Recommended Reading. Entropy/Second law Thermodynamics

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Theodora Francis
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1 Lecture 7. Entropy and the second law of therodynaics. Recoended Reading Entropy/econd law herodynaics wikipedia his site is particularly good. Cheistry and cheical reactivity, Kotz, reichel, ownsend, 7th edition, Chapter 19, pp (Entropy, Gibbs energy) Cheistry 3, Chapter 15, Entropy and Free Energy, pp

2 A rationale for the second law of therodynaics he first law of therodynaics states that the energy of the universe is constant: energy is conserved. his says nothing about the spontaneity of physical and cheical transforations. he first law gives us no clue what processes will actually occur and which will not. he universe (an isolated syste) would be a very boring place (q 0, w 0, ΔU 0) with only the first law of therodynaics in operation. he universe is not boring: tars are born and die, planets are created and hurl around stars, life evolves aongst all this turoil. here exists an intrinsic difference between past and future, an arrow of tie. here exists a readily identifiable natural direction with respect to physical and cheical change. How can this be understood? pontaneous processes and entropy Kotz, Ch.19, pp Discussion on energy dispersal Very good. A process is said to be spontaneous if it occurs without outside intervention. pontaneous processes ay be fast or slow. herodynaics can tell us the direction in which a process will occur but can say nothing about the speed or the rate of the process. he latter is the doain of cheical kinetics. here appears to be a natural direction for all physical and cheical processes. A ball rolls down a hill but never spontaneously rolls back up a hill. teel rusts spontaneously if exposed to air and oisture. he iron oxide in rust never spontaneously changes back to iron etal and oxygen gas. A gas fills its container uniforly. It never spontaneously collects at one end of the container. Heat flow always occurs fro a hot object to a cooler one. he reverse process never occurs spontaneously. Wood burns spontaneously in an exotheric reaction to for CO 2 and H 2 O, but wood is never fored when CO 2 and H 2 O are heated together. At teperatures below 0 C water spontaneously freezes and at teperatures above 0 C ice spontaneously elts. 2

3 he First Law of therodynaics led to the introduction of the internal energy, U. he internal energy is a state function that lets us assess whether a change is perissible: only those changes ay occur for which the internal energy of an isolated syste reains constant. he law that is used to identify the signpost of spontaneous change, the econd Law of therodynaics, ay also be expressed in ters of another state function, the entropy,. We shall see that the entropy (which is a easure of the energy dispersed in a process) lets us assess whether one state is accessible fro another by a spontaneous change. he First Law uses the internal energy to identify perissible changes; the econd Law uses the entropy to identify the spontaneous changes aong those perissible changes. Atkins, de Paula PChe 8e OUP 2008 Ebook. 3

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0 (Br 2 (vap) 245.47 JK -1 ol -1 ice 0 (Br 2 (liq) 152.2 JK -1 ol -1 water Kotz, p.869 What principle can be used to understand and explain all these diverse observations?

his is not correct however since, for exaple the elting of ice which occurs spontaneously at teperatures above 0 C is an endotheric process.

5 0 (Br 2 (vap) JK -1 ol -1 ice 0 (Br 2 (liq) JK -1 ol -1 water Kotz, p.869 What principle can be used to understand and explain all these diverse observations? Early on in therodynaics it was suggested that exothericity ight provide the key to understanding the direction of spontaneous change. his is not correct however since, for exaple the elting of ice which occurs spontaneously at teperatures above 0 C is an endotheric process. he characteristic coon to all spontaneously occurring processes is an increase in a property called entropy (). Entropy is a state function. his idea for the basis of the econd Law of herodynaics. he change in the entropy of the universe for a given process is a easure of the driving force behind that process. In siple ters the second law of therodynaics says that energy of all kinds in the aterial world disperses or spreads out if it is not hindered fro doing so. In a spontaneous process energy goes fro being ore concentrated to being ore dispersed. Entropy change easures the dispersal of energy: how uch energy is spread out in a particular process or how widely spread out it becoes at a specific teperature. 5

econd law of herodynaics he second law of therodynaics states that a spontaneous process is one that results in an increase in the entropy of the universe, universe >

http://entropysite.oxy.edu/students_approach.htl His website is at: http://entropysite.oxy.edu/. oxy edu/ ee also: Cheistry 3 pp.

6 econd law of herodynaics he second law of therodynaics states that a spontaneous process is one that results in an increase in the entropy of the universe, universe > 0, which corresponds to energy being dispersed in the process. total syste + surroundings ee the following excellent account authored by Frank Labert. His website is at: oxy edu/ ee also: Cheistry 3 pp where disorder and entropy are related. he Wikipedia site is also useful. hese is a considerable quantity of dross on the web purporting to define and discuss the entropy concept! 6

Entropy easures the spontaneous dispersal of energy : How uch energy is spread out in a process, or how widely spread out it becoes at a specific teperature.

In cheistry the energy that entropy easures as dispersing is otional energy, the translational, vibrational and rotational energy of olecules, and the enthalpy change associated with phase changes.

7 Entropy easures the spontaneous dispersal of energy : How uch energy is spread out in a process, or how widely spread out it becoes at a specific teperature. Matheatically we can define entropy as follows : entropy change energy dispersed/teperature. In cheistry the energy that entropy easures as dispersing is otional energy, the translational, vibrational and rotational energy of olecules, and the enthalpy change associated with phase changes. Energy transferred as heat Under reversible conditions. syste syste qrev ΔH phasechange Entropy units : J ol -1 K -1 Note that adding heat energy reversibly eans that it is added very slowly so that at any stage the teperature difference between the syste and the surroundings is infinitesially sall and so is always close to theral equilibriu. Entropy changes during phase transforation. Read Cheistry 3 worked Exaple 15.2 p.710. We can readily calculate during a phase change fusion (elting), vaporization, subliation. hese processes occur reversibly and at constant pressure and so we assign q rev ΔH. Vaporization Liquid/vapour transition Δ q Δ vap rev vap Δ vap vap 0 Δ H vap Entropy change at standard pressure (p 1 bar). b H liq 0 Fusion Liquid/solid transition Δ q Δ fus rev fus Δ 0 fus liquid H Δ fush solid b, refer to boiling point and elting point teperatures respectively. 7

eperature variation of syste entropy. ee worked exaple 15.3 Cheistry 3, p.711-712. he entropy of a syste increases as the teperature is increased, but by how uch?

1 then the entropy of that substance at a teperature 2 assued greater than 1 is given by the following expression. Derivation (following Cheistry 3 box 15.11 p.

and also recall the definition of the latter. We now integrate to obtain the necessary result.

864-868 Entropy is a easure of the extent of energy dispersal At a given teperature.

8 eperature variation of syste entropy. ee worked exaple 15.3 Cheistry 3, p he entropy of a syste increases as the teperature is increased, but by how uch? If ( 1 ) denotes the entropy of 1 ol of substance at a tep. 1 then the entropy of that substance at a teperature 2 assued greater than 1 is given by the following expression. Derivation (following Cheistry 3 box p.711) ( ) ( ) C P, 2 ln 1 2 ( ) ( ) 2 1 CP, ln 1 We need to express the definition of entropy in ters of the differential d q rev. and also recall the definition of the latter. We now integrate to obtain the necessary result. CP, d d ( ) ( ) ( ) ( ) 2 1 CP, ln 1 1 d q d d q C rev rev P, 2 CP, d d CP, 1 d 2 1 d Entropy : a icroscopic representation. ee Kotz, section 19.3 pp Entropy is a easure of the extent of energy dispersal At a given teperature. In all spontaneous physical and cheical processes energy changes fro being localized or concentrated in a syste to becoing dispersed or spread out in a syste and its surroundings. Why however does energy dispersal occur? o answer this we need to resort to the icroscopic scale and look at quantized energy levels. his type of approach leads to the real of olecular or statistical therodynaics. pontaneous process tends towards the equilibriu state. 8

9 What entropy is not and what it is. Entropy is not disorder. Entropy is not a easure of disorder or chaos. Entropy is not a driving force. he diffusion, dissipation or dispersion of energy in a final state as copared with an initial state is the driving force in cheistry. Entropy is the index of that dispersal within a syste and between the syste and its surroundings. In short entropy change easures energy s dispersion at a stated teperature. Energy dispersal is not liited to theral energy transfer between syste and surroundings ( how uch situation). It also includes redistribution of the sae aount of energy in a syste ( how far situation) such as when a gas is allowed to expand adiabatically (q 0) into a vacuu container resulting in the total energy being redistributed over a larger final total volue. Entropy easures the dispersal of energy aong olecules in icrostates. An entropy increase in a syste involves energy dispersal aong ore icrostates in the syste s final state than in its initial state. Reference: R.M.Hanson,. Green, Introduction to Molecular herodynaics, University cience Books,

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here are 10 different ways (10 icrostates) to distribute this quantity of energy

11 Possible ways of distributing two packets of energy between four atos. Initially one ato has 2 quanta and three with zero quanta. here are 10 different ways (10 icrostates) to distribute this quantity of energy Microstate 21 ways (21 icrostates) to distribute 2 quanta of energy aong 6 atos. A total of 84 icrostates is possible. Fig. 19-6, p

k ln B W final k k B B initial { lnw lnw } W ln W final final initial initial W nuber of accessible Microstates k B Boltzann constant Microstates with greatest energy

12 Entropy in the context of Molecular herodynaics. Entropy easures the dispersal of energy aong olecules in icrostates. An entropy increase in a syste involves energy dispersal aong ore icrostates in the syste s s final state than in its initial state. k ln B W final k k B B initial { lnw lnw } W ln W final final initial initial W nuber of accessible Microstates k B Boltzann constant Microstates with greatest energy dispersion 1.38 x10-23 J K -1 are ost probable. Reference: R.M.Hanson,. Green, Introduction to Molecular herodynaics, University cience Books, Isotheral expansion of Ideal gas V nr ln V final initial At a given tep the volue V is proportional to the total nuber of icrostates. 12

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CH1101 Physical Chemistry Tutorial 1. Prof. Mike Lyons.

CH1101 Physical Chemistry Tutorial 1. Prof. Mike Lyons. CH111 Physical Chemistry Tutorial 1. Prof. Mike Lyons. CH111 Section A Annual 1 Internal Energy Units: Joules J Internal Energy (U) : total kinetic & potential energy of system. e.g. Gas in container with