The third law implies that the entropy of a system with a nondegenerate ground state approaches zero as its temperature approaches absolute zero. In particular, ordinary equilibrium heat capacities approach zero.
At fixed pressure and material content, . If the equilibrium entropy tends to zero, the Gibbs free energy approaches its zero-temperature value with zero slope. When with and zero residual entropy, integrating gives and . Nonzero residual entropy instead contributes to ; a horizontal limiting tangent requires the zero-entropy hypothesis.
In a regular thermodynamic formulation, a state at absolute zero cannot be reached from positive temperature by finitely many cooling operations with finite control resources. The entropy-difference form of the third law of thermodynamics makes regular entropy curves approach a common limiting entropy. An isentropic process starting above that entropy cannot intersect the common zero-temperature endpoint.
For an illustrative pair of settings with and , , an isothermal entropy-reduction step followed by reversible adiabatic cooling gives . Every finite number of stages leaves . The model illustrates the entropy geometry; a general finite-time impossibility statement additionally needs assumptions about available interactions and cooling rates.
Articles by others on the same topic
The Third Law of Thermodynamics states that as the temperature of a perfect crystal approaches absolute zero (0 Kelvin, or -273.15 degrees Celsius), the entropy of that crystal approaches a minimum value, which is typically taken to be zero. In simpler terms, it implies that at absolute zero, a perfect crystalline substance would have no disorder and hence no entropy. This law has important implications in physics and chemistry, particularly in understanding the behavior of materials at very low temperatures and the concept of absolute zero.