For a process to be in equilibrium, it is necessary that:

Δ S_{s y s t e m} = Δ S_{s u r r o u n d i n g}

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Δ S_{s y s t e m} = - Δ S_{s u r r o u n d i n g}

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Δ S_{s y s t e m} = 0

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Δ S_{s u r r o u n d i n g} = 0

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Solution

The correct option is A $Δ S_{s y s t e m} = - Δ S_{s u r r o u n d i n g}$
At the equlibrium condition, the total entropy change becomes zero,
so, we have $Δ S_{s y s t e m} + Δ S_{s u r r .} = 0$
and $Δ S_{s y s t e m} = - Δ S_{s u r r .}$

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