Biochemistry - Chemical Reactions in Living Cells, Volume 1 - D. Metzler 1980

Bioenergetics of Biochemical Reactions
Thermodynamics
Determination of Entropy via Heat Capacity

It follows from equation (3-8) that for an ideal crystal lacking molecular disorder, S = 0 at T = 0. The Third Law of Thermodynamics states that for ideal crystals, as the thermodynamic Temperature T approaches 0 K, the Entropy S approaches zero. Consequently, at any temperature above 0 K, the entropy is given by the following equation:

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Table 3-2 Entropy of selected substances^a

^a All values are expressed in entropy units (e.u.), i.e., cal∙K^-1∙mol^-1, and in kJ∙K^-1∙mol^-1 at 25 °C (298.16 K).

In this equation, С_р is the heat capacity at constant pressure:

С_Р = (dН/dТ)_р       (3-12)

By measuring C_p at low temperatures approaching 0 K, the absolute value of entropy S can be estimated using equation (3-11). If a phase transition occurs as the temperature rises, the value given by equation (3-11) must be adjusted by adding ∆S, determined from equation (3-6). For certain compounds (e.g., Water; Chapter 4, Section B.4), molecular disorder persists even in the crystalline state at 0 K. In such cases, a term corresponding to the entropy at 0 K must be introduced into equation (3-11).

The entropy values for various substances are listed in Table 3-2. Note how this value increases with structural complexity, with the transition from solid to liquid and further to the gaseous state, and as the hardness of the Materials decreases.