Can we show that the helmholtz free energy at equilibrium is minimized from its second...
Can we show that the helmholtz free energy at equilibrium is minimized from its second derivative?
Answer & Explanation
The first derivative at an extremum point is 0 only when evaluated at . Same goes with the second derivative. So you first have to evaluate the second derivative, then you plug in the specific
For example, take
At , the minimum, , and
If we were to apply your logic however, we would have
So, you have to expand your last line.
Now you apply the condition that you are at equilibrium, so , so that:
Then I guess that if pressure is positive, then the volume is a maximum so so that the first term is positive.