Timeline for How does one "invert" derivatives for intensive variables?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2023 at 22:42 | vote | accept | EE18 | ||
| May 25, 2023 at 22:42 | comment | added | EE18 | Noted, thank you! | |
| May 25, 2023 at 22:23 | comment | added | LPZ | My last sentence was a side note offering a proof of the reciprocity theorem. However it is not relevant for your calculation. Since you didn’t seem too certain on when to use it, I just offered a general way to keep track of everything (no matter the number of variables). | |
| May 25, 2023 at 22:20 | comment | added | LPZ | 2) yes I agree with your derivation in the edit. In particular step (2) is a simple multiplication. The existence of $U$ only comes into play for getting the Maxwell relation. The rest is differential calculus. | |
| May 25, 2023 at 22:18 | comment | added | LPZ | 1) Ok I get what you mean. For me intensive/extensive are just the physicists’ way of treating mathematic homogeneity, that’s why it didn’t seem relevant for me. In general, physicists have a tendency to overlook technical details such as the implicit function theorem, and take for granted the inversion of functions. | |
| May 25, 2023 at 21:57 | comment | added | EE18 | I ask 2) because I'm not sure what you meant by"In fact the expression of the extra partial derivatives I calculated give you the necessary ingredients to derive your reciprocity theorem." | |
| May 25, 2023 at 21:57 | comment | added | EE18 | Just a couple quick questions which I'm not sure I followed. 1) The relevance of the variables being intensive is just that we then need to appeal to the implicit function theorem (whereas if all independent variables were extensive/part of the macrostate there would be no such need)? 2) To confirm, do you agree with my derivation as supplied in the edit? That is, that the $T$ just comes about from choosing to multiply thereby? | |
| May 25, 2023 at 21:32 | history | answered | LPZ | CC BY-SA 4.0 |