I am quite new in thermodynamics and I have never touched it so far. But now I have some basic questions that I hope someone can kindly explain them to me.
I know the Helmholtz free energy is defined as
$$\Phi= U - T S,$$
where $U$ is the internal energy, $T$ is the temperature and $S$ is the entropy.
The first question is how to derive this equation and what are the basic assumptions? I went through some books but they are just accepting it as a presumption.
Next, I would like to know how to derive the following relation,
$$S=-\frac{\partial \Phi}{\partial T},$$
from the first question.