Wow, thank you very much! I've learned so much more from this thread in the last few hours than I did pouring over my textbook and searching through the internet this past week. This stuff finally makes sense to me now.
Oh I think I get it! The equation ##dA = -SdT - PdV## refers specifically to some process between equilibrium states. But this doesn't necessarily apply to spontaneous processes at the infinitesimal level because some cannot be modeled quasi-statically. This isn't a problem because we've already...
Ah thanks for the clarification about the pressure. So would the correct statement be
##dU - T_rdS + P_{surr}dV \leq 0##
where the equality holds for reversible processes and the inequality for irreversible processes?
Also, when my textbook says,
"In a system held at constant T and...
Thanks so much for your help! That makes a lot more sense now. Just to make sure I understand you correctly...
The inequality applies to the temperature of the reservoir and not necessarily that of the system. During an irreversible process, if we were able to define a series of equilibrium...
I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics:
dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS
dU – TdS + PdV ≤ 0
For a process at...