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 d_iS/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 d_iS/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.