The_third_law - The third law ChE210A A bsolute entropies...

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last modified 11/2/2009 © M. S. Shell 2009 1/9 The third law ChE210A Absolute entropies and absolute zero In this lecture we address two questions: Is there such thing as an absolute value of the entropy? That is, is there a way and does it make sense to identify an exact numerical value of g for a particular system and a particular state point, rather than a change in entropy between two state points? What is the behavior of the entropy and other thermodynamic functions as G ap- proaches absolute zero? Recall the microscopic definition of the entropy, g ± ² ³ lnΩ As we have seen, the interpretation of is that it counts the number of microscopic states of a system. The behavior of depends on whether or not we have a quantum or classical view- point of the world: classical description – In this approximation, we cannot count exactly the number of microstates, since we can continuously change the positions and velocities of all the atoms. Therefore, there are an infinite amount of configurations. While we cannot count absolute numbers of configurations, we can count relative numbers, and hence obtain entropy differences. For example, if a volume ´ containing a single particle is expanded to , the number of microstates doubles such that Δg ± ² ³ lnµ2´ ´ ⁄ ¶ ± ² ³ ln 2 . quantum description – Quantum mechanics says that there are discrete quantum states a system can occupy. For example, for a particle in volume ´ ± · ¸ , only states whose energy is given by ¹ ± º » ¼½¾ » ¿À Á Â Ã À Ä Â Ã À Å Â Æ are allowed, where À Á Ä , and À Å are all positive integers. Therefore, in a quantum description and in reality, it is possible to count microstates exactly. These considerations show that a quantum description is required if we are to have an absolute entropy, whereby we can count exactly. Is this enough to give us an absolute entropy? What if, in contrast to the above equation, we had defined the entropy using
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last modified 11/2/2009 © M. S. Shell 2009 2/9 g G ± ² lnΩ ³ g ref where g ref is some universal, material-independent constant? Would this re-defining of the entropy imply any physical changes to the equilibrium behavior of a system, as given by the relationships that the entropy function implies? It turns out that this addition would not change any aspect of the physical behavior of our system. Recall that ´, µ, and all derive from derivatives of g ; therefore, the g ref constant vanishes in the relationship between ·,¸,¹ and these properties, for any substance. It is for the same reason, in fact, that classical descriptions, which cannot have an absolute entropy, can describe the properties of many systems. There is no reason why we could not define the entropy with a nonzero value for
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This note was uploaded on 12/29/2011 for the course CHE 210a taught by Professor Staff during the Fall '08 term at UCSB.

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The_third_law - The third law ChE210A A bsolute entropies...

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