INTRODUCTION AND APPLICATIONS OF NON-EQUILIBRIUM THERMODYNAMICS represented by Varinder Khepar ( PhD Chemistry), Punjab Agricultural University, Ludhiana, 141004

1. NON-EQUILIBRIUM
THERMODYNAMICS
VARINDER KHEPAR
Ph.D. Chemistry

2. CONTENTS
Introduction
Flux and gradient
Phenomenological laws
Coupled reaction
Non- coupled reaction
Entropy production

3.  INTRODUCTION
 Non-equilibrium thermodynamics is a
branch of thermodynamics that deals with
physical systems which are not in
thermodynamic equilibrium
 Almost all systems found in nature are
irreversible and are not in
thermodynamic equilibrium

4. FLUX AND GRADIENT
All irreversible process, involved transfer of heat, mass,
momentum or electric charge.
The quantity which is transported is called flux and the
driving force for the flux is called gradient.
It can be represented by
J = LX
Where J is flux
X is gradient
L is transport coefficient

5. S.No. Flux Driving force
1 Heat Temperature
2 Mass Concentration
3 Momentum Reduced mass
4 Electric current Potential
Table: Driving force for different flux

6. These transport phenomenon can be
represented by different equations
JQ = -K dT/dX
Jm = -D dC/dX
JM = -µ dµ/dX
Je = -λ dE/dX
Fourier’s law
Fick’s law
Newton’s law
Ohm’s law

7.  K, D, µ, λ are transport coefficients. These four laws are
called Phenomenological laws.
 When more than one solute is present then movement of
second solute is also influenced by movement of first
solute.
 In that case, rate of change of solute concentration is
represented by
dm1/dt = D dc1/dX + E dc2/dX
dm2/dt = F dc2/dX + G dc1/dX
Similarly, for second solute
D, E, F, G are diffusion coefficients

8. So the equation J = LX can be modified as
J = Li1X1 + Li2X2 + _ _ _ _ _ _LinXn
Where, I = 1, 2, _ _ _ _ _ _
This equation is called linear phenomenological
relation
Lii is called primary phenomenological coefficients and Lij is
called Onsagar’s phenomenological coefficients
In Onsagar’s phenomenological coefficients, subscript ‘I’
denotes the flux and ‘j’ denotes the driving force
Onsagar shows that for multicomponent system
This is called Onsagar reciprocal relationLii = Lij

9. 1. In living system, unfavorable reactions takes place with
other reaction which leaves sufficient amount of energy –
so, this type of reactions are called coupled reactions
e.g. Conversion of glucose to glucose-6-phosphate is not
favored thermodynamically and this reaction is coupled with
reaction ATP to ADP.
∆G = -30.5 KJ/mole
2. Conversion of creatine phosphate into creatine is
coupled with change of ADP into ATP. The ∆G is negative
for this reaction.
Coupled reaction

10. Difference between coupled and non-coupled
reaction
If A → B and B → C , reaction conversion occur
independently
But A → C does not occur
Then number of elementary reactions are same as
number of independent reactions are known as NON
–COUPLED REACTION
If A → C is possible
Then number of elementary reactions (3) are greater
than number of independent reactions (2) are known
as COUPLED REACTION

11. ENTROPY PRODUCTION
Let a system have n flows, J1, J2 ……Jn
And forces are X1, X2…….Xn
If system attain the state of equilibrium , then entropy production is
Where,σ = entropy production per unit time per unit volume
For two component system, entropy production is
σ = J1X1 + J2X2 ………….(1)
As, J1 = L11X1 + L12X2 and J2 = L21X1 + L22X2 , put in eq. (1), becomes

12. σ = L11X1
2 +( L12+ L21)X1 X2+ L22X2
2 > 0
either X1 is zero or X2 is zero, then
L11X1
2 > 0 and L22X2
2 > 0
It means both primary coefficients must be positive , then
determinant is
(L11 L22 - L12 L21) > 0
According to Onsagar reciprocal relation
L12 = L21 , then
L11 L22 > L12
2
Lij < (Lii Ljj )1/2

13. Thank you