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At constant volume, delta u = q because there is no work being done. Work requires that there is a change in volume, as the book defines work as "the process of achieving motion against an opposing force". At constant pressure, delta u = q - P*delta V because you can rearrange the equation delta h = delta u + P*delta V (change in enthalpy at constant pressure) to find delta u.
You are correct. For constant volume, since there is no volume change, there is no work being done, so internal energy would just equal heat. (U=q) For constant pressure, there can be both heat transfer and work being done, so then U=q+w. Since in this case there is constant pressure, then heat is just equal to enthalpy (q= delta H). So then U=delta H + work, which is also U= (delta H) - P*(delta V)
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