Entropy change of the universe

Calculate the total entropy change of the universe (system + surroundings). 

To find the equilibrium distribution, we consider a system of fixed volume10 and number of particles in contact with a thermal reservoir at temperature T. By the second law, at equilibrium there must be a zero entropy change of the universe for all infinitesmal changes in the system, because Auniv is a maximum at equilibrium. In particular, for the change involved in increasing the number of molecules in the jih state (with e = e7) of the system by 1, while decreasing the number of molecules in the lowest state of the system (with e = 0)... 

If the system is at equilibrium, the entropy change (of the universe) for this process must be zero ... 

In order to know whether or not a process in a closed system will occur spontaneously, it would be necessary to measure the entropy change in the surroundings (the rest of the universe) and obviously this is not possible. A device is needed to allow deduction of the entropy change of the universe from the process in the closed system. 

Entropy Change of the Universe In a familiar form, for a system plus its surroundings, or universe, the second law for reversible change is... 

The degree of disorder of a system is measured by the state function called entropy (S). The more disordered a system is, the greater is its entropy value. According to the second law, the entropy change of the universe is positive for every spontaneous process. The increase may take place in any part of the universe (A.S sys or A.S sun) ... 

Note that we have merely organized the expression for the entropy change of the universe, eliminating AAu iv and equating the free-energy change of the system (AG) with -TA univ. so that we can focus on changes in the system. We can now summa-... 

Describe the equilibrium condition in terms of the entropy changes of a system and its surroundings. What does this description mean about the entropy change of the universe ... 

The sum of the entropy of a system plus the entropy of the surroundings is everything there is, and so we refer to the total entropy change as the entropy change of the universe, AS niy. We can therefore state the second law of thermodynamics in terms of two equations ... 

Solution Suppose that a small amount of heat, Q, defined with respect to system 1, is transferred between the two systems. For this process to be feasible the entropy change of the universe must be positive. This entropy is the sum of the entropy change in the two systems... 

The first term on the right-hand side is the entropy change of the fluid during a pass through the process the second term is the entropy change of the bath during the same time. At steady state, the sum of the two constitutes the entropy change of the universe. 

Because nature always tends to proceed toward a more probable state, we can assert an equivalent form of the second law of thermodynamics In any spontaneous process, the total entropy change of the universe is positive, (ASu > 0). That this statement of the second law is equivalent to our original version is not at all obvious. But remember, energy that is not converted into work (a process that would decrease entropy) is transferred to the surroundings as heat. Thus the entropy of the surroundings increases, and the total entropy change in the system and surroundings is positive. 

Figure 1.6 Schematic diagram showing how an open system can become ordered but increase the disorder of the surroundings. The overall entropy change of the universe is...

A negative value for the Gibbs free energy change, AG , and a positive value for the entropy change of the universe, ASgmi gpjg, are equivalent criteria for spontaneity. 

In this chapter, we show that spontaneous processes are ones in which the entropy of the universe (system and surroundings) increases, and that for reversible processes, the total entropy change of the universe is zero. These conclusions lead us to the second and third laws of thermodynamics. 

We started the last chapter with the question, Will a process occur spontaneously We found that it is the total entropy change of the universe—the system and the surroundings—that determines spontaneity. If AS niv is greater than zero, the process is spontaneous. However, it may not always be convenient to determine the entropy change of both the system and the environment. To have a spontaneity condition that depends on the system would be more convenient for assessing chemical reactions. It would also be convenient if this spontaneity condition were useful under conditions that are common for chemical reactions, mainly fixed temperature and fixed pressure. In this chapter, we will determine such a spontaneity condition and apply it to physical and chemical systems. 

At room temperature and normal atmospheric pressure, is the entropy change of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid ... 

The property s quantitatively tells us about the directionahty of nature, reversibility vs. irreversibility, and the maximum work that we can get out of a process (or the minimum work we need to put in). We cannot deduce this supposition directly from the definition in Equation (3.1), but rather, as we shall see, it just works out that way Specifically, we will need to determine the entropy change of the universe for a particular process of interest. Recall that the universe is comprised of the system together with the surroundings. 

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