Spontaneity spontaneous processes

If you let go of a book, it falls to tiie floor because of gravity. At its initial height, it has a higher potential energy than it has when it is on tire floor. Unless it is restrained, tiie book falls and so loses energy. This fact leads us to the first basic principle identifying spontaneous processes and the direction tiiey take Processes in which the aiergy content of the system decreases tend to occur spontaneously. Spontaneous processes tend to be exotiiermic. (Section 5.4, "Strate-... 

Thus, for spontaneous processes at constant temperature and volume a new quantity, the Helmholtz free energy A, decreases. At equilibrium under such restrictions cL4 = 0. 

For spontaneous processes at constant temperature and pressure it is the Gibbs free energy G that decreases, while at equilibrium under such conditions dG = 0. 

It should be noted that the differential expressions on the right-hand side of equation (A2.1.33). equation (A2.1.34), equation (A2.1.35), equation (A2.1.36), equation (A2.1.37), equation (A2.1.38), equation (A2.1.39) and equation (A2.1.40) express for each fiinction the appropriate independent variables for that fiinction, i.e. the variables—read constraints—drat are kept constant during a spontaneous process. 

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... 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

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. 

Laser radiation is emitted entirely by the process of stimulated emission, unlike the more conventional sources of radiation discussed in Chapter 3, which emit through a spontaneous process. 

The more negative the value of AG, the more energy or useful work can be obtained from the reaction. Reversible processes yield the maximum output. In irreversible processes, a portion of the useful work or energy is used to help carry out the reaction. The cell voltage or emf also has a sign and direction. Spontaneous processes have a positive emf the reaction, written in a reversible fashion, goes in the forward direction. 

Thus the formation of an ideal solution from its components is always a spontaneous process. Real solutions are described in terms of the difference in the molar Gibbs free energy of their formation and that of the corresponding ideal solution, thus ... 

The oxidation of hydrogen to water (Hj -t- i Oj -> HjO) is thermodynamically spontaneous and the energy released as a result of the chemical reaction appears as heat energy, but the decomposition of water into its elements is a non-spontaneous process and can be achieved only by supplying energy from an external source, e.g. a source of e.m.f. that decomposes the water electrolytically. Furthermore, although the heat produced by the spontaneous reaction could be converted into electrical energy, the electrical... 

All of us are familiar with certain spontaneous processes. For example—... 

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 relationship between entropy change and spontaneity can be expressed through a basic principle of nature known as the second law of thermodynamics. One way to state this law is to say that in a spontaneous process, there is a net increase in entropy, taking into account both system and surroundings. That is,... 

Notice that the second law refers to the total entropy change, involving both system and surroundings. For many spontaneous processes, the entropy change for the system is a negative quantity. Consider, for example, the rusting of iron, a spontaneous process ... 

A spontaneous process is capable of producing useful work. 

Coupled reactions are common in human metabolism. Spontaneous processes, such as the oxidation of glucose,... 

Key Terms enthalpy, H free energy of formation, AG standard entropy change, AS° entropy, S spontaneous process standard free energy change, AG° free energy, G... 

Second law of thermodynamics A basic law of nature, one form of which states that all spontaneous processes occur with an increase in entropy, 457 Second order reaction A reaction whose rate depends on the second power of reactant concentration, 289,317q gas-phase, 300t... 

Thermodynamic, second law The entropy of the universe increases in a spontaneous process and remains unchanged in a reversible process. It can never decrease. 

Since q >0, and l/T > /T2 with T2 >7), we conclude that AS for this allowed, spontaneous process is greater than zero. Having obtained this result for the specific case, we can extend it to the general case, because our earlier conclusion that there is an allowed direction to spontaneous adiabatic processes applies to all thermodynamic systems. 

Equation (5.47) gives the criterion for reversibility or spontaneity within subsystem A of an isolated system. The inequality applies to the spontaneous process, while the equality holds for the reversible process. Only when equilibrium is present can a change in an isolated system be conceived to occur reversibly. Therefore, the criterion for reversibility is a criterion for equilibrium, and equation (5.47) applies to the spontaneous or the equilibrium process, depending upon whether the inequality or equality is used. 

Equation (5.52) is the first of our criteria. The subscripts indicate that equation (5.52) applies to the condition of constant entropy, volume, and total moles, with the equality applying to the equilibrium process and the inequality to the spontaneous process. 

Entropy is a measure of disorder according to the second law of thermodynamics, the entropy of an isolated system increases in any spontaneous process. Entropy is a state function. 

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