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The system is the reaction itself, and the surroundings are the "chamber". So if the reaction is endothermic, the surroundings should lower in temperature while the system, the reaction, gains heat. If the reaction is exothermic, the surroundings should increase in temperature while the system (rxn) loses heat.
The calorimeter often consists of the container and a solvent(typically water). The system refers to the chemical reaction happening right inside the solution, and the surroundings would be the solvent(the water) and the container.
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