University College - Chemistry Chem 112A Lecture Notes - Lecture 20: Galvanic Cell, Electrochemistry
14 Aug 2018
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Derivation of the relationship between g and maximum non-expansion work. We have seen that g is the key parameter in determining spontaneity in chemical processes. Interestingly, it also represents the maximum amount of non-expansion work that can be obtained from a process. Non-expansion work is any kind of work other than that due to expansion against an opposing pressure. To derive this relation, we first write the equation for g, expressed as an infinitesimal change: dg = dh tds (constant t) We then express the enthalpy change, dh, in terms of u and pv: Therefore, dg = du + pintdv tds dh = du + pintdv (constant p) Recall that du = dq + dw and, if a process is carried out reversibly, du = dqrev + dwrev. We consider the reversible case, because this yields maximum work. Therefore, dg = dqrev + dwrev + pintdv tds. But ds = dqrev/t, so tds = dqrev.
