Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.

Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing the system's entropy. When heat is supplied to the system, it propels the molecules into higher energy states, further increasing the number of microstates and, consequently, the entropy.

At absolute zero temperature (T = 0), all thermal motion ceases. In an ideal crystal, atoms or ions align in a perfect lattice structure, leading to zero entropy. This is because there is only one possible arrangement of the molecules when they are all in their lowest energy state, resulting in an entropy value of zero. This concept forms the foundation of the third law of thermodynamics, which asserts that the absolute entropy of a perfectly ordered crystalline substance is zero at absolute zero temperature.

However, there might be residual entropy due to persistent disorder or alternative molecular configurations even at T = 0. Entropies reported on the basis that S(0) = 0 are referred to as Third-Law entropies. When a substance exists in its standard state at a certain temperature T, the standard (Third Law) entropy is denoted S^°(T).