I've got a few issues with the topic of thermodynamic expansion, ΔU, etc.
With ΔU=q+w, this w is to mean work done on the system (positive contribution to ΔU) minus work done by the system (i.e. negative contribution to internal energy), so then how do we summarize this for cases of expansion? Because if we say that ΔU=q-Δ(pV) then this suggests that ΔH=q even without constant pressure because ΔH=ΔU+Δ(pV). But if we instead say that ΔU=q-pΔV which gives the right relationships ( ΔU=q at constant volume, ΔH=q at constant pressure), doesn't this assume constant pressure - how can we instead evaluate ΔU in terms of q, Δp and V for an isochoric process with changing pressure?
With ΔU=q+w, this w is to mean work done on the system (positive contribution to ΔU) minus work done by the system (i.e. negative contribution to internal energy), so then how do we summarize this for cases of expansion? Because if we say that ΔU=q-Δ(pV) then this suggests that ΔH=q even without constant pressure because ΔH=ΔU+Δ(pV). But if we instead say that ΔU=q-pΔV which gives the right relationships ( ΔU=q at constant volume, ΔH=q at constant pressure), doesn't this assume constant pressure - how can we instead evaluate ΔU in terms of q, Δp and V for an isochoric process with changing pressure?