Third Law of Thermodynamics
The Third Law of Thermodynamics states that the entropy of a pure crystalline substance is zero at absolute zero because the crystal arrangement must show the greatest orderliness at this temperature.  We now can determine the absolute entropy of any crystal through a knowledge of its heat capacity Cp.
Delta S = Integral between 0 and T of Cp/T dT
or
Integral between 0 and T of Cp d lnT
from T = 0 where S = 0 to T where S = S
Free Energy Functions and Applications
We now will discuss two new terms.  The Gibbs free energy "G"  and Helmholtz free energy "A"

G is defined as the isothermally available energy  A is defined as the isothermally available intenal energy.

Thus we now have two new equations:
1)    H = G + TS where H is the total energy and TS is the isothermally unavailable energy and G is the Gibbs free energy.
2)    E = A + TS where E is the total internal energy and A is the Helmholtz free energy.

Free energy is a very useful concept and will be referred to over and over again.  A process that causes the system to have a net loss in free energy will spontaneously happen while one that requires free energy or work will not.

Clausius - Clapeyron Equation:

The change in pressure with respect to a change in temperature is equal to the Pressure times change in heat content or Hv divided by the gas constant R time the temperature in degrees kelvin squared.  The integration of that relationship is

ln P2/P1 = Hv (T2 - T1)/RT1T2
The above equation can be used to calculate the Heat of Vaporization if you know the vapor pressure of a liquid at two temperatures. Conversely when the heat of vaporization is known we can calculate the vapor pressure of a liquid at a given temperature.  This is useful as we design aerosol dosage forms.

The above equation can also be written using equilibrium constants K in place of  vapor pressure P
and substituting the heat of reaction for the heat of vaporization.  Write that equation?

Example:  What is the vapor pressure of water at 950 C??  We will do this in class.

Gibbs - Helmholtz

For an isothermal process at constant pressure proceeding between the initial and final states

delta G =  delta H + {d( delta G)/dt}p