Chemistry 163B Heuristic Tutorial Second Law, Statistics and Entropy falling apples excited state ground state chemistry 163B students

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Lecture 8 Chemistry B Winter 0 Introduction to nd Law Lower energy states are more stable Systems naturally go to lower energy?

uk/onlinestuff/snot/ if_the_earths_a_big_ball_why_dont_we_fall_off_the_bottom_of_it.aspx http://www.thespectroscopynet.com/ images/pi_as_eb_ste.jpg http://www.

What are the limitations on things that do occur spontaneously? Energy lost by system means energy gained by surroundings.

But: some salts cool when dissolving and why do gasses diffuse if no energy difference SADI CARNOT Carnot cycle (E&R. pp.

included Lagrange, Fourier, Laplace, Berthelot, Ampere, dulong and had as classmates Cauchy, Coriolis, Poisson, Petit, Fresnel 8 went into Corps of Engineers and

1 Lecture 8 Chemistry B Winter 0 Introduction to nd Law Lower energy states are more stable Systems naturally go to lower energy???? Chemistry B Heuristic Tutorial Second Law, Statistics and Entropy falling apples excited state ground state chemistry B students if_the_earths_a_big_ball_why_dont_we_fall_off_the_bottom_of_it.aspx images/pi_as_eb_ste.jpg sleeping_student.jpg But..??? First Law of Thermodynamics The second law of themodynamics The energy lost has to go somewhere??? Why do things happen? What are the limitations on things that do occur spontaneously? Energy lost by system means energy gained by surroundings. First Law of Thermodynamics ΔU sys =-ΔU surr ΔU universe = 0 (also consider E=mc ) H < 0 was considered by Berthelot to be the driving principle for spontaneity But: some salts cool when dissolving and why do gasses diffuse if no energy difference SADI CARNOT Carnot cycle (E&R. pp and HW prob #0) Problem #0 born 79, son of Lazare Carnot and antimonarchist named Sadi after Persian poet and mystic went to Polytechnique Ecole whose faculty included Lagrange, Fourier, Laplace, Berthelot, Ampere, dulong and had as classmates Cauchy, Coriolis, Poisson, Petit, Fresnel 8 went into Corps of Engineers and when monarchy reestablished was sent to boondocks outpost 8 wrote Reflections on the Motive Power of Heat and Machines Adapted for Developing this Power isothermal reversible expansion at T (00K) adiabatic reversible expansion T T (00K) isothermal compression at T (00K) adiabatic compression T T (00K)

Lecture 8 Chemistry B Winter 0 Introduction to nd Law Carnot cycle (graphical interpretation; w sys =-ÚP ext dv ; review) Carnot cycle: (graphical

surr >0 wengine sys > DOES 0, w surr work < 0 on T iso surroundings = T L + = net work for cycle: w surr >0 engine DOES work on surroundings w surr > 0

0 q out at T iso = T Lower Carnot cyclic engine net work ON surroundings 8 from Carnot cycle for system in complete cycle: U=0; q >0; w <0 (work DONE on

T statements of the Second Law of Thermodynamics (also see handout). Macroscopic properties of an isolated system eventually assume constant values (e.g.

It is impossible to construct a device that operates in cycles and that converts heat into work without producing some other change in the surroundings.

It is impossible to have a natural process which produces no other effect than absorption of heat from a colder body and discharge of heat to a warmer

2 Lecture 8 Chemistry B Winter 0 Introduction to nd Law Carnot cycle (graphical interpretation; w sys =-ÚP ext dv ; review) Carnot cycle: (graphical interpretation; w sys =-ÚP ext dv ; review) expansions, steps I-II w sys < 0, w surr > 0 T iso = T U net work for cycle: compressions, steps III-IV w surr >0 wengine sys > DOES 0, w surr work < 0 on T iso surroundings = T L + = net work for cycle: w surr >0 engine DOES work on surroundings w surr > 0 w surr < 0 w surr > 0 w surr < 0 7 expansions, steps I-II w sys < 0, w surr > 0 q in at T iso = T Upper compressions, steps IIII-IV w sys > 0, w surr < 0 q out at T iso = T Lower Carnot cyclic engine net work ON surroundings 8 from Carnot cycle for system in complete cycle: U=0; q >0; w <0 (work DONE on surr) (#0E) q > 0 (q in ) at higher T ; q < 0 (q out ) at lower T efficiency= -w/q (how much net work out for heat in ) efficiency will depend on T and T statements of the Second Law of Thermodynamics (also see handout). Macroscopic properties of an isolated system eventually assume constant values (e.g. pressure in two bulbs of gas becomes constant; two block of metal reach same T) [Andrews. p7]. It is impossible to construct a device that operates in cycles and that converts heat into work without producing some other change in the surroundings. Kelvin s Statement [Raff p 7]; Carnot Cycle. It is impossible to have a natural process which produces no other effect than absorption of heat from a colder body and discharge of heat to a warmer body. Clausius s Statement, refrigerator. In the neighborhood of any prescribed initial state there are states which cannot be reached by any adiabatic process ~ Caratheodory s statement [Andrews p. 8] 9 0 Tolman s perpetual motion machine first a look at disorder and its relation to entropy and nd Law S= k ln W Boltzmann

3 Lecture 8 Chemistry B Winter 0 Introduction to nd Law disorder and entropy microstates and macrostates configuration macrostate L R W no. of microstates L L L L 0 L L L R L L R L L R L L R L L L L L R R L R L R R L L R L R R L R L R L R R L L ~ L etc. R ~ 0 W= (n total )! (n L )! (n R )! microstates and macrostates macrostates and microstates configuration macrostate L R W no. of microstates L L L L 0 L L L R L L R L LR L L R L L L L L R R L R L R RL LR L R R L R L R L R R L L ~ L etc. R microstate: one of the EQUALLY PROBABLE configurations of molecules (e.g. LLLL vs LRLR) macrostate: state with specific macroscopic properties e.g. L= R= ~ 0 W= (n total )! (n L )! (n R )! macrostates for large numbers moral of the story although each allowed microstate (e.g. LLRR or LLLL) is equally probable the overwhelming number of microstates correspond to macrostates with almost identical macroscopic properties (e.g. ~ 0-0 RvsL) W, the number of microstates corresponding to the macrostate, is a measure of the DISORDER of the system in that macrostate a system meanders through all available microstates; but you are only likely to observe it in one of the overwhelming number that correspond to the equilibrium macrostate 7 8

4 Lecture 8 Chemistry B Winter 0 Introduction to nd Law famous quote how energy changes affect disorder disorder happens n =0 n = n = n =0 n = 9 0 how energy changes affect disorder reversible adiabatic expansion ( U sys < 0 ; q rev = 0 ) change in energy due to change in energy levels, e.g. D quantum p.i.b. change in energy levels as box changes size change in energy due to change redistribution of molecules among energy levels, e.g. put in more total energy to fixed size D quantum p.i.b. heat smaller V larger V quantum: expansion, bigger box, energy levels more closely spaced Total energy of system decreases ( U sys < 0 for adiabatic expansion) NO CHANGE IN LEVEL POPULATIONS if expansion done slowly, reversibly work q rev = 0 ; NO CHANGE IN DISORDER (W) reversible isothermal expansion ideal gas ( U sys = 0 ; q rev > 0; w= q ) What happens to W as thermal energy raised? to maintain U = 0 need to put in heat T increases, W (disorder) increases Levels get closer due to V > 0 ; w < 0 To maintain U = 0, q>0 and the level populations have to change and thus W changes q rev > 0 ; INCREASE IN W, INCREASE IN DISORDER

5 Lecture 8 Chemistry B Winter 0 Introduction to nd Law What happens to W as thermal energy goes to zero (T 0K)? Boltzmann and Entropy T 0K S= k ln W W decreases, in fact W only one way to distribute at 0ºK S is entropy k=boltzmann s constant= J K - disorder increases entropy increases take home messages take home messages Disorder, W, did not change during an adiabatic reversible expansion (q rev =0) Disorder, W, increased in isothermal reversible expansion (q rev >0) Disorder, W, increased with T increase (q>0) A sample problem : Two bodies 00 molecules each one at T A =. T f, the other at T B =.7 T f bring into thermal contact cold T A =. T f + HOT T B =.7 T f W (microstates) 0 0,0 Disorder, W, decreased with T decrease (q<0) As T 0, W STAY COLD-HOT??. T f.7 T f 0 = 0 0 â0 or or EQUILIBRIUM?? T E = T f adapted from Nash, ChemThermo, Addison Wesley, pp take home message continued take home message continued The equilibrium macrostate is time more likely than the hot-cold state, even though every (microstate) hot-cold has the same likelihood as a (microstate) equilibrium. No more than one time in 0 8 a measurement will find the blocks in a half-hot and half-cold configuration. If you had observed the microstate of the system 0 times a second constantly (without a msec of rest!) from the beginning of the universe until your midterm Friday (0 0 years) the odds against ever seeing a (microstate) hot-cold are :0!!!.. a progressive increase in disorder necessarily accompanies an approach to equilibrium characterized by the assumption of macrostates with ever-increasing values of W. And what may at first appear to be a purposeful drive towards states of maximal disorder, can now be seen to arise from the operation of blind chance in an assembly where all microstates remain equally probable, but where the overwhelming proportion of microstates is associated with the maximally disordered (nearly identical) macrostates corresponding to equilibrium macroscopic properties. adapted from Nash, ChemThermo, Addison Wesley, pp 7-7 adapted from Nash, ChemThermo, Addison Wesley, p. 9 0

Lecture 8 Chemistry B Winter 0 Introduction to nd Law MUCH MORE much more molecules, probability, statistical mechanics,

beautiful oh Romeo my Romeo CHEMISTRY C End Of Introductory Lecture on Second Law and Disorder heuristic Saadi literal

serving to indicate or point out; stimulating interest as a means of furthering investigation.

If one member is afflicted with pain, Other members uneasy will remain.

6 Lecture 8 Chemistry B Winter 0 Introduction to nd Law MUCH MORE much more molecules, probability, statistical mechanics, yes dear Juliet, you have nice eyes BUT ---heat, work, efficiency, probability, disorder, entropy the nd Law is so beautiful oh Romeo my Romeo CHEMISTRY C End Of Introductory Lecture on Second Law and Disorder heuristic Saadi literal translation (Farzaneh): heu ris tic [hyoo-ris-tik or, often, yoo-] adjective. serving to indicate or point out; stimulating interest as a means of furthering investigation. interpretative translation on UN building: Human beings are members of a whole, In creation of one essence and soul. If one member is afflicted with pain, Other members uneasy will remain. If you have no sympathy for human pain, Nicolas Léonard Sadi Carnot (79-8) in the dress uniform of a student of the École Polytechnique The name of human you cannot retain. French Thermodyamicist Persian Poet th Century Namesake 9 th century Saadi and Sadi

Chemistry 163B Heuristic Tutorial Second Law, Statistics and Entropy

Chemistry 163B Heuristic Tutorial Second Law, Statistics and Entropy 3 Lower energy states are more stable Systems naturally go to lower energy???? falling apples excited state ground state chemistry 163B