Spontaneous processes defined

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

While this is an easy calculation to make, Eq. (3.7) does little to clarify exactly what AS means. Phenomenological proofs that AS as defined by Eq. (3.7) is a state variable often leave us with little more than a lament for the inefficiency of spontaneous processes. 

Perhaps the simplest way to define spontaneity is to say that a spontaneous process is one that moves the reaction system toward equilibrium. A nonspontaneous process moves the system away from equilibrium. 

The Helmholtz and Gibbs energies on the other hand involve constant temperature and volume and constant temperature and pressure, respectively. Most experiments are done at constant Tandp, and most simulations at constant Tand V. Thus, we have now defined two functions of great practical use. In a spontaneous process at constant p and T or constant p and V, the Gibbs or Helmholtz energies, respectively, of the system decrease. These are, however, only other measures of the second law and imply that the total entropy of the system and the surroundings increases. 

The chemical potential is defined as the increase in free energy of a system on adding an infinitesimal amount of a component (per unit number of molecules of that component added) when T, p and the composition of all other components are held constant. Clearly, from this definition, if a component i in phase A has a higher chemical potential than in phase B (that is, xf > pf) then the total free energy will be lowered if molecules are transferred from phase A to B and this will occur in a spontaneous process until the chemical potentials equalize, at equilibrium. It is easy to see from this why the chemical potential is... 

Cell Line A defined population of cells which has been maintained in a culture for an extended period and which has usually undergone a spontaneous process of transformation conferring an unlimited culture lifespan on the cells. 

Emission bands from the 42Z, B2n, C2n, and D2X states have been observed and decay rates of fluorescence have been measured extensively [Callear et al. (167-171, 174, 175)]. Various spontaneous processes of electronically excited NO are given in Table V-5. These states are quenched to a different degree by various gases. Quenching half pressures, p1/2, in torr defined as P112 — where is the quenching rate constant in sec-1 torr-1... 

We have defined a spontaneous process as one that proceeds on its own without any external influence (Section 8.13). The reverse of a spontaneous process is always nonspontaneous and takes place only in the presence of some continuous external influence. Consider, for example, the expansion of a gas into a vacuum. When the stopcock in the apparatus shown in Figure 17.1 is opened, the gas in bulb A expands spontaneously into the evacuated bulb B until the gas pressure in the two bulbs is the same. The reverse process, migration of all the gas molecules into one bulb, does not occur spontaneously. To compress a gas from a larger to a smaller volume, we would have to push on the gas with a piston. 

In words when a system undergoes a change, the increase in entropy of the system is equal to or greater than the heat absorbed in the process divided by the temperature. On the other hand, the equality, which provides a definition of entropy increment, applies to any reversible process, whereas the inequality refers to a spontaneous (or irreversible) process, defined as one which proceeds without intervention from the outside. Example 1 illustrates the reversible and irreversible reactions. 

Define what is meant by a spontaneous process and by entropy. Is entropy a form of energy ... 

Another important thermodynamic concept is that of entropy. Entropy is a measure of the level of randomness or disorder in a system. The Second Law of Thermodynamics states that the total entropy of a system and its surroundings always increases for a spontaneous process. At first glance, this law appears to contradict much common experience, particularly about biological systems. Many biological processes, such as the generation of a well-defined stmcture such as a leaf from carbon dioxide gas and other nutrients, clearly increase the level of order and hence decrease entropy. Entropy may be decreased locally in the formation of such ordered structures only if the entropy of other parts of the universe is increased by an equal or greater amount. 

Spontaneous processes are particular examples of irreversible processes defined in Section 12.1. In stark contrast with reversible processes, they do not proceed through a sequence of equilibrium states, and their direction cannot be reversed by an infinitesimal change in the direction of some externally applied... 

What determines whether a process under consideration will be spontaneous Where does a spontaneous process end How are energy, volume, and matter partitioned between the system and surroundings at equilibrium What is the nature of the final equilibrium state These questions cannot be answered by the first law. Their answers require the second law and properties of the entropy, and a few developments are necessary before we can address these questions. We define entropy by molecular motions in Section 13.2 and by macroscopic process variables in Section 13.3. Finally, we present the methods for calculating entropy changes and for predicting spontaneity in Section 13.5. 

For constant temperature and pressure, dG = 0 defines the condition of an equilibrium state. The second law of thermodynamics requires for spontaneous processes that... 

It must be borne in mind that a reversible process or cycle is a limiting case which we can never quite realise in practice All naturally occurring or spontaneous processes are irreversible We have already defined an irreversible process as one in which energy is dissipated or departs from the system permanently (though, of course, it cannot be destroyed, but must appear somewhere m space accoiding to the prin-... 

Spontaneous processes may occur in such a system when it is not at equilibrium with a consequent decrease in the free energy. When A is a minimum and dA = 0 no further spontaneous changes can occur and the system is at equilibrium. Again we see the parallel between the free energy A and the potential energy in a mechanical system. If the latter system is not harnessed to do work the position of equilibrium could be defined in terms of minimum energy. 

Consideration of idealized heat engines (largely omitted), combined with a statement based on experience (the Second Law), allows us to define a parameter, the entropy, which has the useful property of always increasing in adiabatic spontaneous processes. We would like to have similar parameters for other kinds of processes, i.e., to have... 

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