Entropy, and temperature

In phenomenological description (comparable to a kind of wanted poster ), the entropy appears as a kind of stufF which is distributed in space, can be stored or transferred, collected or distributed, soaked up or squeezed out, concentrated or dispersed. It is involved in aU thermal effects and can be considered their actual cause. Without it, there would be no hot and no cold. It can be easily generated, if the required energy is available, but it cannot be destroyed. Actually, entropy can be easily recognized by these effects. This direct understanding of the quantity S is deepened by a simplified molecular kinetic interpretation. 

Misjudged and Avoided The central concepts of thermodynamics are entropy S and temperature T. While everyone is familiar with temperature, entropy is considered as especially difficult, in a way the black sheep among physicochemical quantities. School books avoided it totally in the past, introductory physics books often only mention it, and even specialists in the field like to avoid it. 

But why is the subject of entropy avoided when it is actually something rather simple It is just what is considered heat in everyday life (Fig. 3.1)  

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Our most important insight into the connection between thermodynamics and black holes comes from a celebrated result obtained by Bardeen, Carter and Hawking [bard73], that the four laws of black hole physics can be obtained by replacing, in the first and second laws of thermodynamics, the entropy and temperature of a thermodynamical system by the black hole event horizon (or boundary of the black hole) and surface gravity (which measures the strength of the gravitational field at the black hole s surface). 

A further illustration and summary of the entropy and temperature changes involved upon moving between two magnetic fields is shown in Figure 9.2 [13]. 

The Gibbs free energy (G) is a thermodynamic function that combines the enthalpy, entropy, and temperature ... 

Now recall the reaction between mercury and oxygen. It favours the formation of HgO below about 400°C, but the decomposition of HgO above 400°C. This reaction highlights the importance of temperature to favourable change. Enthalpy, entropy, and temperature are linked in a concept called free energy. 

The relationship among heat capacity, entropy, and temperature in crystalline solids may be understood on the basis of two fundamental concepts the Boltzmann factor and the partition function (or summation over the states, from the German term Zustandsumme). Consider a system in which energy levels Eq,... 

The Entropy and Temperature activity (eChapter 17.4) has 5 distinct regions where entropy is changing as temperature is increasing. Explain the changes that are occurring at the molecular level that would account for the increase in entropy. 

Although we shall not directly use these four postulates of irreversible thermodynamics as a foundation to our study of molecular transport in separations, a number of important principles are illuminated here. For instance, postulate 2 permits us to use—and this is in no way obvious— equilibrium parameters such as entropy and temperature in descriptions of systems where no equilibrium exists. The importance of this is evident when we ask ourselves how we would describe a system if these parameters were not available. Postulate 3 demonstrates that in the range of our typical experiences, the fluxes of matter or of heat are proportional to the gradients or forces that drive them. However, there are exceptions nonlinear terms enter if the forces become intense enough. 

Gibbs free energy describes the spontaneity of chemical reactions in terms of enthalpy, entropy, and temperature. Negative values signify a spontaneous reaction, while positive values are nonspontaneous. A free energy of zero denotes equilibrium conditions. 

This expression serves as a precise mathematical definition of temperature. It is interesting to note that temperature, a variable with which we have intuitive and sensory familiarity, is defined based on entropy, one with which we may be less familiar. In fact, we shall see that entropy and temperature are intimately related in the concept of free energy, in which temperature determines the relative importances of energy and entropy in driving thermodynamic processes. 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

As AG° becomes more negative, K becomes larger a decrease in free energy favors a given reaction. As we saw in Chapter 10, free energy depends on enthalpy, entropy, and temperature. For a process at constant temperature,... 

The intensive porperty Temperature is supplemented by a complementary extensive property, entropy. In the case of energy in form of heat it gives the number of degrees of freedom among which the average energy of motion (of the material particles involved), characterized by the temperature, is distributed. Entropy and temperature are complementary state variables. 

The thermodynamic relationships examined in Chapter 1 involving polymorphism and solubility have been applied to the methylprednisolone system [13]. The solubilities of the two polymorphs of this steroid were determined at various temperatures in water, decyl alcohol, and dodecyl alcohol. Because the chemical potential and thermodynamic activity of the drug in the solid state and in each saturated solution are constant, the solubility ratios for the two forms (which can be found in Table 1) were found to be independent of the solvent. The enthalpy, entropy, and temperature of transition calculated from the data were 1600 cal/mol, 4.1 cal/K mol, and 118°C, respectively. 

Free energy denoted by the letter G is a thermodynamic quantity, with which we can predict the spontaneity of a reaction. The change in free energy (AG) is related to the changes in enthalpy and entropy, and temperature as indicated by the equation ... 

You might want to consider why sulfonation is reversible at high temperature in the light of our discussion of entropy and temperature on p. 248. 

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