Chapter 19 - Entropy &amp; Free Energy

# Chapter 19 - Entropy &amp; Free Energy - Entropy the...

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115 Entropy, the 2 nd Law of Thermodynamics Gibbs Free Energy & the connection to Equilibrium 1 ST Law just keeps track of energy There is a natural direction of physical & chemical processes not explained by the 1 st Law. Eg. 1 A gas expands spontaneously into a vacuum The reverse of this process is never seen though it is allowed by the 1 st law. Eg. 2 Heat flows from a hot body (on the right) to a cold body (on the left). T 1 increases & T 2 decreases until the two systems achieve the same temperature thermal equilibrium Heat never flows the other way, though the 1 st Law would allow it. T 1 T 2 T 1 < T 2 q

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116 Egs. 3. Spontaneous mixing of gases, miscible liquids, ( natural ) dissolution of soluble salts Random motions of individual molecules leads to irreversible mixing of gases . Methanol & water are miscible - they spontaneously form a solution - a more disordered state when added together. NaCl(s) dissolves spontaneously when added to water - the resulting solution is more disordered than solid salt + water. Though these examples include energy considerations, they illustrate that increasing disorder is a driving force causing some processes to proceed , while prohibiting the reverse Spontaneous mixing of two ideal gases is the best illustration. In this case, interactions between molecules can be neglected (i.e. no energy considerations ), yet the mixing is spontaneous.
117 123 an ordered state a disordered state disorder increases In Eg. 2, kinetic energy spreads from the hot body to the cold body. energy is more spread out a more disordered state In Eq. 3, dissolution of salt in water ... the ions have greater freedom in solution - due to increased volume (in comparison to solid) final state has more freedom more disorder In a natural (i.e. spontaneous) process there is a spontaneous increase in disorder . Entropy, S, measures this disorder S increases true for S of entire universe How do we measure "disorder"? or How is S defined?

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118 Consider a deck of cards - continuously reshuffled. If the card shuffler doesn’t cheat , then any ordering of the card is possible the cards are disordered . However, if the card shuffler cheats - eg. producing an ordered deck of cards with each shuffle (eg. always ensuring that the dealer gets a royal flush) the cards are more ordered . supplementary - you are not responsible for the formulae from here to the next dividing line . .. Boltzmann proposed the following formula for entropy in terms of the "number of arrangements of the system which produce the same state" S = k ln W This formula is engraved on Boltzmann's headstone. In the case of the shuffled cards, the "number of arrangements
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## This note was uploaded on 01/13/2011 for the course CHEM CHEM 1E03 taught by Professor Barbier during the Fall '08 term at McMaster University.

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Chapter 19 - Entropy &amp; Free Energy - Entropy the...

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