Total change of entropy

When solid AgCl is in contact with its saturated aqueous solution, we have found that, if additional ion pairs are transferred from the surface of the crystal to the solution, the total change of entropy is equivalent to 52.8 e.u Since the entropy of the solid is 23.0 e.u., we find that the partial molal entropy of AgCl in its saturated aqueous solution at 25°C is... 

We see that the total change in entropy is a positive quantity for both these spontaneous processes, even though one process is exothermic and the other is endothermic. When this type of calculation is carried out for other processes, the same result is always obtained. For any spontaneous process, the total change of entropy is a positive quantity. Thus, this new state function of entropy provides a thermod3mamic criterion for spontaneity, which is summarized in the second law of thermodynamics ... 

Now in a similar way we draw the membrane (2) to the right, extracting external work reversibly and letting heat flow in to keep the temperature constant. By similar arguments, the increase of entropy in this process is —Rni hi ci. And the total change of entropy in this reversible mixing is JCal... 

In Section 13.5, we showed that the change in entropy of a system plus its surroundings (that is, the total change of entropy, AStoJ provides a criterion for deciding whether a process is spontaneous, reversible, or impossible ... 

A metal rod is in thermal contact with two heat reservoirs both at constant temperature, one at 100 K and the other at 200 K. The rod conducts 1000 J of heat from the warmer to the colder reservoir. If no energy is exchanged with the surroundings, what is the total change of entropy ... 

Because the process is adiabatic, the surroundings undergo no change as a result of this process and, hence, A,S sun=0. which is in accordance with the Second Law of Thermodynamics, which states that the total change of entropy for a reversible process is zero. 

This equation shows that, although ASb is proportional to Nb, as expected, it does not depend explicitly on the value of b, so that the total change of entropy AS per unit volume of the network is... 

Total change of entropy in the incoming and outgoing flows of the column and in the sources and receivers of heat should be equal to zero [Eq. (4.3)] in the case of the thermodynamically reversible process of distillation. 

In real processes of distillation, total change of entropy is always above zero because of thermodynamic losses, and here lies the reason of nonreversibUity ... 

Since the cyclic engine returns to its initial state, whether it is reversible or irreversible, there is no change in its entropy. On the other hand, since the heat transferred to the reservoirs and the irreversible engine have opposite sign, the total change of entropy of the reservoirs is... 

What does entropy have to do with favourable chemical changes and equilibrium systems All favourable changes involve an increase in the total amount of entropy. Recall the endothermic reaction in Figure 7.4. 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

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. 

Note that this change in entropy is greater than the decrease in entropy of the system, —22.0 J-K 1, which we calculated from the difference in entropy of the solid and liquid states of water in Table 7.2. Therefore, the total change in entropy is positive at — 10°C, and the freezing of water is spontaneous at that temperature. 

EXAMPLE 7.9 Judging the spontaneity of a reaction from the total change in entropy... 

This expression is the negative of the expression for AS, so we know that ASsurr = —7.6 J-K 1 and therefore that AStot = 0. This value is in accord with the statement that the process is reversible, (b) For the irreversible process, AS is the same, at +7.6 J-K-1. No work is done in free expansion (Section 6.7), so iv = 0. Because AU = 0, it follows that q = 0. Therefore, no heat is transferred into the surroundings, and their entropy is unchanged ASSUrr = 0. The total change in entropy is therefore AStot = +7.6 J-K 1. The positive value is consistent with an irreversible expansion. 

The classical definition of entropy based on the second law of thermodynamics has given the total differential of entropy in the form of dQrev / / . With a reversible heat transfer into a closed system receiving a differential amount of heat dQrev, the system changes its entropy by the differential amount of dS as shown in Eq. 3.8 ... 

Distinguishing the created entropy deSrev from the transferred entropy dtSirT, we express the total change in entropy as the sum of the two parts shown in Fig. 3.2 and Eq. 3.12 ... 

Suppose the heat added to the water in the boiler in Prob. 16.2 comes from a furnace temperature of 500°C. What is the total rate of entropy change as a result of the heating pr What is Wloat ... 

Equation (1.90) is the total differential of the entropy as a function of the variables U and V only. To generalize this relation, we also consider the changes in the amounts of species. Using the mole amounts for the species, we have a general expression for the change of entropy from the Gibbs relation... 

Equation (3.200) is the expression for a nonconservative change in local entropy density, and allows the determination of the entropy production from the total change in entropy and the evaluation of the dependence of on flows and forces. 

The total rate of entropy change for the hot and cold streams is... 

The change of total entropy is dS d,.S + d S. The term dJS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term dtS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is djS/dt = %JkXk. A near equilibrium system is stable to fluctuations if the change of entropy production is negative A S < 0. For isolated systems,... 

The total change in entropy per unit volume for the N chains constituting the network is obtained by addition of the N contributions represented by Eq. (3.21). 

If we assume that the systems C obey local equilibrium thermodynamics (see Ref. 2, page 30) an entropy can be associated to these non equilibrium systems and one can show that the total change of their entropy can be written as... 

The following general statements may be made about entropy. It resembles the total energy, U, in that It is a function of the state of a thermodynamic system. Only changes of entropy are of practical significance since absolute entropies are unknown. This arbitrariness may, however, be removed by choosing some standard condition as a point of reference. In general... 

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