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Summary of First and Second Law by Clausius

Clausius summarized the thermodynamics laws 1st &2nd in the following sentences.

(a) The energy of the universe remains constant.

(b) The entropy of the universe tends towards a maximum.

In an isolated system, the entropy always increases and it is maximum at   equilibrium state.

s isol = f(x)

where x is a parameter.

S isol = s max

at a point x = x eq

where X eq is the value of the parameter x at equilibrium state

So                                dS / dx = 0 at x = x eq represents e equilibrium state.

 

Thus dS = 0 at equilibrium state, it means at equilibrium state any conceivable change in entropy would be zero.