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The equation for entropy is q rev/ T. The heat lost by the system will be gained by the surroundings and vice versa. So on the equations for entropy will have -q. Furthermore, when the system loses entropy, the surroundings gain it. Hope this helps!
I think usually the signs for delta s in the surroundings and system depend on the reaction itself. I believe the surroundings and the system would essentially be the opposites of each other. As stated above, delta s is basically q/T, so we could determine signs from heat either absorbed or released.
The signs of the system and surrounding are opposite to one another usually when one loses and the other gains heat. For example, if the surroundings are losing heat, the system will gain heat, making delta Ssurr negative and delta Ssys positive.
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