Entropy change of system

Since heat transfer with respec t to the surroundings and with respect to the system are equal but of opposite sign, = —Q. Moreover, the second law requires for a reversible process that the entropy changes of system and surroundings be equalbut of opposite sign AS = —AS Equation (4-356) can therefore be written Q = TcAS In terms of rates this becomes... 

ASt = total entropy change of system and surroundings Qi = heats from heat reservoirs except the surroundings at To ASi = entropy change of these reservoirs... 

Gibbs free energy can easily be derived from the equation relating total entropy to the entropy changes of system and surroundings. 

Second Law of Thermodynamics. The entropy change of any system together with its surroundings is positive for a real process, approaching zero as the process approaches reversibiUty ... 

The entropy change of any. system and its. surroundings, considered together, re.sulting from any real proce.s.s is positive, approaching zero when the proce.s.s approaches reversibility. 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

The entropy change of a system during any process depends only upon its initial and final states and not upon the path of the process by which it proceeds from its initial to its final state. Thus one can devise a reversible idealized process to restore a system to its initial state following a change and thereby determine AS =... 

AS° for this system at 25°C and 1 atm can be calculated from a table of standard entropies it is found to be —358.4 J/K. The negative sign of AS° is entirely consistent with the second law. All the law requires is that the entropy change of the surroundings be greater than 358.4 J/K, so that ASunIverse > 0. 

Entropy is an important concept in chemistry because we can use it to predict the natural direction of a reaction. However, not only does the entropy of the reaction system change as reactants form products, but so too does the entropy of the surroundings as the heat produced or absorbed by the reaction enters or leaves them. Both the entropy change of the system and that of the surroundings affect the direction of a reaction, because both contribute to the entropy of the universe. We explore the contribution of the system in this section and the contribution of the surroundings in the next section. 

We can use Eq. 1 to calculate the entropy change of the surroundings, provided that we assume that the surroundings are so large that their temperature and pressure remain constant. If the enthalpy change of the system is AH, then, for heat transfers at constant pressure, gSLlrr = —AH. We can now use Eq. 1 to write... 

FIGURE 7.17 (a) In an exothermic process, heat escapes into the surroundings and increases their entropy, (b) In an endothermic process, the entropy of the surroundings decreases. The red arrows represent the transfer of heat between system and surroundings, and the green arrows indicate the entropy change of the surroundings. 

The entropy change of the surroundings due to a process taking place at constant pressure and temperature is equal to —AH/T, where AH is the change in enthalpy of the system. 

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

Entropy change of the surroundings for a process in a system with enthalpy change AH ... 

A Hsys — < sys (constant P) Remember also that the heat flow for a system is always equal in magnitude but opposite in sign to the heat flow of the surroundings sys = - surr S o A H s = < surr Furthermore, we have already required constant temperature, so the heat flow of the surroundings measures the entropy change of <75 c,... 

Time relaxation = Entropy change of the system in Onsager s sense = Convective accumulative effects and initial entropy of the system and entropy change of the system... 

The sum is equal to zero for reversible processes, where the system is always under equilibrium conditions, and larger than zero for irreversible processes. The entropy change of the surroundings is defined as... 

The crystallization process involves a system (which we are interested in) and the surroundings. In terms of the component entropies in this example, we say AS,iSyiSlcm, is the entropy of the solute crystallizing and that A.S liSlllTOimdmgiS I represents the entropy change of the solvent molecules released. 

We call the sum of the system and its surroundings the thermodynamic universe (see Figure 4.3). A thermodynamic universe is described as that volume large enough to enclose all the thermodynamic changes . The entropy change of the thermodynamic universe during crystallization is A (totai), which equates to... 

B—The system is insulated and no work can be done on or by the system (rigid container) thus, the energy is constant. At the melting point, some of the gallium will melt and some will freeze, the entropy change of these two processes cancel each other so there is no net entropy change. 

Entropy will be represented by the letter S. Entropy is a measure of randomness or disorder in a system and has SI units of J/K. Recall that the Second Law of Thermodynamics states that the entropy change of all processes must be positive. We will see that the origins of entropy are best described from statistical thermodynamics, but for now let us concentrate on how we can use entropy to describe real material systems. 

It may be necessary to transfer a quantity of heat, dQ, from the reservoir into the system in order to maintain constant temperature in the system the total entropy change of the system plus reservoir, dS, will then be... 

The actual system and its surroundings constitute the isolated system to which the second law refers (Fig. 7.14). We have seen how to calculate the entropy change of the system now we turn our attention to the entropy changes in its surroundings. Only if the total entropy change... 

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