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I have a hard time determining what the system is in a reaction. Is there a way of easily identifying what it is or do we have to memorize that for certain examples one is the system and thus the other is the surroundings?
Usually, the system is the actual thing we are dealing with in the question. For example, if we are looking at the piston and identifying characteristics like work, heat, etc., the piston is the system, while the surroundings is what is supplying heat or what the system is losing heat to or the surroundings is what does work on the piston or what the piston is doing work on. I would say it is usually very easy to identify what is the system based off the question if it is not already explicitly identified.
Yes, the system vs. surrounding should not be something you have to memorize. As mentioned before, the system is simply the situation in question, such as a piston. Since the first law of thermodynamics states the conservation of energy, a change in energy of the system means a resultant change in surroundings to balance it out.
System vs. surrounding should be evident depending on the question that is given. It usually just determines whether a certain value is positive or negative in relation to the system at hand. For example, if the question states the surroundings gained x amount of energy, then energy left the system, so the energy change of the system would have to be negative while the surroundings would have a positive value in energy change.
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