I know that ΔS=qrev/T for any process, but what is qrev here? It can't be identical to the q in ΔU=q+w - if it was, why don't we just write it q? The other problem is that it would mean that ΔS(surroundings)=-ΔS(system) which need not always be true. Secondly I want to derive the equation for ΔS(surroundings) in terms of ΔH(system). How do I go about this? Somehow ΔH(surroundings)=qrev seems to be used, but that can't be right - ΔH(system)=q at constant pressure is certainly true but q and qrev are not the same and the system need not necessarily be at constant pressure, and finally this equation gives ΔH(system) rather than ΔH(surroundings)! Sorry for the many complaints. Any explanation of qrev and this derivation, with relation to the q meaning heat gain of the system as in ΔU=q+w, would be very appreciated.