Entropy, enthalpy and volume of perfect crystals at limiting high pressure and the third law of thermodynamics

According to the third law of thermodynamics, the entropy of a perfect crystal, S-cryst, at ambient pressure is zero at 0 K, or (partial derivative S-cryst/partial derivative T)(P) = 0 at T = 0 K. Here we consider isothermal variations of its entropy and enthalpy as the applied pressure P is varied, employing the Maxwell relation and estimating the respective limit of the Boltzmann equation. We deduce that as P is increased, (i) S-cryst at a fixed T and (partial derivative S-cryst/partial derivative P)(T) would asymptotically (progressively more slowly) decrease to zero, (ii) the enthalpy and the Gibbs free energy would asymptotically increase to the same limiting values, and (iii) the volume would asymptotically decrease to some constant limiting value. The approach of S-cryst and (partial derivative S-cryst/partial derivative P)(T) to zero with increase in P at a fixed T may be considered as complementary to the third law of thermodynamics. Variations of these thermodynamic functions in response to isothermal change of pressure are compared against their variations in response to isobaric change of temperature.

Automated summary

In accordance with the third law of thermodynamics, as pressure increases, the entropy of a perfect crystal gradually decreases towards zero, while the enthalpy and Gibbs free energy approach limiting values and the volume approaches a constant value. These changes are complementary to the third law and differ from the response to isobaric changes in temperature.