The Scientific Group Thermodata Europe SGTE maintains thermodynamic databanks for inorganic and metallurgical systems. Data from their 'pure element database' is plotted below.

Typically, experiments are performed at constant pressure *p*, temperature *T*, and number *N*.
Under these conditions, the system will go to the minimum of the Gibbs energy *G = U + pV - TS*.
Here *U* is the internal energy, *V* is the volume, and *S* is the entropy.
The top plot is the Gibbs energy per mole.

Ag

Since the Gibbs energies of the different phases fall almost on top of each other, it is convenient to plot them relative to the phase that has the lowest Gibbs energy at low temperature.

The entropy per mole is *S = -dG/dT*.
To plot the entropy, the derivative of the of the Gibbs energy of the phase with the lowest Gibbs energy was taken numerically.
A jump in the entropy occurs at a first order phase transition when there is a latent heat.
The latent heat is *L = T*(*S*(*T*^{+}_{c})-*S*(*T*^{ -}_{c})),
where *S*(*T*^{ -}_{c}) and *S*(*T*^{+}_{c}) are the entropies just above and below the phase transition.

The enthalpy is *H = G + TS = U + PV*. The enthalpy is the
relevant thermodynamic quantity for systems held at constant pressure.
Energy must be added to a solid to increase its temperature. Some of
this energy increases the internal energy of the solid and some is
needed to push the environment back at constant pressure as the solid
expands. For a solid, the volume changes very little as the temperature
changes so the enthalpy is very nearly the internal energy plus a
constant.

The specific heat at constant pressure is *c _{p} =
dH/dT*. For most solids this is nearly the same as the specific heat
at constant volume

The formulas for the Gibbs energies used to make these plot can be found by right clicking on the page and selecting 'View Page Source'. Scroll down until you see the definitions of the free energies.