Entropy of a system

The paradox involved here ean be made more understandable by introdueing the eoneept of entropy ereation. Unlike the energy, the volume or the number of moles, the entropy is not eonserved. The entropy of a system (in the example, subsystems a or P) may ehange in two ways first, by the transport of entropy aeross the boundary (in this ease, from a to P or vice versa) when energy is transferred in the fomi of heat, and seeond. 

There exists a state function S, called the entropy of a system, related to the heat Dq absorbedfrom the surroundings during an infinitesimal change by the relations... 

A general expression for the entropy of a system, involving any phase transitions, is... 

Thus, in adiabatic processes the entropy of a system must always increase or remain constant. In words, the second law of thermodynamics states that the entropy of a system that undergoes an adiabatic process can never decrease. Notice that for the system plus the surroundings, that is, the universe, all processes are adiabatic since there are no surroundings, hence in the universe the entropy can never decrease. Thus, the first law deals with the conservation of energy in any type of process, while the sec-... 

The problem which the classical thermodynamics leaves over for consideration, the solution of which would be a completion of that system, is therefore the question as to the possibility of fixing the absolute values of the energy and entropy of a system of bodies. 

With the entropy, however, the case is quite otherwise, and we shall now go on to show that as soon as we are in possession of a method of determining the absolute value of the entropy of a system, all the lacunae of the classical thermodynamics can be completed. The required information is furnished by a hypothesis put forward in 1906 by W. Nernst, and usually called by German writers das Nernstsche Wdrmetheorem. We can refer to it without ambiguity as Nernsfs Theorem. ... 

We need a quantitative definition of entropy to measure and make precise predictions about disorder. Provided that the temperature is constant, it turns out that a We generalize the definition in the change in the entropy of a system can be calculated from the following expression next section to changes in which the... 

Because entropy is a state function, the change in entropy of a system is independent of the path between its initial and final states. This independence means that, if we want to calculate the entropy difference between a pair of states joined by an irreversible path, we can look for a reversible path between the same two states and then use Eq. 1 for that path. For example, suppose an ideal gas undergoes free (irreversible) expansion at constant temperature. To calculate the change in entropy, we allow the gas to undergo reversible, isothermal expansion between the same initial and final volumes, calculate the heat absorbed in this process, and use it in Eq.l. Because entropy is a state function, the change in entropy calculated for this reversible path is also the change in entropy for the free expansion between the same two states. 

The entropy of a system increases when its temperature increases and when its volume increases. 

The change in Gibbs free energy for a process is a measure of the change in the total entropy of a system and its surroundings at constant temperature and pressure. Spontaneous processes at constant temperature and pressure are accompanied by a decrease in Gibbs free energy. 

The second law of thermodynamics states that the total entropy of a system must increase if a process is to occur spontaneously. Entropy is the extent of disorder or randomness of the system and becomes maximum as equilibrium is approached. Under conditions of constant temperature and pressure, the relationship between the free energy change (AG) of a reacting system and the change in entropy (AS) is expressed by the following equation, which combines the two laws of thermodynamics ... 

This distribution follows automatically if we require that the entropy of a system with many members that is in equilibrium is at maximum. The denominator in the Boltzmann distribution ensures that the frequencies P are normalized and add up to unity, or 100%. This summation of states (Zustandssumme in German) is called a partition function ... 

Entropy A measure of randomness. Without the addition of energy, the entropy of a system tends to increase—to go from less random to more random. 

An increase in the number of ways to store energy increases the entropy of a system. Thus, an estimate of the pre-exponential factor A in TST requires an estimate of the ratio g /gr. A common approximation in evaluating a partition function is to separate it into contributions from the various modes of energy storage, translational (tr), rotational (rot), and vibrational (vib) ... 

The entropy of a system and its surroundings increases in the course of a spontaneous change, AAlol > 0. 

Let us now consider a slightly more complex system, the system AC-BD. The ideal configurational entropy of a system like this that contains two cations A+ andB+ and two anions C and D- is readily derived as... 

This result of AS(totai) being positive helps explain how considering the entropy of a system s surroundings can obviate the apparent problems caused by only considering the processes occurring within a thermodynamic system. It also explains why crystallization is energetically feasible. 

Entropy, which has the symbol S, is a thermodynamic function that is a measure of the disorder of a system. Entropy, like enthalpy, is a state function. State functions are those quantities whose changed values are determined by their initial and final values. The quantity of entropy of a system depends on the temperature and pressure of the system. The units of entropy are commonly J K1 mole-1. If S has a ° (5°),... 

The change in state from liquid to solid as a material crystallizes, is driven by thermodynamics and the principle of free energy minimization, in turn this results from a trade between the total enthalpy and entropy of a system. 

An ordered arrangement of particles (atoms, ions, or molecules) has lower entropy (smaller disorder) than the same number of particles in random arrangements. Thus, the entropy of a pure substance depends on its state. The entropy of a system increases (becomes more disordered) with temperature, because the motion of particles becomes more chaotic at higher temperatures. See Figure 7.6 on the next page. 

Note that the entropy of a system cannot increase forever. Eventually, a maximum state of disorder is reached. When this happens, the system appears to have constant properties, even though changes are still taking place at the molecular level. We say that a chemical system is at equilibrium when it has constant observable properties. Therefore, equilibrium occurs when a system has reached its maximum entropy. In the next section, you will look more closely at the reactants and products of chemical systems and learn how equilibrium is measured. 

In equilibrium, impurities or vacancies wiU be distributed uniformly. Similarly, in the case of two gases, as above, once a thorough mixture has been formed on both sides of the partition, the diffusion process is complete. Also at that stage, the entropy of the system has reached its maximum value because the information regarding the whereabouts of the two gases has been minimized. In general, it should be remembered that entropy of a system is a measure of the information available about that system. Thus, the constant increase of entropy in the universe, it is argued, should lead eventually to an absolutely chaotic state in which absolutely no information is available. 

In statistical mechanics entropy of a system with respect to a particular state is related to the probability, W, of a system being in that state ie.,S = kBltiW + b where is a constant and /cb is the Boltzmann constant. Hence, entropy represents the degree of disorder within a sys-... 

In statistical mechanics, Boltzmann defined entropy of a system as... 

Entropy is a thermodynamic quantity that is a measure of disorder or randomness in a system. When a crystalline structure breaks down and a less ordered liquid structure results, entropy increases. For example, the entropy (disorder) increases when ice melts to water. The total entropy of a system and its surroundings always increases for a spontaneous process. The standard entropies, S° are entropy values for the standard states of substances. 

What happens to the entropy of a system as the components of the system are introduced to a larger number of possible arrangments, such as when liquid water transforms into water vapor ... 

To a chemist the entropy of a system is a macroscopic state function, i.e., a function of the thermodynamic variables of the system. In statistical mechanics, entropy is a mesoscopic quantity, i.e., a functional of the probability distribution, viz., the functional given by (V.5.6) and (V.5.7). It is never a microscopic quantity, because on the microscopic level there is no irreversibility. ... 

The connection between the microscopic description of any system in terms of individual states and its macroscopic thermodynamical behavior was provided by Boltzmann through statistical mechanics. The key connection is that the entropy of a system is proportional to the natural logarithm of the number of levels available to the system, thus ... 

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