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I'm confused about the sign of entropy change since q is negative when it is released by a system and positive when it is gained by the system's surroundings. That being said, when calculating the change in entropy how do you know what sign to use? Also how does positive entropy differ from negative entropy?
Just to edit what you wrote, Q is positive when the system absorbs energy. The change in entropy depends on whether heat is released or not. Sometimes its best to use your intuition on whether its negative or not. For example, the heat of vaporization (or the change in entropy from liquid to gas) of water is a very high positive value. This is obvious because it takes a long time on the stove to heat the water to make it boil, the system is absorbing energy.
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