Question

Assume that the system is in equilibrium but that the energy does NOT have its smallest possible value consistent with the given entropy. Show by logical deduction that the entropy of the system could not be at maximum.

Answer 1

dG=dH-TdS ;

at equilibrium dG=0 ,which means dS=dH/T

in order to mamimise the entropy ,dH should be zero,which means there should be no heat flow into the system,however which means there is no fluctions allowed,if entropy is at it's maximum or if a little change occurs ,the entropy cannot be maximum.

Also thermodynamic equilibrium are considered on basis of system chosen.For absolute maximum of entropy is possible only when there is no surrounding or system is purely isolated system.This can be infered from the Second Law of Thermodynamics which says any spontaneous change will inccese the entropy . In an isolated system, when the system's entropy reaches the maximum, the system stays there because any further change would reduce entropy. therefor for absolute maximum entropy ,even the samllest value of energy should be consistent with given entropy.