Isolated system spontaneous changes

The second law of thermodynamics (Clausius formulation) In isolated systems, spontaneous changes are always accompanied by a net increase in entropy. 

A third statement of the second law is based on the entropy. In reversible systems all forces must be opposed by equal and opposite forces. Consequently, in an isolated system any change of state by reversible processes must take place under equilibrium conditions. Changes of state that occur in an isolated system by irreversible processes must of necessity be spontaneous or natural processes. For all such processes in an isolated system, the entropy increases. Clausius expressed the second law as The entropy of the universe is always increasing to a maximum. Planck has given a more general statement of the second law Every physical and chemical process in nature takes place in such a way as to increase the sum of the entropies of all bodies taking any part in the process. In the limit, i.e., for reversible processes, the sum of the entropies remains unchanged. 

Any isolated system spontaneously attains a state that undergoes no further changes. Such a state is called equilibrium. In the case of equilibrium, the thermodynamic parameters of a. sy.stem are time-independent unless some perturbation occurs. 

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. 

Now consider an isolated system consisting of both the system that interests us and its surroundings (again like that in Fig. 7.15). For any spontaneous change in this isolated system, we know from Eq. lib that ASun > 0. If we calculate for a particular hypothetical process that A5tot < 0, we can conclude that the reverse of that process is spontaneous. 

Remember that G, H and S are all thermodynamic functions of state, i.e. they depend only on the initial and final states of the system, not on the ways the last is reached. As we have seen, for AG = 0 the reaction has reached equilibrium (and in isolated systems AS has reached a maximum). If AG < 0 the reaction was spontaneous, but if AG > 0 the reaction could not have taken place unless energy was provided from other coupled source. If the source is external then the system is not isolated it is closed if there is no exchange of material or open if there is such exchange. In both cases the environmental changes must be taken into account. 

Hence, for an isolated system, the entropy of the system alone must increase when a spontaneous process takes place. The second law identifies the spontaneous changes, but in terms of both the system and the surroundings. However, it is possible to consider the specific system only. This is the topic of the next section. 

An irreversible change is always spontaneous in an isolated system because no external force can interact with the system. Only at equilibrium can a change in an isolated system be conceived to occur reversibly. At equilibrium any infinitesimal flucmations away from equilibrium are opposed by the natural tendency to remrn to equilibrium. Therefore, the criterion of reversibility is a criterion of equilibrium, and the criterion of irreversibility is a criterion of spontaneity for an isolated system. 

The second law of thermodynamics states that the total entropy of a chemical system and that of its surroundings always increases if the chemical or physical change is spontaneous. The preferred direction in nature is toward maximum entropy. Moving in the direction of greater disorder in an isolated system is one of the two forces that drive change. The other is loss of heat energy, AH. 

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. 

An isolated system is one that exchanges neither matter nor energy with the surroundings. What is the entropy criterion for spontaneous change in an isolated system Give an example of a spontaneous process in an isolated system. 

The entropy provides a criterion of spontaneous change and equilibrium at constant U and V because (dS) y 0. Thus the entropy of an isolated system can only increase and has its maximum value at equilibrium. The internal energy also provides a criterion for spontaneous change and equilibrium. That criterion is (dl/)s>K < 0, which indicates that when spontaneous changes occur in a system described by equation 2.2-1 at constant S and V, U can only decrease and has its minimum value at equilibrium. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

This fundamental equation for the entropy shows that S has the natural variables U, V, and n . The corresponding criterion of equilibrium is (dS) 0 at constant U, V, and n . Thus the entropy increases when a spontaneous change occurs at constant U, V, and ,. At equilibrium the entropy is at a maximum. When U, V, and , are constant, we can refer to the system as isolated. Equation 2.2-13 shows that partial derivatives of S yield 1/T, P/T, and pJT, which is the same information that is provided by partial derivatives of U, and so nothing is gained by using equation 2.2-13 rather than 2.2-8. Since equation 2.2-13 does not provide any new information, we will not discuss it further. 

In an isolated system there can be no net change in enthalpy. A net increase in entropy, so that a system can change spontaneously, is related to a decrease in Gibbs energy,... 

In this connection note again the very nature of an irreversible process one can never return to the starting point without incurring other changes in the universe there is no way of influencing a process that occurs in an isolated system. If an irreversible process proceeds at all, it must go in the spontaneous direction that increases the entropy. 

The deduction of a criterion for the evolution of an open system to its stationary state resembles the classical thermodynamic problem of predict ing the direction of spontaneous irreversible evolution in an isolated system According to the Second Law of thermodynamics, in the latter case the changes go only toward the increase in entropy, the entropy being maximal at the final equilibrium state. 

An isolated system which has changed spontaneously from one state to another cannot be brought back to its original state without the expenditure of work. 

All natural spontaneous changes in an isolated system involve an increase in its entropy. 

Conversely, we conclude that an isolated system will not undergo a spontaneous change, i.e. will be in equilibrium, if all possible changes which are consistent with the character of the system leave the entropy imaltered, or cause it to diminish. In other words, the system is in equilibrium when its entropy is a maximum. 

We can now always combine our isothermal system with such a thermostat, so that the two together form an isolated system. The second law tells us that any spontaneous change of state in this isolated system must be of such a nature that if carried out reversibly it will yield work. Since the thermostat can neither do nor consume work, the whole system will be in equihbrium when the isothermal system is incapable of doing work. 

A convenient measure of the randorrmess or disorder of a system is the entropy (S). When a system becomes more chaotic, its entropy increases in line with the degree of increase in disorder caused. This concept is encapsulated in the second law of thermodynamics which states that the entropy of an isolated system increases in a spontaneous change. 

Second law - For spontaneous change, the entropy of an isolated system increases. 

Note that in an isolated system, every spontaneous event that occurs always increases the total entropy. Therefore, at equilibrium, where the properties of a system no longer change, the entropy of the system will be maximized. 

If the system be isolated in this case, dQ is again zero and therefore dS > o, i e the entropy increases as a result of the physical or chemical change occurring spontaneously in the isolated system To cover both >... 

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