The material that is part of the system that absorbed heat is : The water
During Endothermic reactions heat is absorbed from the surroundings therefore the container becomes cold when touched as seen in the experiment.
The ammonium nitrate after been poured into the water at room temperature is not evenly distributed but after stirring with the stirring rod it becomes evenly distributed and its heat is been absorbed by the water, which causes the container to become cold to touch instead of becoming hot due to the high temperature of ammonium nitrate.
Hence we can conclude that The material that is part of the system that absorbed heat is : The water
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