Explain the role of thermodynamics in the extraction of elements. Or,explain how thermodynamics is helpful in the selection of a reducing agent for metallurgical operations.

(N/A) To understand the theory of metallurgical transformations,the Gibb's free energy change $(\Delta G)$ is the most significant term. For any reaction,the Gibb's free energy change is given by:
$\Delta G = \Delta H - T \Delta S$
Where,$\Delta H$ is the enthalpy change,$T$ is the temperature in Kelvin,and $\Delta S$ is the entropy change for the process.
The criterion for the feasibility of a thermal reduction is that at a given temperature,the Gibb's free energy change for the reaction must be negative. When the value of $\Delta G$ is negative,the reaction will proceed.
Under the following conditions,the value of $\Delta G$ is negative:
$(i)$ If $\Delta S$ is positive,on increasing the temperature $(T)$,the value of $T \Delta S$ increases such that $\Delta H < T \Delta S$. In this situation,$\Delta G$ becomes negative on increasing the temperature.
$(ii)$ If the coupling of two reactions (reduction and oxidation) results in a negative value of $\Delta G$ for the overall reaction,the final reaction becomes feasible. Such coupling can be understood by studying plots of $\Delta_r G^\circ$ versus $T$ for the formation of oxides. These plots are drawn for free energy changes when one gram mole of oxygen is consumed.
The graphical representation of Gibb's free energy versus temperature was first used by $H.J.T. Ellingham$,which provides the basis for considering the choice of a reducing agent in the reduction of oxides. This is known as the $Ellingham$ diagram. Such diagrams help in predicting the feasibility of the thermal reduction of an ore.