Chem 759 Entropy Part III Examples Clausius uncertainty Carnot cycle Asymmetry of heat and work Perpetual mobile Heat pump 10 version of 2 nd law Updated PowerPoints with in-class solutions, go to http://www.uweburghaus.us/classes/chem759 -intermediate%20pchem.html, 2017 Uwe Burghaus, Fargo, ND, USA
Molecular thermodynamics D.A. McQuarrie, J.D. Simon Chapter 6 & Supplemental E R. Chang, Physical chemistry for biosciences, Chapter 4 (pages 81-85) I.N. Levine, Physical chemistry, Chapter 3
Entropy definitions hermodynamics definition Statistical definition S qrev S W2 kb ln( ) W 1 2 1 he entropy change of a system in a reversible process equals the heat absorbed divided by the temperature at which the process occurs. he entropy change of a system is given by the probability ratio of the final and initial states. S is a state function but heat not. hus, the path must be specified in the definition of the entropy. For any reversible process and constant temperature.
he 2 nd law has many faces... 0 for reversible > 0 for irreversible process 2 nd law It is impossible to build a cyclic machine which converts heat into work with an efficiency of 100 %. S Ssys he total Sentropy surr is increasing { in any irreversible process S } 0. 2 nd law It is impossible to build a cyclic machine which converts heat into work he entropy of an isolated system which is not in equilibrium will with an efficiency of 100 %. he total entropy is increasing in any irreversible process S 0. tend to increase over time, approaching a maximum value at equilibrium. A system develops towards the state with the greatest probability. Simplest way to motivate that I know is an example like that one: Example 4.2, page 89, read chapter 4.3 (Chang) which I used in the last class Related to that is Clausius inequality later today.
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Examples Important one Examples are from R. Chang, Physical chemistry for biosciences, You can find similar examples in any Pchem book.
2 nd law summary One can probably find 10 different ways to write this down he entropy of an isolated system increases in an irreversible process and remains unchanged in a reversible process. he total entropy can never decrease. 0 for reversible S Ssys Ssurr { } > 0 for irreversible process A system develops towards the state with the greatest probability. Heat cannot flow from a colder body to a warmer one without external aid.
Examples Examples are from R. Chang, Physical chemistry for biosciences, Only briefly in this survey class You can find similar examples in any Pchem book.
Carnot cycle Heat engine 1 (hot) https://en.wikipedia.org/wiki/nicolas_l%c3 %A9onard_Sadi_Carnot Nicolas Sadi Carnot q 1 device w q 2 2 (cold) h = 1 + q 2 /q 1 = 1 2 / 1 Limit 1 = 0 2 oo h 1 (max) & Clausius 2 nd law http://www.bpreid.com/applets/carnotdemo.html
Another version of the 2 nd law It is impossible for an engine (i.e. a cyclic process) to transfer heat between heat reservoirs and do an equal amount of work on the surroundings. w q2 w cold 2 h 1 1 h 1 1 1 q q q 1 1 1 hot 1 1 (hot) device q 1 q 2 w 2 (cold) e.g. see Molecular thermodynamics D.A. McQuarrie, J.D. Simon Chapter 6-7
Asymmetry of heat and work w q h1 Conversion of heat into other forms of energy can never be 100% efficient, even in principle, but. q w h1 1 (hot) + - w electric q R device q 1 w hese examples could have 100% conversion of work into heat. q 2 2 (cold) h carnot w q hot cold 1 1 hot Read notes section to this slide http://web.mit.edu/16.unified/www/fall/ther modynamics/notes/node22.html http://theory.uwinnipeg.ca/mod_tech/node80. html
he 2 nd law has many faces... 2 nd law 0 for reversible S Ssys Ssurr { } > 0 for irreversible process 2 nd law It is impossible to build a cyclic machine which converts heat into work he entropy of an isolated system which is not in equilibrium will with an efficiency of 100 %. he total entropy is increasing in any irreversible process S 0. tend to increase over time, approaching a maximum value at equilibrium. A system develops towards the state with the greatest probability. 2 nd law It is impossible for an engine (i.e. a cyclic process) to transfer heat between heat reservoirs and do an equal amount of work on the surroundings. 2 nd law It is impossible to build a cyclic machine which converts heat into work with an efficiency of 100 %.
Examples Examples are from R. Chang, Physical chemistry for biosciences, Questions? You can find similar examples in any Pchem book.
Laws in hermodynamics - CONCEPS 1 st law A first degree perpetuum mobilie does not exist. 2 nd law It is impossible to build a cyclic machine which converts heat into work A 2 nd degree with perpetuum an efficiency mobilie of 100 %. does not exist. he total entropy is increasing in any irreversible process S 0. * * *
Example for this perpetual motion
4.5 What about processes that increase the order (reduce entropy). Does this violate the 2 nd law? Crystallization Protein synthesis from amino acids system model system surroundings
Example heat pump
Example Hot summer in New York. Opening a freezer to cool down an apartment? Is that smart? Look up Carnot cycle Heat pump Etc.
Carnot cycle & inverted Carnot cycle Heat engine Heat pump 1 (hot) 1 (hot) q 1 q 1 device w w device q 2 q 2 2 (cold) 2 (cold) h = 1 + q 2 /q 1 = 1 2 / 1
Example phase change Read page 91: entropy change of a phase change (Chang) he molar heat of vaporization of a liquid is H vap. he boiling point is B. How to calculate the entropy change associated with the vaporization? Similar to 4.7 in Chang s book https://en.wikipedia.org/wiki/latent_heat Latent heat is energy released / absorbed during a constant-temperature process.
https://en.wikipedia.org/wiki/clausius_theorem Example: reversible vs. irreversible hat s how you can determine entropies experimentally. q irr S rev Clausius inequality If you don t understand this, don t worry too much: it s the most obscure topic in thermodynamics.
q irr S rev see whiteboard
simple version of it q irr S rev see whiteboard
entropy q irr S rev another version of it In an isolated system (energy=constant) entropy changes are due to spontaneous processes only Generally entropy can change due to Spontaneous process (produced by the system) Energy transfer due to heat transfer ds produced ds exchange equilibrium time q ds exchange 0 0 0 depending on direction of heat flow spontaneous processes ds produced 0 his is from Molecular thermodynamics, D.A. McQuarrie, J.D. Simon Chapter 6-4 (page 247, 248)
ds produced q irr S q ; dsexchange We can distinguish these two contributions to S for any process. (see last slide) rev another version of it ds ds produced ds exchange otal entropy change for any process. q q rev Reversible process ds 0 sys produced ds q because 0 for reversible S S Ssurr { } > 0 for irreversible process see last class rev ds exchange q rev Irreversible (/ spontaneous) process q q irr ds produced ds 0 q irr ds exchange q irr ds q integrate S q
6 in 1: 2 nd law he entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. No heat engine can run with 100% efficiency dq rev 0 S S S sys S surr qrev Not really fundamental / official versions: q Heat cannot flow from a colder body to a hotter. irr S h 1 rev cold hot Clausius inequality 0 for reversible { }process >0 for irreversible A 2 nd class perpetual mobile does not exists.
Write down the most abstract version of the 2 nd law you know. Write down a practical version of the 2 nd law. What is a perpetual mobile? What is a heat engine? Calculate the efficiency of a heat engine. Use the simplest approach. Remember the sign definitions for heat and work. How was heat defined again? Is there a cold in thermodynamics? Remember: what was reversible / irreversible all about?
http://en.wikipedia.org/wiki/perpetual_motion http://en.wikipedia.org/wiki/nicolas_l%c3%a9onard_sadi_carnot http://en.wikipedia.org/wiki/history_of_the_internal_combustion_engine http://commons.wikimedia.org/w/index.php?title=file%3aotto_engines_- _WMSR_Montage_2.ogg http://science.howstuffworks.com/transport/eng ines-equipment/steam1.htm
Class 1-4 Class 5-7 Class 8-9 Class 10-16 Chapter 5 Chapter 6 Chapter 7 Chapter 8, 12 tentative schedule 1 st law 2 nd law 3 rd law Gibbs intro, 1 st law, enthalpy, heat capacity, gas expansions energy conservation Entropy Equilibrium stat thermo version of the laws