Entropy, reversible

Because this process is a reversible one, the heat associated with it gives the surface entropy... 

Obviously die first law is not all there is to the structure of themiodynamics, since some adiabatic changes occur spontaneously while the reverse process never occurs. An aspect of the second law is that a state fimction, the entropy S, is found that increases in a spontaneous adiabatic process and remains unchanged in a reversible adiabatic process it caimot decrease in any adiabatic process. 

The surfaces in which the paths satisfying the condition = 0 must lie are, thus, surfaces of constant entropy they do not intersect and can be arranged in an order of increasing or decreasmg numerical value of the constant. S. One half of the second law of thennodynamics, namely that for reversible changes, is now established. 

The volumes are changed adiabatically and reversibly from and to V and, during which change the entropy remains constant at... 

Figure A2.1.6. Entropy as a fimction of piston position / (the piston held by stops). The horizontal lines mark possible positions of stops, whose release produees an inerease in entropy, the amount of whieh ean be measured by driving the piston baek reversibly.

Two subsystems a. and p, in each of which the potentials T,p, and all the p-s are unifonn, are pennitted to interact and come to equilibrium. At equilibrium all infinitesimal processes are reversible, so for the overall system (a + P), which may be regarded as isolated, the quantities conserved include not only energy, volume and numbers of moles, but also entropy, i.e. there is no entropy creation in a system at equilibrium. One now... 

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

Figure A2.1.10. The impossibility of reaching absolute zero, a) Both states a and p in complete internal equilibrium. Reversible and irreversible paths (dashed) are shown, b) State P not m internal equilibrium and with residual entropy . The true equilibrium situation for p is shown dotted.

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

The phenomenological definition for the change in entropy associated with the isothermal, reversible absorption of an element of heat dq is... 

Equation (3.7) gives a simple procedure for evaluating the entropy change accompanying a change of state. At the normal boiling point of a liquid, for example, the heat is absorbed reversibly and equals the heat of vaporization AH,. Since T is constant, the entropy of vaporization is AH,/T. For benzene, for example, AS, = (30.8 k J mol" )/353 = 87 J K mol. ... 

The Carnot cycle is formulated directly from the second law of thermodynamics. It is a perfectly reversible, adiabatic cycle consisting of two constant entropy processes and two constant temperature processes. It defines the ultimate efficiency for any process operating between two temperatures. The coefficient of performance (COP) of the reverse Carnot cycle (refrigerator) is expressed as... 

These derivatives are of importance for reversible, adiabatic processes (such as in an ideal turbine or compressor), since then the entropy is constant. An example is the Joule-Tnomson coefficient. 

There exists a propei ty called entropy, which for systems at internal equilihnum Is an intnnsic propeity of the system, functionally related to the measurable coordinates which characterize the system. For reversible processes, changes in this propeity may be calculated by the equation ... 

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. 

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... 

When a process is completely reversible, the equahty holds, and the lost work is zero. For irreversible processes the inequality holds, and the lost work, that is, the energy that becomes unavailable for work, is positive. The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus, every irreversibility carries with it a price. 

The Carnot refrigeratiou cycle is reversible and consists of adiabatic (iseutropic due to reversible character) compression (1-2), isothermal rejection of heat (2-3), adiabatic expansion (3-4) and isothermal addition of heat (4-1). The temperature-entropy diagram is shown in Fig. 11-70. The Carnot cycle is an unattainable ideal which serves as a standard of comparison and it provides a convenient guide to the temperatures that should be maintained to achieve maximum effectiveness. 

Thermodynamic Analyses of Cycles The thermodynamic quahty measure of either a piece of equipment or an entire process is its reversibility. The second law, or more precisely the entropy increase, is an effective guide to this degree of irreversibility. However, to obtain a clearer picture of what these entropy increases mean, it has become convenient to relate such an analysis to the additional work that is required to overcome these irreversibihties. The fundamental equation for such an analysis is... 

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