Question

In an equilibrium of two systems, why is not true that $\frac{\delta S_{1}}{\delta N_{1}} = \frac{\delta S_{2}}{\delta N_{2}}$?

Answer 1

It is true, instead, that δF1δN1=δF2δN2δF1δN1=δF2δN2.

My thoughts: FF also takes into account the energy gained or lost by interacting components of some system. As a result, minimizing FF (remember that −ΔF=Wby−ΔF=Wby) also forces system components to do work and reduce in energy.

Answer 2

$hello$
If you take the derivative first with respect to N and then with respect to T, the internal energy term UU in F=U−TSF=U−TS can be shown to drop out in a system with the same type of particles (and, thus, which have the same value for U=NΔU=NΔ. However, am I right that δS1/δN1δS1/δN1is meaningless when we have different particle