get from above Analysis of thermo-electric circuits We need to find values of the kinetic coeffs. from exptly obtainable data.
