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Delta U is given by the energy supplied to the system by heat (q) plus the energy transferred by compression work (w). When the system is under constant pressure, q is equal to Delta H, so Delta H becomes a part of how Delta U is calculated.
Delta U indicates internal energy, and is composed of both delta H (enthalpy) and work. When no work is done, Delta U is equal to delta H. When no energy is transferred through heat and delta H is therefore 0, then Delta U is equal to work.
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