Isolated system entropy change

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

Consider any number of systems that may do work on each other and also transfer heat from one to another by reversible processes. The changes of state may be of any nature, and any type of work may be involved. This collection of systems is isolated from the surroundings by a rigid, adiabatic envelope. We assume first that the temperatures of all the systems between which heat is transferred are the same, because of the requirements for the reversible transfer of heat. For any infinitesimal change that takes place within the isolated system, the change in the value of the entropy function for the ith system is dQJT, where Qt is the heat absorbed by the ith system. The total entropy change is the sum of such quantities over all of the subsystems in the isolated system, so... 

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. 

We see evidence that the universe tends toward highest entropy many places in our lives. A campfire is an example of entropy. The solid wood bums and becomes ash, smoke, and gases, all of which are more disordered than the solid fuel. For isolated systems, entropy never decreases. This fact has several important consequences in science it prohibits perpetual motion machines, it implies that the arrow of entropy has the same direction as the arrow of time, and so on. Increases in entropy corresponds to irreversible changes in a system, because some energy is expended as waste heat, limiting the amount of work a system can do. 

This is frequently stated for an isolated system, but the same statement about an adiabatic system is broader.) A2.1.4.6 IRREVERSIBLE CHANGES AND THE MEASUREMENT OF ENTROPY... 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

E3.7 A block of copper weighing 50 g is placed in 100 g of HiO for a short time. The copper is then removed from the liquid, with no adhering drops of water, and separated from it adiabatically. Temperature equilibrium is then established in both the copper and water. The entire process is carried out adiabatically at constant pressure. The initial temperature of the copper was 373 K and that of the water was 298 K. The final temperature of the copper block was 323 K. Consider the water and the block of copper as an isolated system and assume that the only transfer of heat was between the copper and the water. The specific heat of copper at constant pressure is 0.389 JK. g l and that of water is 4.18 J-K 1-g 1. Calculate the entropy change in the isolated system. 

We will take this isolated system and displace it from equilibrium by an infinitesimal amount in some manner. The system will then return to equilibrium and an entropy change will occur in the system given by... 

The system ot interest and its surroundings constitute the isolated system to which the second law refers (Fig. 7.15). Only if the total entropy change,... 

As in the case of the isolated system, the asymmetric part of the transport matrix does not contribute to the scalar product or to the steady-state rate of first entropy production. All of the first entropy produced comes from the reservoirs, as it must since in the steady state the structure of the subsystem and hence its first entropy doesn t change. The rate of first entropy production is of course positive. 

The most likely rate of change of the first entropy of the isolated system is... 

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. 

Thus, the entropy change for an irreversible process occurring in an isolated system is greater than or equal to zero, with the equal sign applying to the limiting case of a reversible process. 

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. 

IL-6 There exists a macroscopic state property S ( entropy ) that achieves the character of a maximum with respect to variations that do not alter the energy of an isolated system at equilibrium, and whose differential changes at equilibrium are given by dS = dq/T. 

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 change in the value of the entropy function of an isolated system... 

Having defined the entropy function, we must next determine some of its properties, particularly its change in reversible and irreversible processes taking place in isolated systems. (In each case a simple process is considered first, then a generalization.)... 

The temperature can be factored from the sum, because it has the same value for all sytems. However, dQf = 0 because the total system is isolated. Consequently, the change in the value of the entropy function of the isolated system is zero. The change for a finite process is simply the sum of the... 

It is a general observation that any system that is not in equilibrium will approach equilibrium when left to itself. Such changes of state that take place in an isolated system do so by irreversible processes. However, when a change of state occurs in an isolated system by an irreversible process, the entropy change is always positive (i.e., the entropy increases). Consequently, as the system approaches equilibrium, the entropy increases and will continue to do so until it obtains the largest value consistent with the energy of the system. Thus, if the system is already at equilibrium, the entropy of the system can only decrease or remain unchanged for any possible variation as discussed in Section 5.1. 

---