Question

what is meant by the notion delta S_universe ? how are spontaniety of a process and equilibrium state of the process related to delta S_universe ? point out the limitation of entropy criterion of sponteniety.

Answer 1

Dear Student,

According to the second law of thermodynamics, in any spontaneous process there is always an increase in entropy of the universe or we can say that entropy of universe is increasing.
$$\begin{gathered} \mathrm{The}\mathrm{notion}∆{\mathrm{S}}_{\mathrm{universe}}\mathrm{implies}\mathrm{total}\mathrm{entropy}\mathrm{change}\mathrm{of}\mathrm{the}\mathrm{universe} \\ ∆{\mathrm{S}}_{\mathrm{universe}}=∆{\mathrm{S}}_{\mathrm{system}}+∆{\mathrm{S}}_{\mathrm{surroundings}}>0 \\ \mathrm{This}\mathrm{violates}\mathrm{the}\mathrm{conservation}\mathrm{laws}. \\ \mathrm{If}∆{\mathrm{S}}_{\mathrm{universe}}>0\mathrm{i}.\mathrm{e}.\mathrm{positive}\mathrm{then}\mathrm{the}\mathrm{reaction}\mathrm{is}\mathrm{spontaneous}\mathrm{in}\mathrm{the}\mathrm{direction}\mathrm{written}. \\ ∆{\mathrm{S}}_{\mathrm{universe}}<0\mathrm{i}.\mathrm{e}.\mathrm{negative}\mathrm{then}\mathrm{the}\mathrm{proess}\mathrm{is}\mathrm{spontaneous}\mathrm{in}\mathrm{opposite}\mathrm{direction}. \\ ∆{\mathrm{S}}_{\mathrm{universe}}=0\mathrm{System}\mathrm{is}\mathrm{at}\mathrm{equilibrium} \\ \mathrm{Limitations}: \\ \mathrm{The}\mathrm{main}\mathrm{drwaback}\mathrm{of}\mathrm{entropy}\mathrm{criterion}\mathrm{is}\mathrm{that}∆{\mathrm{S}}_{\mathrm{surr}}\mathrm{cannot}\mathrm{be}\mathrm{easily}\mathrm{calculated}\mathrm{for}\mathrm{different}\mathrm{processes}\mathrm{occuring}\mathrm{in}\mathrm{the}\mathrm{universe}. \\ \left(\mathrm{i}\right)∆\mathrm{S}>0\mathrm{because}\mathrm{two}\mathrm{gaseous}\mathrm{moles}\mathrm{of}\mathrm{reactants}\mathrm{are}\mathrm{converted}\mathrm{into}\mathrm{four}\mathrm{gaseous}\mathrm{moles}. \\ \left(\mathrm{ii}\right)∆\mathrm{S}<0\mathrm{because}3\mathrm{moles}\mathrm{of}\mathrm{aqueous}\mathrm{ions}\mathrm{are}\mathrm{getting}\mathrm{converted}\mathrm{into}2\mathrm{moles}\mathrm{of}\mathrm{ions}\mathrm{in}\mathrm{aqueous}\mathrm{medium}. \end{gathered}$$