[Ciubba]

I want to make sure that my understanding of heat at constant temperature versus constant pressure is correct.

As I understand it, enthalpy is "arbitrarily" defined as H=U+PV which means that ΔH=ΔU+ΔPV+PΔV+ΔPΔV

Internal energy is defined as U=q+w and work=-PΔV

Thus, at constant pressure: ΔUp=qp-PΔV; at constant volume: ΔUv=qv (work doesn't exist at constant volume) and, finally, at constant pressure: ΔH=ΔU+PΔV. This implies that H=qp.

Based on this, is it safe to say that ΔUp≠ΔUv and that qp+wp=qv? I'm also curious if it can be said that ΔHv=qv.

[Ciubba]

Looking back at this, it is obvious that qp+wp=qv. There is also a typo; it should say that ΔUv=ΔUp rather than ΔUv≠ΔUp

I'm still not sure if it's appropriate to say that ΔHv=qv.