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So basically, U = q + w refers to the fact that it is the total energy that the system is involved with, i.e the energy from the heat generated or loss plus the energy of the work done on or against the system
It's important to remember than delta U is the change in internal energy rather than just the internal energy of a system. It's a state function that looks at how the internal energy of a system changes over the course of a process (if a system releases or absorbs energy).
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