How would you define the concept of equilibrium in terms of free energy and entropy?
Consider the following equilibrium:
Initially we have
The total free energy of the system
For much more details on this topic, watch this video on:
Thermodynamics | Free Energy, Pressure & Equilibrium.
At a general equilibrium,
An example of an equilibrium is a phase transition, such as vaporization, freezing, etc. Let's say we looked at vaporization, the liquid-vapor dynamic equilibrium at a boiling point.
That would be looking at the enthalpy change (e.g.
ENTHALPY VS. TEMPERATURE, ENTROPY, PRESSURE, AND VOLUME
From this equation we can derive the relationship between enthalpy change, temperature, entropy, pressure, and volume (Physical Chemistry: A Molecular Approach, McQuarrie):
#H = U + PV#
#\mathbf(dH = dU + d(PV))#
#= delq_"rev" + delw_"rev" + PdV + VdP#
#= TdS - cancel(PdV + PdV) + VdP#
#color(blue)(dH = TdS + VdP)#
#color(blue)(DeltaH = TDeltaS + VDeltaP)#
ACHIEVING "THE" THERMODYNAMICS RELATIONSHIP
Now, it would be nice to know how to rewrite
Therefore, an expression for Gibbs' free energy is a way to do it. We could start at the Maxwell relation, which is:
#\mathbf(dG = -SdT + VdP)#
At a constant temperature, the partial derivative of the Gibbs' free energy with respect to pressure is the volume (
#((delG)/(delP))_T = V#
Therefore, we can substitute to get:
#dH = TdS + ((delG)/(delP))_TdP#
Phase changes where you watch something while it boils is at a constant atmospheric and vapor pressure (stuff is vaporizing while the vapor pressure is equal to the atmospheric pressure) as well as a constant temperature.
Since the Gibbs' free energy is supposed to change with respect to pressure, when pressure doesn't change, at least for an ideal substance,
Therefore, for something boiling:
#dG_"vap" = 0 -> color(blue)(dH_"vap" = T_"vap"dS_"vap")#
#DeltaG_"vap" = 0 -> color(blue)(DeltaH_"vap" = T_"vap"DeltaS_"vap")#
So when something is boiling, if you know the enthalpy and the temperature, you should able to calculate the entropy if the pressure is also constant.