path-independent means that U is a function of state and the value of ∆U = U_f - U_i is independent of the details of how you got from i=initial to f=final. So if reversible paths give you this dU, then all irreversible paths produce the same dU.

hope this will be useful to students and instructors!

Unfortunately, there is one wrong word in this video... microstate "2" has only >one< microscopic realization, namely {1,1}. But I couldn't find the internal energy U to record it again 😅

Gemini 2.5 pro is the best for physical chemistry. While it's hard to know the training sources, I believe Wikipedia is a big part of it. Good or bad, I predict that Wikipedia will be absorbed into some forms of LLM. Perhaps they should develop/integrate their own if financially possible?

Only if you completely rely on AI summaries. Otherwise, it's just a fancier form of Google Scholar search. All of this is forced on us by the extreme volume of papers. My retired faculty colleagues still tried to read every paper in J. Phys. Chem. ... now you publish on page 13517 in JPC C

The internal energy of an ideal gas depends only on temperature, so during adiabatic expansion (q=0), a drop in U means a drop in T. Therefore, peeVee gets colder, not sweatier 🧊🥶

Bring back real pchem labs!

For **real gases**, particles do have intermolecular forces (like van der Waals forces). Therefore, changing the volume does change the internal energy, even at constant temperature, because it alters the potential energy component.