Thermodynamics

states of that system, called thermodynamic probability p, by the Boltzmannrelation, expressed asS k ln p(7–20)where k 1.3806 10 23 J/K is the Boltzmann constant. Therefore, froma microscopic point of view, the entropy of a system increases whenever themolecular randomness or uncertainty (i.e., molecular probability) of a systemincreases. Thus, entropy is a measure of molecular disorder, and themolecular disorder of an isolated system increases anytime it undergoes aprocess.As mentioned earlier, the molecules of a substance in solid phase continuallyoscillate, creating an uncertainty about their position. These oscillations,however, fade as the temperature is decreased, and the moleculessupposedly become motionless at absolute zero. This represents a state ofultimate molecular order (and minimum energy). Therefore, the entropy of apure crystalline substance at absolute zero temperature is zero since there isno uncertainty about the state of the molecules at that instant (Fig. 7–21).This statement is known as the third law of thermodynamics. The thirdlaw of thermodynamics provides an absolute reference point for the determinationof entropy. The entropy determined relative to this point is calledabsolute entropy, and it is extremely useful in the thermodynamic analysisof chemical reactions. Notice that the entropy of a substance that is not purecrystalline (such as a solid solution) is not zero at absolute zero temperature.This is because more than one molecular configuration exists for suchsubstances, which introduces some uncertainty about the microscopic stateof the substance.Molecules in the gas phase possess a considerable amount of kineticenergy. However, we know that no matter how large their kinetic energiesare, the gas molecules do not rotate a paddle wheel inserted into the containerand produce work. This is because the gas molecules, and the energythey possess, are disorganized. Probably the number of molecules trying torotate the wheel in one direction at any instant is equal to the number ofmolecules that are trying to rotate it in the opposite direction, causing thewheel to remain motionless. Therefore, we cannot extract any useful workdirectly from disorganized energy (Fig. 7–22).Now consider a rotating shaft shown in Fig. 7–23. This time the energy ofthe molecules is completely organized since the molecules of the shaft arerotating in the same direction together. This organized energy can readily beused to perform useful tasks such as raising a weight or generating electricity.Being an organized form of energy, work is free of disorder or randomnessand thus free of entropy. There is no entropy transfer associated withenergy transfer as work. Therefore, in the absence of any friction, theprocess of raising a weight by a rotating shaft (or a flywheel) does not produceany entropy. Any process that does not produce a net entropy isreversible, and thus the process just described can be reversed by loweringthe weight. Therefore, energy is not degraded during this process, and nopotential to do work is lost.Instead of raising a weight, let us operate the paddle wheel in a containerfilled with a gas, as shown in Fig. 7–24. The paddle-wheel work in this caseChapter 7 | 347LOADFIGURE 7–22Disorganized energy does not createmuch useful effect, no matter howlarge it is.W shPure crystalT = 0 KEntropy = 0FIGURE 7–21A pure crystalline substance atabsolute zero temperature is inperfect order, and its entropy is zero(the third law of thermodynamics).WEIGHTFIGURE 7–23In the absence of friction, raising aweight by a rotating shaft does notcreate any disorder (entropy), and thusenergy is not degraded during thisprocess.