Absolute Entropies and the Third Law of Thermodynamics

The Boltzmann relationship defines absolute entropy as proportional to the natural logarithm of the number of possible microstates, or particle arrangements, in a system. This makes entropy unique among state functions because it possesses a measurable, absolute value. The more microstates available to a system, the higher its entropy.

When a gas-filled container expands, the volume increases, allowing energy levels to become more closely spaced and more densely populated. This increases the total number of accessible microstates at the same temperature, thereby increasing the system's entropy. Larger volume directly enables greater molecular disorder.

The Third Law of Thermodynamics states that at absolute zero temperature, all thermal motion ceases. In a perfectly ordered crystal, atoms align in a singular, unique arrangement with only one possible microstate. Since the natural logarithm of one equals zero, the entropy of a perfect crystal is zero at absolute zero.

Residual entropy persists at absolute zero when molecules become frozen in different orientations rather than a single perfect arrangement. For example, carbon monoxide molecules may face random directions even at zero kelvin. This persistent molecular disorder means entropy remains slightly above zero despite the absence of thermal motion.

Absolute entropy is the measurable entropy value of any system based on the Boltzmann relationship. Third-Law entropy, denoted S°(T), is calculated assuming the entropy of a perfectly ordered crystalline substance equals zero at absolute zero. Third-Law entropies account for residual disorder and are reported relative to this reference point.

When heat is supplied to a system, it propels molecules into higher energy states, increasing the number of available energy levels and accessible microstates. This expansion of available molecular arrangements directly increases the system's entropy. Heat input enables greater disorder and more possible particle configurations.

Entropy stands alone among state functions as the only one whose absolute values can be determined through the Boltzmann relationship. Other state functions lack this measurable absolute reference point. This uniqueness allows scientists to calculate absolute entropy values directly from the number of possible microstates.