# 8: The Third Law, Absolute Entropy, and the Gibbs Free Energy of Formation

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• 8.1: Heat Capacity as a Function of Temperature
The heat capacity of the solid substance decreases to zero as the absolute temperature decreases to zero; the curve meets the abscissa at the zero of temperature and does so asymptotically. That this is true for all substances seems like an odd sort of coincidence. Why should all solid substances exhibit essentially the same heat capacity (zero) at one temperature (absolute zero)?
• 8.2: The Third Law
The idea that the entropy change for a pure substance goes to zero as the temperature goes to zero finds expression as the third law of thermodynamics: If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature, every substance has a positive finite entropy; but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.
• 8.3: Absolute Entropy
At any given temperature, the entropy value that is obtained in this way is called the substance’s absolute entropy or its third-law entropy. When the entropy value is calculated for one mole of the substance in its standard state, the resulting absolute entropy is called the standard entropy. The standard entropy is usually given the symbol So . It is usually included in compilations of thermodynamic data for chemical substances.
• 8.4: Evaluating Entropy Changes Using Thermochemical Cycles
As for the standard enthalpy of reaction, we can obtain the standard entropy of reaction at a new temperature by evaluating entropy changes around a suitable thermochemical cycle. To do so, we need the standard entropy change at one temperature. We also need heat capacity data for all of the reactants and products.

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