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The calorimeter can also be apart of the surroundings, as some calorimeters absorb some of the heat released in the reaction. In general though, the water is the surrounding and whatever you're adding is the system.
It depends on the context of the problem but water is considered the surroundings if something is placed in the water. However, the amount of energy absorbed by a calorimeter can be used to calculate heat released to the surroundings as well.
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