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I experimentally calculated the specific heat capacities of solutions by heating them in a copper calorimeter- will I need to take the specific heat capacity of copper into account during my calculations?

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Yes because a copper calorimeter might have a significant thermal capacity ie heat is required to raise its temperature.

More recently materials like polystyrene are used for the containing vessel as polystyrene has a low specific heat capacity and also is a comparatively good insulator.

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