Entropy spontaneity determination

The evolution of living species is concomitant indeed, with obvious ordering of the substance consisted therein. In terms of the classical ther modynamics, this seems like a spontaneous decrease in the entropy of living systems and, obviously, interferes with the Second Law of thermo dynamics. However, this is only an apparent contradiction the entropy increase determines the routes of spontaneous processes in isolated systems but not in open systems that are the living species. In real conditions, the total entropy of the living organisms in their evolution decreases on the condition that... 

We then see that entropy is the thermodynamic function for predicting the spontaneity of a reaction. On a molecular level, the entropy of a system can in principle be calculated from the number of microstates associated with the system. We learn that in practice entropy is determined by calorimehic methods and standard entropy values are known for many substances. (18.3)... 

Discussing the problem of the adequate use of the Second Law for biological systems, McClare indicated that from the point of conventional equilibrium thermodynamics, entropy is a macroscopic function of the system s state. Entropy change determines the direction of spontaneous irreversible processes in the whole system. At the intermediate level of structural organization, described within the approach of statistical mechanics, entropy is a mesoscopic value which is determined by the probability partition function. On the other hand, because of the reversibility of physical processes at the microscopic level, entropy cannot be a microscopic value. This statement had been clearly argued as early as 1912 by Paul and Tatyana Ehrenfest [8]. Following this line of argument, McClare deduced that entropy cannot be a characteristic function of molecules at the microscopic level. 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

An example of the role of the surroundings in determining the spontaneous direction of a process is the freezing of water. We can see from Table 7.2 that, at 0°C, the molar entropy of liquid water is 22.0 J-K 1-mo -1 higher than that of ice... 

For many reactions entropy effects are small and it is the enthalpy that mainly determines whether the reaction can take place spontaneously. However, in certain... 

In words, in any process that occurs at constant T and P, the free energy change for the system is negative whenever the total entropy change is positive that is, whenever the overall process is spontaneous. Defining a new function and imposing some restrictions provides a way to use properties of a system to determine whether a process is... 

In thermodynamics, entropy enjoys the status as an infallible criterion of spontaneity. The concept of entropy could be used to determine whether or not a given process would take place spontaneously. It has been found that in a natural or spontaneous process there would be an increase in the entropy of the system. This is the most general criterion of spontaneity that thermodynamics offers however, to use this concept one must consider the entropy change in a process under the condition of constant volume and internal energy. Though infallible, entropy is thus not a very convenient criterion. There have, therefore, been attempts to find more suitable thermodynamic functions that would be of greater practical... 

The total energy of a system involves both enthalpy and entropy. Thus, whichever causes the greater change in overall energy during the reaction will be the one controlling the reaction and determining whether it is exothermic, endothermic, spontaneous, or not spontaneous [11]. 

Two recent publications [8] determined the entropy change on binding small ligands to proteins, spontaneous reactions, and found that the entropy changes are negative. 

Definition of enthalpy and entropy Definition of free energy Enthalpy (a measure of the change in heat content of the reactants and products) and entropy (a measure of the change in the randomness or disorder of reactants and products) determine the direction and extent to which a chemical reaction will proceed. When combined mathematically, they can be used to define a third quantity, free energy, which predicts the direction in which a reaction will spontaneously proceed. 

The dilemma is resolved when we realize that the second law refers to an isolated system. That is, if we want to determine whether a change is spontaneous or not, we must consider the total change in entropy of the system itself and the surroundings with which it is in contact and can exchange energy. 

Two factors determine the spontaneity of a chemical or physical change in a system a release or absorption of heat (AH) and an increase or decrease in molecular randomness (AS). To decide whether a process is spontaneous, both enthalpy and entropy changes must be taken into account ... 

The second law, however, provides a clear-cut criterion of spontaneity. It says that the direction of spontaneous change is always determined by the sign of the total entropy change ... 

Free energy, G = H — TS, is a state function that indicates whether a reaction is spontaneous or nonspontaneous. A reaction at constant temperature and pressure is spontaneous if AG < 0, nonspontaneous if AG > 0, and at equilibrium if AG = 0. In the equation AG = AH — TAS, temperature is a weighting factor that determines the relative importance of the enthalpy and entropy contributions to AG. 

Fig. 6.8. A Principle of frequency-multiplexed CARS microspectroscopy A narrow-bandwidth pump pulse determines the inherent spectral resolution, while a broad-bandwidth Stokes pulse allows simultaneous detection over a wide range of Raman shifts. The multiplex CARS spectra shown originate from a 70 mM solution of cholesterol in CCI4 (solid line) and the nonresonant background of coverglass (dashed line) at a Raman shift centered at 2900 cm-1. B Energy level diagram for a multiplex CARS process. C Schematic of the multiplex CARS microscope (P polarizer HWP/QWP half/quarter-wave plate BC dichroic beam combiner Obj objective lens F filter A analyzer FM flip mirror L lens D detector S sample). D Measured normalized CARS spectrum of the cholesterol solution. E Maximum entropy method (MEM) phase spectrum (solid line) retrieved from (D) and the error background phase (dashed line) determined by a polynomial fit to those spectral regions without vibrational resonances. F Retrieved Raman response (solid line) calculated from the spectra shown in (E), directly reproducing the independently measured spontaneous Raman response (dashed line) of the same cholesterol sample...

Equation 2.2-8 indicates that the internal energy U of the system can be taken to be a function of entropy S, volume V, and amounts nt because these independent properties appear as differentials in equation 2.2-8 note that these are all extensive variables. This is summarized by writing U(S, V, n ). The independent variables in parentheses are called the natural variables of U. Natural variables are very important because when a thermodynamic potential can be determined as a function of its natural variables, all of the other thermodynamic properties of the system can be calculated by taking partial derivatives. The natural variables are also used in expressing the criteria of spontaneous change and equilibrium For a one-phase system involving PV work, (df/) 0 at constant S, V, and ,. ... 

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