Q. How can you apply Onsager
Reciprocity relation to Peltier Effect?
In case of Peltier effect, when a current flows because of an external potential
difference, between the two junctions of two conducting wires joined at two ends
(i.e., a thermocouple), there occurs a heat flow from one junction to another so
that one junction gets colder while the other gets hotter. In this process, the
temperature difference and the electrical potential difference (between the two
junctions) act as the generalised forces while this heat flow and the current
flow are the generalised flows. Peltier effect discusses the dependence of the
heat flow on the potential difference (a cross phenomena) while the associated
phenomenon of Seebeck effect deals with the reciprocal dependence of the current
flow on the temperature difference. The coefficients for these two coupled
effects are thus directly related by the Onsager reciprocity relation, as was
found in case of the experimental first Thomson relation (P
= S.T) relating the two coefficients.
Q. Explain the concepts of forced flow
and coupled flow.
Forced flow: Any generalised flow in non-equilibrium thermodynamics such as heat
flow, diffusion or chemical reaction is the result of a generalised force such
as inverse-temperature difference, chemical potential difference or chemical
affinity. Thus, any generalised flow may be termed as a forced flow, i.e., a
result of some generalised force.
Coupled flow: Sometimes, a pair of generalised forces, such as heat flow and
diffusion, may arise as a reult of a pair of generalised forces, say
inverse-temperature difference and difference in chemical potential. In such
cases, rate of either of the flows are dependent on the extent of each of the
forces, generally dependent in a linear way. Another example is the simultaneous
occurrence of two or more chemical reactions. In case of coupled flows, one of
the flows, say one reaction, may even occur in a direction contrarary to its own
generalised force, provided the other flow occurs normally.
Q. State the Onsager reciprocity
relation and discuss its significance.
Onsager reciprocity relation states that when two generalised forces C1
and C2 are simultaneously present, the
cross-coefficients in the two linear relations for the properly defined
corresponding flows (J1 and J2) are equal. Thus if, for a
system with two generalised forces, the forces and flows are defined in a way
such that diS/dt (the rate of internal entropy production) equals J1C1
+ J2C2, and if the set of
phenomenological linear relations are J1 = L11C1
+ L12C2 and J2
= L21C1 + L22C2,
then the two cross-coefficients would be equal, i.e., L12 = L21.
The Onsager relation relates the two phenomenological cross-coefficients for a
coupled pair of flows: it states that the two cross-coefficients relating the
1st flow with the 2nd force, and the 2nd force with the 1st flow are equal to
each other. So, from knowledge of one of these coefficients, the value of the
other could be found without actually measuring it. It also implies that if one
generalised force contributes to another kind of flow, its corresponding flow
will also get contributed by the other kind of generalised force in the same
manner.
Q. Discuss the application of Onsager
reciprocity relation in a coupled thermoelectric system.
In case of a two-conductor thermocouple with its two junctions maintained at two
different temperatures, and with also an external electrical potential
difference artificially introduced between the two junctions, the Seebeck and
the Peltier effects will be simultaneously present. Thus, this is a coupled
system with two generalised forces (electrical potential difference and
temperature difference) and two resulting flows (heat flow and current flow).
Here the Seebeck effect deals the dependence of the electrical flow on the
thermal force (temperature difference between the two junctions), whereas the
Peltier effect deals with the dependence of the thermal flow on the electrical
force (externally induced potential difference between the two junctions). If
the two forces and the two flows are properly defined satisfying diS/dt
= J1C1 + J2C2,
the two coefficients for these two effects would have been equal.
However the mathematical relations for the Seebeck and the Peltier effects have
not in practice been defined obeying this criterion, and so the defined Seebeck
and Peltier coefficients (S and P respectively) are
only proportional to each other obeying the first Thomson relation (P
= T.S, with Kelvin temperature T being the proportionality constant.