Physical Chemistry Lecture: Partial Derivatives in Thermodynamics Part 1

[@ltan11]

Thank you so much for posting them keep them coming!!!!!!

[@kristofasbarsauskas7491]

from 21:00 to 22:00 when you take the whole equation and are multiplying both sides by of it by 1/(partial)dr holding x constant. Why do the initial dz, dx and dy that are complete derivatives become partial derivatives when you divide? And what exactly does that change mean?

[@GlennLo]

Initially, the dz, dx, and dy are just differentials or changes "in general." Once you divide by dr "at constant x" then the dz, dx, and dy are now specifically the changes in z, x, and y "at constant x" as well. The last term would now mean: dy at constant x, divided by dr at constant x, which requires us to use the partial symbols. For these variables, all ratios of differentials must be partial derivatives because you have more than one independent variable.

[@GlennLo]

For as long as you have more than one independent variable, you need to use partial symbols for both numerator and denominator and specify what variable you are holding constant.