Thermodynamics

346 | ThermodynamicsTT HT L4A1 2W netS 1 = S 4 S 2 = S 3FIGURE 7–19The T-S diagram of a Carnot cycle(Example 7–6).3BSSolution The Carnot cycle is to be shown on a T-S diagram, and the areasthat represent Q H , Q L , and W net,out are to be indicated.Analysis Recall that the Carnot cycle is made up of two reversible isothermal(T constant) processes and two isentropic (s constant) processes.These four processes form a rectangle on a T-S diagram, as shown in Fig.7–19.On a T-S diagram, the area under the process curve represents the heattransfer for that process. Thus the area A12B represents Q H , the area A43Brepresents Q L , and the difference between these two (the area in color) representsthe net work sinceW net,out Q H Q LTherefore, the area enclosed by the path of a cycle (area 1234) on a T-S diagramrepresents the net work. Recall that the area enclosed by the path of acycle also represents the net work on a P-V diagram.SOLIDINTERACTIVETUTORIALSEE TUTORIAL CH. 7, SEC. 6 ON THE DVD.Entropy,kJ/kg • KGASLIQUIDFIGURE 7–20The level of molecular disorder(entropy) of a substance increases as itmelts or evaporates.7–6 ■ WHAT IS ENTROPY?It is clear from the previous discussion that entropy is a useful property andserves as a valuable tool in the second-law analysis of engineering devices.But this does not mean that we know and understand entropy well. Becausewe do not. In fact, we cannot even give an adequate answer to the question,What is entropy? Not being able to describe entropy fully, however, doesnot take anything away from its usefulness. We could not define energyeither, but it did not interfere with our understanding of energy transformationsand the conservation of energy principle. Granted, entropy is not ahousehold word like energy. But with continued use, our understanding ofentropy will deepen, and our appreciation of it will grow. The next discussionshould shed some light on the physical meaning of entropy by consideringthe microscopic nature of matter.Entropy can be viewed as a measure of molecular disorder, or molecularrandomness. As a system becomes more disordered, the positions of the moleculesbecome less predictable and the entropy increases. Thus, it is not surprisingthat the entropy of a substance is lowest in the solid phase andhighest in the gas phase (Fig. 7–20). In the solid phase, the molecules of asubstance continually oscillate about their equilibrium positions, but theycannot move relative to each other, and their position at any instant can bepredicted with good certainty. In the gas phase, however, the molecules moveabout at random, collide with each other, and change direction, making itextremely difficult to predict accurately the microscopic state of a system atany instant. Associated with this molecular chaos is a high value of entropy.When viewed microscopically (from a statistical thermodynamics point ofview), an isolated system that appears to be at a state of equilibrium mayexhibit a high level of activity because of the continual motion of the molecules.To each state of macroscopic equilibrium there corresponds a largenumber of possible microscopic states or molecular configurations. Theentropy of a system is related to the total number of possible microscopic