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1 Chem 759 Entropy Part II Practical definition of S Entropy of reversible & irreversible processes PowerPoints Summaries -intermediate%20pchem.html Formulas (version for undergr. chem. majors nearly the same as this class) Uwe Burghaus, Fargo, ND, USA

2 entropy Entropy: last class I PChem It is a measure of the randomness of molecules in a system and is central to the second law of thermodynamics and the fundamental thermodynamic relation, which deal with physical processes and whether they occur spontaneously. spontaneous spontaneous

3 entropy Last class Entropy definition It is a measure of the randomness of molecules in a system. 2 nd law of thermodynamics The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. Reversing a spontaneous process is impossible. Universal law of increasing entropy. Maximum at equilibrium. equilibrium time [ wikipedia ]

4 Molecular thermodynamics D.A. McQuarrie, J.D. Simon Chapter 6 & Supplemental E R. Chang, Physical chemistry for biosciences, Chapter 4.2 / 4.3 (pages 86-91) I.N. Levine, Physical chemistry, Chapter 3

5 Question: write one version of the 2 nd law Seen on a student midterm exam: A spontaneous process is always irreversible, never reversible Correct? Yes/No? Why? Spontaneous processes are irreversible since they can be reversed only by taking a different path to their original state. I guess that s a correct version to write it. A reversible process can take the same path to return to its original state. example spontaneous gas expansion w = 0 w > 0

6 Concepts in thermodynamics / last class I PChem 0 th law Definition of the temperature considering the equilibrium of systems. 1 st law E E E 0 U q w uni sys surroundings 2 nd law It is impossible to build a cyclic machine which converts heat into work The entropy of an isolated system which is not in equilibrium will with an efficiency of 100 %. The 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. 3rd law later

7 S k B ln(w) Use as statistical description of entropy entropy thermodynamic probability, w Boltzmann constant

8 Two classes, I guess. practical definition of S examples

9 Entropy definitions I PChem Thermodynamics definition Statistical definition S W2 kb ln( ) W 1 2 The entropy change of a system is given by the probability ratio of the final and initial states. 1 Three topics today: 1) S = S(q, H, V, T, ) =?? 2) S irr, S rev =?? 3) Entropy 2 nd law

10 Thermodynamics / practical definition see whiteboard

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12 Thermodynamics / practical definition Three topics today: 1) S = S(q, H, V, T, ) =?? 1) Summary: S = q rev / T Thermodynamics definition of entropy.

13 Entropy definitions I PChem Thermodynamics definition Statistical definition S qrev T S W2 kb ln( ) W The entropy change of a system in a reversible process equals the heat absorbed divided by the temperature at which the process occurs. The 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. Thus, the path must be specified in the definition of the entropy. For any reversible process and constant temperature.

14 Concept If state functions and non-state functions are combined in the same equation, then the path (/process) need to be specified. state function non-state function Panic H = q p S qrev T Pass/process: P=constant, non cyclic, reversible, PV work only Pass/process: reversible process, T = constant

15 Reversible Irreversible Entropy is strange... Concepts in Thermodynamics Entropy: It is a measure of the randomness of molecules in a system and is central to the second law of thermodynamics and the fundamental thermodynamic relation, which deal with physical processes and whether they occur spontaneously.

16 That s not very quantitative. What has this to do with the 2 nd law of thermodynamics? S q T rev S k W2 B ln( ) W I PChem 2 nd law It is impossible to build a cyclic machine which converts heat into work The entropy of an isolated system which is not in equilibrium will with an efficiency of 100 %. The 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. What has this (entropy) quantitatively to do with the 2 nd law of thermodynamics? How is the entropy connected to the 2 nd law of thermodynamics? What about reversible & irreversible processes? OBJECT: I try to find a quantitative version of the 2 nd law & deeper understanding I have an example - Chang: Example 4.2, page 89, read chapter 4.3 Levine: Chapter 3.5 see whiteboard rev. / irr.

17 Reversible process Why do we need to consider a T=constant process? If temperature would change the process would not be reversible. Why? Another version of 2 nd law: heat flows only from T larger to T smaller Reversible requires that we can go in both directions.

18 Irr-reversible process Chang: Example 4.2, page 89, you may read chapter 4.3

19 Irr-reversible process No work is done because of the vacuum. Therefore, also no heat exchange between system and surrounding, i.e., ds(surroundings)=0

20 Was that example convincing? A detailed discussion of this is also in Levine, 5 th Ed., chapter 3.5 But, this is a lengthy description comparing in a more abstract fashion reversible and irreversible changes of a system. -- I don t think we would gain too much from this.

21 Quantitative version Take home message 2 nd law of thermodynamics I PChem The entropy of an isolated system increases in an irreversible process and remains unchanged in a reversible process. The 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.

22 entropy read notes section to this slide Simple reasoning for this I PChem 0 for reversible S Ssys Ssurr { } > 0 for irreversible process spontaneous equilibrium spontaneous processes time Just look at these figures. spontaneous

23 Laws in Thermodynamics - CONCEPTS I PChem 0 th law Definition of the temperature considering the equilibrium of systems. 1 st law U q w 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 The total Sentropy surr is increasing { in any irreversible process S } 0. 3rd law G lim ( ) P 0; lim S 0 0K T T 0K T The absolute zero temperature 0 Kelvin cannot be reached. What is a concept? No manual for science.

24 In a practical sense, understanding a concept is equivalent to being able to work with it. Entropy is wired Not really. I PChem

25 The 2 nd law has many faces... Take home message I PChem 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 The 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 The entropy of an isolated system which is not in equilibrium will with an efficiency of 100 %. The 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 Entropy can be created but not destroyed. 1 st law Energy cannot be created or destroyed.

26 Preview next class - examples I PChem We can call it a day, look at examples, watch a movie. your choice

27 2 nd law movies Try one of these I PChem Entropy short version (1:20) Entropy (6:00) 2 nd law taped class (2:00) 2 nd law from Atkins voice recording only (5:00) If you find a better one uwe.burghaus@ndsu.edu