1. Non equilibrium Thermodynamics
Module 8
Non equilibrium Thermodynamics

2. Lecture 8.1
Basic Postulates

3. NON-EQUILIRIBIUM THERMODYNAMICS
Steady State processes. (Stationary)
Concept of Local thermodynamic eqlbm
Heat conducting bar
define properties
Specific property
Extensive property

4. 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.

5. NON-EQLBM THERMODYNAMICS
Postulate II
Entropy gen rate
affinities
fluxes

6. NON-EQLBM THERMODYNAMICS
Purely “resistive” systems
Flux is dependent only on affinity
at any instant
at that instant
System has no “memory”-

7. NON-EQLBM THERMODYNAMICS
Coupled Phenomenon
Since Jk is 0 when affinities are zero,

8. NON-EQLBM THERMODYNAMICS
where
kinetic Coeff
Relationship between affinity & flux from ‘other’ sciences
Postulate III

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

10. NON-EQLBM THERMODYNAMICS
Postulate IV
Onsager theorem {in the absence of magnetic fields}

11. NON-EQLBM THERMODYNAMICS
Entropy production in systems involving heat Flow T1 T2 x dx A

12. NON-EQLBM THERMODYNAMICS
Entropy gen. per unit volume

13. NON-EQLBM THERMODYNAMICS

14. NON-EQLBM THERMODYNAMICS
Entropy generation due to current flow : I dx
Heat transfer in element length

15. NON-EQLBM THERMODYNAMICS
Resulting entropy production per unit volume

16. NON-EQLBM THERMODYNAMICS
Total entropy prod / unit vol. with both electric & thermal gradients
affinity
affinity

17. NON-EQLBM THERMODYNAMICS

18. 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”

19. Analysis of thermo-electric circuits
 Above equations can be written as
Substituting for affinities, the expressions derived earlier, we get

20. 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

21. End of Lecture

22. Thermoelectric phenomena
Lecture 8.2
Thermoelectric phenomena

23. Analysis of thermo-electric circuits
The basic equations can be written as
Substituting for affinities, the expressions derived earlier, we get

24. 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

25. 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

26. Analysis of thermo-electric circuitsor
Seebeck coeff.
Using Onsager theorem

27. Analysis of thermo-electric circuits
Further from the basic eqs for Je & JQ, for Je = 0
we get

28. Analysis of thermo-electric circuits
For coupled systems, we define thermal conductivity as
This gives

29. Analysis of thermo-electric circuits
Substituting values of coeff. Lee, LQe, LeQ calculated above, we get

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

31. 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

32. PETLIER EFFECT
Under Isothermal Conditions a b
JQ, ab Je
Heat flux

33. PETLIER EFFECT Heat interaction with surroundings Peltier coeff.
Kelvin Relation

34. PETLIER REFRIGERATOR

35. THOMSON EFFECT Total energy flux thro′ conductor is JQ, surr Jedx
Using the basic eq. for coupled flows

36. THOMSON EFFECT
The heat interaction with the surroundings due to gradient in JE is

37. THOMSON EFFECT
Since Je is constant thro′ the conductor

38. THOMSON EFFECT Using the basic eq. for coupled flows, viz.
above eq. becomes
(for homogeneous material,
Thomson heat
Joulean heat

39. THOMSON EFFECT
reversible heating or cooling experienced due to current flowing thro′ a temp gradient
Thomson coeff
Comparing we get

40. THOMSON EFFECT
We can also get a relationship between Peltier, Seebeck & Thomson coeff. by differentiating the exp. for ab derived earlier, viz.

41. End of Lecture

42. Analysis of thermo-electric circuits
 Above equations can be written as
Substituting for affinities, the expressions derived earlier, we get

43. 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