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Lecture 10

Lecture 10. Cassandra Paul Physics 7A Summer Session II 2008. Announcments. Final is WEDNESDAY! This room, 9:30-10:45 BRING YOUR STUDENT ID! Be here at 9:15 so we can check you in. The second half of today’s class is optional To be posted: Quiz 5 grades, rubric, solutions for quiz 5.

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Lecture 10

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  1. Lecture 10 Cassandra Paul Physics 7A Summer Session II 2008

  2. Announcments • Final is WEDNESDAY! • This room, 9:30-10:45 • BRING YOUR STUDENT ID! • Be here at 9:15 so we can check you in. • The second half of today’s class is optional • To be posted: • Quiz 5 grades, rubric, solutions for quiz 5

  3. Today • Finish where Yen left off • Entropy • Reversible vs. Irreversible • Gibbs Free Energy • Spontaneous vs. Non spontaneous • Final Review

  4. Recap… What was entropy again? Physical systems have an equilibrium state (the one with the most microstates, and therefore the highest entropy) If we wait “long enough” the system will most likely evolve to that equilibrium state. (by the laws of chance) For large (i.e. moles of atoms) systems, the system is (essentially) always evolving toward equilibrium. Therefore the total entropy never decreases: Second law of Thermodynamics

  5. This is only for total entropy! air (200C) heat flowsthis way Heat ice(00C=273K) Ebond  ml  Heat entering ice: dQice = Tice dSice > 0 =>Sice increasing Heat leaving air: dQair = Tair dSair < 0 =>Sairdecreasing Are the changes in entropy the same?

  6. Heat entering ice: dQice = Tice dSice > 0 =>Sice increasing Heat leaving air: dQair = Tair dSair < 0 =>Sairdecreasing The magnitudes of the Q’s must be the same, but the signs are opposite. The T’s are different, but always positive. The change in entropy for the lower temperature object is always positive, and always has a greater magnitude, than the entropy of the lower temperature object. dStot = dSice + dSair > 0

  7. Let’s See Why….

  8. Low temp High temp Energy leaves hot objects in the form of heat Energy enterscold objects in the form of heat Evolving Towards Thermal equilibrium Tfinal

  9. Low temp Evolving AWAY FROM Thermal equilibrium Do Does this happen? Tfinal High temp From everyday experience, we know that the process of heat leaving the higher temperature object and entering the lower temperature object is irreversible and spontaneous…. But how can we figure it out for less obvious situations?

  10. First Definitions: • Reversible Process: • No heat is transferred across a temperature difference • No friction occurs ΔS=0 • Spontaneous Process: • The process occurs in one specific direction. ΔG<0 note: (ΔG=0 means both the forward and reverse processes are in equilibrium)

  11. Let’s Get Quantitative!

  12. A B The two blocks A and B are both made of copper, and have equal masses: ma = mb = 100 grams. The blocks exchange heat with each other, but a negligible amount with the environment. a) What is the final state of the system?b) What is the change in entropy of block A? c) What is the change in entropy of block B? d) What is the total change in entropy? (Heat of melting)

  13. A B The two blocks A and B are both made of copper, and have equal masses: ma = mb = 100 grams. The blocks exchange heat with each other, but a negligible amount with the environment. What is the final state of the system? What is the final equilibrium temperature of the system? ΔEthA+ ΔEthB = 0 Ethermal Ethermal B A Ti=100 Tf=x Ti=200 Tf=x   (.1)(385)(x-100)+ (.1)(385)(x-200)= 0   Tf=x=150 (Heat of melting)

  14. A B Okay, now we have found the equilibrium state. What is the final state of the system? b) What is the change in entropy of block A? c) What is the change in entropy of block B? d) What is the total change in entropy? How do we calculate the change in entropy?

  15. What about the entropy change for this process? Does the temperature remain constant for block A or block B? ΔS=Q/T (IF constant temperature) ΔS=Cln(Tf/Ti) (IF temp is changing) dS=dQ/T In this case Tf = 150 K = Tf,A = Tf,B Ti,A = 100 K, Ti,B = 200 K m c In (Tf,A/Ti,A) = m c In (Tf,B/Ti,B) =

  16. What about the entropy change for this process? In this case Tf = 150 K = Tf,A = Tf,B Ti,A = 100 K, Ti,B = 200 K ∆Stotal > 0 Irreversible and spontaneous process Wait, how do we know it’s spontaneous? We haven’t talked about ΔG yet.

  17. Gibbs Free Energy G = H - TS is a state function:- H depends only on state of system- T depends only on state of system- S depends only on state of system=> G depends only on state of system Why is this useful?….

  18. Gibbs Free Energy • G = H - TS • dG = dH - TdS + SdT At Const T, dG = dH - TdS or ∆G = ∆ H - T ∆S Remember ∆H = Q for Const P process. (tells you whether a reaction is endothermic or exothermic) So then, Gibbs free energy reflects the change in the enthalpy of the system as well as the change in the entropy of the system Still …Why is this useful?

  19. To find out if something happens spontaneously we must know about the environment as well as the system…. If something happens spontaneously, the total change in entropy must be greater than 0: Δ(entropy of system) +Δ(entopy of environment) > 0 Same as saying: ΔS-ΔH/T> 0 Or, multiplying by –T: -TΔS + ΔH < 0 The left side is equal to ΔG!!!!! So for a process to happen spontaneously, ΔG must be negative.

  20. So How did I know our example was spontaneous? ΔH=0 T is positive ΔS is positive So ΔG must be negative. ∆G = ∆ H - T ∆S A B

  21. Laws of Thermodynamics Remember conservation of energy? (if there’s no change in ∆Emechanical), ∆ U First law of Thermodynamics Total entropy never decreases. spontaneous changes occur with an increase in entropy. ∆Stotal or  0 the system always evolves toward equilibrium. Second law of Thermodynamics

  22. Conserve energy?Why, energy is always conserved! Found in the PHYSICS department!

  23. The rest of the story… An inescapable truth defined by the 2nd law of Thermodynamics2nd Law of Thermodynamics tells you the direction of the energy flow. Each time energy gets transferred, some of it gets less useful… until finally, it becomes simply useless…. All of energy we use, sooner or later, ends up being low-grade thermal energy… Brake!

  24. The rest of the story… An inescapable truth defined by the 2nd law of Thermodynamics2nd Law of Thermodynamics tells you the direction of the energy flow. Each time energy gets transferred, some of it gets less useful… until finally, it becomes simply useless…. All of energy we use, sooner or later, ends up being low-grade thermal energy… Falling rock

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