Nice presentation. I first came across the Legendre transform in Thermodynamics without an explicit reference to what it entailed. "A graphical derivation of the Legendre Transform" by Sam Kennerly (12 April 2011) and "Making sense of the Legendre transform" by Zia, Redish & McKay, American Journal of Physics, vol. 77, (7), July 2009 present enlightening discussions on the Legendre Transform.
There's a way of conceptually linking F with the standard argument for temperature equilibration that I really like. The standard argument in day one of a stat mech course goes as follows: you have two systems that can exchange energy, and we want to find the equilibrium partitioning of the total energy E = E1 + E2. This is found by maximizing Omega_1(E1) Omega_2(E - E1), or equivalently by maximizing the log of that, S(E1) := S1(E1) + S2(E - E1). Maximizing S(E1) with respect to E1 then shows that the equilibrium is achieved when the temperatures are equal. To see how F comes about, you can just run this argument but take system 2 to be much larger than system 1, so you can expand the second term. This gives S(E1) ~ S1(E1) + S2(E) - E1/T = -1/T (E1 - T S1(E1)). So we see that equilibrium at constant temperature is enforced by minimizing F = E1 - T S1(E1). F from this perspective is a way of ignoring the details of the reservoir (system 2) and determining equilibrium solely by looking at system 1.
Basically yes :) from thermo to the theory of phase transitions hopefully, then move onto some modern topics! Hopefully it looks like something resembling a crash course in stat mech by the end of it.
living system operates at constan temp and at constant pressure. Hence dT=0,and dP= 0 and concentrations of particles are in steady state or in dynamic equilibriumi, i,e dC/dt =0 at any instant of time,since it is an open System. Free energy=summation of meu× dn. Meu is the chemical potential of the k th particle exchanged.at constant T& P.
