Criterion for Spontaneous Change The Second Law of Thermodynamics

Is the standard molar entropy related to the amount of energy stored in a substance  

The answer to this question is yes, provided we focus only on substances that are solids at 298.15 K, and we interpret the energy stored in a substance to be the amount of heat required to raise the temperature of the solid from 0 K to 298.15 K at a constant pressure of 1 bar. The following figure is a plot of standard molar entropy, S°, versus AH°, for several monatomic solids. Here, AH represents the enthalpy change per mole of solid when it is heated from 0 to 298.15 K at a constant pressure equal to 1 bar. 

The result indicates that the standard entropy value, S°, at 298.15 K is proportional to the heat absorbed by that solid to get it from 0 to 298.15 K with the proportionality constant 0.00671 K . The heat that is absorbed by the solid in this process is dispersed through the various energy levels of the solid. The simple relationship clearly shows that the greater the amount of heat (energy) that is absorbed when one mole of the solid is heated from 0 to 298.15 K, the greater its standard molar entropy. Thus, the standard molar entropy of a solid is a direct measure of the amount of energy stored in the solid. 

The proportionality constant 0.00671 may be expressed as a temperature by taking the reciprocal of this value 1/(0.00671 K ) = 149 K. This temperature is exactly half way between 0 K and 298.15 K. We explore reasons for this in Exercise 94. 

A FIGURE 13-7 Standard molar entropies of some hydrocarbons 

---

Clausius s Ideas Absolute Entropies 13-4 Criterion for Spontaneous Change The Second Law of Thermodynamics... 

We see that the total change in entropy is a positive quantity for both these spontaneous processes, even though one process is exothermic and the other is endothermic. When this type of calculation is carried out for other processes, the same result is always obtained. For any spontaneous process, the total change of entropy is a positive quantity. Thus, this new state function of entropy provides a thermod3mamic criterion for spontaneity, which is summarized in the second law of thermodynamics ... 

Thus, the second law of thermodynamics provides us with a measure of this exhaustion, the entropy change A5, to be used as the fundamental criterion of spontaneity. For a closed region of space (for which, therefore, MJ = 0) including aU changes under observation. 

The First Law of Thermodynamics Any Change in the Energy of a System Requires an Equal and Opposite Change in the Surroundings The Second Law of Thermodynamics In Any Spontaneous Process the Total Entropy of the System and the Surroundings Increases Free Energy Provides the Most Useful Criterion for Spontaneity... 

The first law of thermodynamics provides a description of the energy balance for a given process the second law provides a criterion for deciding whether or not the process will occur spontaneously. The second law of thermodynamics defines the entropy change (A5, in units of J K l) associated with a change in a closed system in terms of the heat absorbed by the system at constant temperature T ... 

The deduction of a criterion for the evolution of an open system to its stationary state resembles the classical thermodynamic problem of predict ing the direction of spontaneous irreversible evolution in an isolated system According to the Second Law of thermodynamics, in the latter case the changes go only toward the increase in entropy, the entropy being maximal at the final equilibrium state. 

Our interest in chemical potentials (and activities) arises from the fact that the Gibbs energy of a mixture can be expressed in terms of the amounts of the substances and their chemical potentials, as shown by equations (13.31) and (13.32). These two equations, and the second law of thermodynamics, can be used to develop the criterion for predicting the direction of spontaneous chemical change. 

---