q/T

[Manseej Khatri 2B]

In one of the lectures Dr. Lavelle derived that when the change in internal energy is 0, q = -w, which is how he was able to show that the change in entropy is q/T. However in contexts where the change in internal energy is not 0, such as a phase change or the cooling of an object, why are we still able to use the relationship q/T = delta S to derive the formulas such as for a change in entropy due to volume or temperature.

[ColmConnolly3D]

As per this page on ChemLibreTexts, for processes occuring at a constant temperature not a constant Internal energy. I think that this is just a condition of the equation given, as no rationale is listed but it would make sense that work could change in this type of scenario as long as the temperature remains the same (since this is the property we are plugging in).

Hope this helps!
Colm