Surroundings entropy

There exists a state function S, called the entropy of a system, related to the heat Dq absorbedfrom the surroundings during an infinitesimal change by the relations... 

In Equation (5.58) the outer summation is over the p points q which are used to sample the Brillouin zone, is the fractional weight associated with each point (related to the volume of Brillouin zone space surrounding q) and vi are the phonon frequencies. In addition to the internal energy due to the vibrational modes it is also possible to calculate the vibrational entropy, and hence the free energy. The Helmholtz free energy at a temperature... 

Hq and Sq = enthalpy and entropy of the same stream at equiUbrium with the surroundings and Tq = temperature of the surroundings (sink). 

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 ... 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

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 reqmres that the entropy of an isolated system either increase or, in the limit, where the system has reached an equilibrium state, remain constant. For a closed (but not isolated) system it requires that any entropy decrease in either the system or its surroundings be more than compensated by an entropy increase in the other part or that in the Emit, where the process is reversible, the total entropy of the system plus its surroundings be constant. 

The entropy change of the surroundings, found by integration of Eq. (4-3), is AS = QJTa, whence... 

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... 

The total rate of entropy increase (in both system and surroundings) as a result of a process is... 

To understand the flow in turbomachines, an understanding of the basic relationships of pressure, temperature, and type of flow must be acquired. Ideal flow in turbomachines exists when there is no transfer of heat between the gas and its surroundings, and the entropy of the gas remains unchanged. This type of flow is characterized as a rever.sible adiabatic flow. To describe this flow, the total and static conditions of pressure, temperature, and the concept of an ideal gas must be understood. 

The entropy of the system plus surroundings is unchanged by reversible processes the entropy of the system plus surroundings increases for irreversible processes. 

The second part of the second law states that where system undergoes an adiabatic process (system surrounded by insulating walls), i—and the process is reversible, the entropy is not changed, while when the adiabatic process is not reversible the entropy must increase ... 

Thus, in adiabatic processes the entropy of a system must always increase or remain constant. In words, the second law of thermodynamics states that the entropy of a system that undergoes an adiabatic process can never decrease. Notice that for the system plus the surroundings, that is, the universe, all processes are adiabatic since there are no surroundings, hence in the universe the entropy can never decrease. Thus, the first law deals with the conservation of energy in any type of process, while the sec-... 

For any reversible process, the sum of the changes in entropy for the system and its surroundings is zero. All natural or real processes are irreversible and are accompanied by a net increase in entropy. 

On the other hand, in any irreversible process although the system may gain (or lose) entropy and the surroundings lose (or gain) entropy, the system plus surrounding will always gain in entropy (equation 20.141). Thus for a real process proceeding spontaneously at a finite rate... 

The relationship between entropy change and spontaneity can be expressed through a basic principle of nature known as the second law of thermodynamics. One way to state this law is to say that in a spontaneous process, there is a net increase in entropy, taking into account both system and surroundings. That is,... 

Notice that the second law refers to the total entropy change, involving both system and surroundings. For many spontaneous processes, the entropy change for the system is a negative quantity. Consider, for example, the rusting of iron, a spontaneous process ... 

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. 

In principle, the second law can be used to determine whether a reaction is spontaneous. To do that, however, requires calculating the entropy change for the surroundings, which is not easy. We follow a conceptually simpler approach (Section 17.3), which deals only with the thermodynamic properties of chemical systems. 

In some cases, an alternative explanation is possible. It may be assumed that any very complex organic counterion can also interact with the CP matrix with the formation of weak non-ionic bonds, e.g., dipole-dipole bonds or other types of weak interactions. If the energy of these weak additional interactions is on the level of the energy of the thermal motion, a set of microstates appears for counterions and the surrounding CP matrix, which leads to an increase in the entropy of the system. The changes in Gibbs free energy of this interaction may be evaluated in a semiquantitative way [15]. 

If any cyclic process is performed with a given material system, the entropy of all the surrounding bodies which have in any way been involved in the process, either as emitters or absorbers of heat, either remains unchanged, if the cycle is reversible, or else increases, if the cycle is performed irreversibly. 

Loss of motivity (dissipation of energy) is therefore accompanied by increase of entropy, but the two changes are not wholly co-extensive, because the former is less the lower the temperature T0 of the auxiliary medium, whilst the latter is independent of T0, and depends only on the temperature of the parts of the system. If T0 = 0, i.e., the temperature of the surroundings is absolute zero, there is no loss of motivity, whilst the entropy goes on increasing without limit as the heat is gradually conducted to colder bodies. 

Adiabatic processes are examples of (d). If a mole of ideal gas is allowed to expand adiabatically into an evacuated bulb to twice its initial volume, the entropy of the gas increases by 5.76 J K-1 mol-1. No entropy change occurs in the surroundings, since there is no exchange of heat. Hence, 5.76 J K-1 mol-1 is the net increase in entropy in the universe. 

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