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In a reaction there are variables that change. If the pressure is constant, the temperature or volume or number of moles or other things could be changing. In fact if the pressure is constant it would be an isobaric process where heat could be used to both do work and change the internal energy of the system.
A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in a liquid solution. In that case, the gaseous pressure above the solution remains constant, and we say that the reaction is occurring under conditions of constant pressure.
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