- #1

Silviu

- 624

- 11

## Homework Statement

Show that for a reaction occurring at constant T and V, F is minimized at equilibrium.

## Homework Equations

##F=U-TS##

##TdS=dU+pdV-\mu dN##

## The Attempt at a Solution

##dF=dU-d(TS)=dU-TdS-SdT=dU-dU -pdV+ \mu dN -S dT=-pdV - SdT + \mu dN##. At constant T and V this reduces to ##dF = \mu dN##. But I don't know what to do from here. Also in the next problem we have to use the fact that F is minimized at equilibrium to prove a relation between the chemical potentials of certain elements involved in a chemical reaction, so I assume i can't set ##dN=0##, as in a chemical reaction N changes and it seems that the fact that F is minimal at equilibrium holds in chemical reactions, too.

How can I solve this? Thank you!