entropy changes in open, closed vs isolated systems

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km1865

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I just wanted to clear up the following:

in isolated systems (no matter or energy exchange), the entropy must ALWAYS increase right? (I know it can never decrease for these systems, but can it remain zero.. like if its a reversible process in an isolated system, the entropy change wont necessarily increase right? it would be zero in this case (the entropy change NOT the value of entropy itself?)

in closed and open systems, the entropy changes can be either way.. so in these thermodynamic systems the entropy can increase, decrease (provided that the entropy of the surroundings increases to compensate) OR remain the same?

Also, I'm a little confused about the equation dS is greater than/ equal to Q/T.. why must dS be EQUAL to the quantity Q/T for reversible processes.. shouldn't it be zero since entropy DOES NOT change for reversible processes

Thanks! Hopefully the MCAT will not go into these technicalities, but it would be a stupid question to get wrong if it comes up

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